Tuesday, January 31, 2006

Extended Finite Element Method

Since its introduction in the summer of 1999, the eXtended Finite Element Method (X-FEM) has enjoyed a considerable level of success and popularity from researchers in the computational and applied mechanics communities. In just under six years, several hundred peer-reviewed journal articles dealing with fundamentals or applications of the X-FEM and related methods have appeared in the literature. This post provides some background on the method and comments on its capabilities and usefulness for the broad applied mechanics community. We also welcome questions from the community in the comments area following the post.

The X-FEM grew out of research into meshfree methods by the computational mechanics group at Northwestern University directed by Ted Belytschko. Related methods include the Generalized Finite Element Method (G-FEM) developed at the University of Texas at Austin and Texas A&M University. The basic philosophy of the X-FEM is that features of interest in a problem, for example crack surfaces, phase boundaries, and fluid-structure interfaces, can be represented independently of the finite element mesh. As a result, simulating the evolution of these features is greatly facilitated. This is particularly true when they exhibit changes in topology, such as when multiple crack fronts merge or a single crack front branches. The finite element mesh need not explicitly "fit" these features with the X-FEM, circumventing the need to re-mesh in many cases and facilitating adaptivity in others. The Figure below shows an example of the evolution of a phase boundary in a hydrogel as simulated using a fixed mesh with the X-FEM. The sharp gradients in the deformation (observable in the deformed mesh on the right) have been captured using enrichment.

The basic ideas behind the method are easy to understand. Most finite element approximations to bulk fields (e.g. displacement, temperature) can be expressed as a linear combination of nodal shape functions. These shape functions are only able to represent discontinuities in the bulk fields if the mesh is constructed in a particular way. For example, the classical approach to representing the jump in displacement field across a crack front is to explicitly mesh both crack faces. With the X-FEM, the classical mesh need only overlap the geometry of the crack front and does not need to be carefully aligned with it. The linear combination is then augmented with enrichment functions that capture the jump in displacement field across the crack. Crack growth can in turn be simulated through the identification of additional enriched nodes and a new construction for the enrichment function, a process that is typically much simpler than re-meshing. If additional information about the solution is known---such as the asymptotic behavior of the crack-tip fields---it can also be included in the enrichment to garner coarse-mesh accuracy. The mathematical underpinnings behind this construction---the partition-of-unity method---were established by Ivo Babuska and colleagues at Maryland in the early nineties.

Although the X-FEM was originally designed for linear elastic fracture mechanics, it has since been adapted to a wide range of applications. These include the representation of complex microstructures, multi-phase flow, virtual surgery, and general fluid-structure interaction problems. Recently, many researchers have coupled the X-FEM to the Level-Set Method, a technique for representing surfaces through implicit functions. The combination is a powerful one for simulating evolving boundary value problems. Although similar fixed-grid techniques have been used by the finite-difference community for some time, the variational framework naturally employed by the X-FEM makes the incorporation of enrichment straightforward.

In addition to new applications, research into fundamental issues continues at Northwestern University, Ecole Centrale Nantes, the University of California Davis, and Duke University, among others. Many X-FEM researchers maintain websites dedicated to the method and its applications, and interested readers are encouraged to seek them out.

Monday, January 30, 2006

Webcasts of "Leaders in Mechanical Engineering Lecture Series" at University of Maryland

The Department of Mechanical Engineering at University of Maryland holds a "Leaders in Mechanical Engineering Lecture Series", and archives the webcasts.

Featured speakers and their topics include:

Subra Suresh, M.I.T.

Charles Steele, Stanford University
Some Basic Mechanics of the Middle and Inner Ear

Roger Howe, University of California, Berkeley
Will MEMS Ever Really Matter to the Semiconductor Industry?

Earl Dowell, Duke University
Linear and Nonlinear Dynamics of Very High Dimensional Systems

This information was brought to my attention by my friend Dr. Teng Li. If you find any other such interesting sources, please share with us.

Thin Film Materials: Stress, Defect Formation and Surface Evolution, By L.B. Freund and S. Suresh

This monograph is a perfect text for a mechanics graduate course in thin films.
The authors combine the both theoretical and practical aspects of thin film technology and mechanics in such a way that it provides a unique insight into the subject from the mechanician's perspectives. Two thumbs up !

Thin Film Materials, by L. B. Freund and S. Suresh, Cambridge University Press

Nonlinear Finite Elements for Continua and Structures, by Ted Belytschko, Wing Kam Liu, Brian Moran

This is a graduate-level textbook written by established researchers in the field. At amazon.com, the book has receieved 4 stars, and 10 customer reviews.

Saturday, January 28, 2006

Possible WLC Models for Three-Dimensional Entropic Elasticity

Professor Ray W. Ogden and his colleagues published a critical review on how to extend the worm-like chain (WLC) model to three-dimensional elasticity.

On worm-like chain model within the three-dimensional continuum mechanics framework,'' By Ray W. Ogden, Giuseppe Saccomandi, and Ivaonne Sgura, Proceedings of Royal Society of London, A doi:10.1098/rspa.2005.1592

The WLC model, e.g. Marko and Siggia, Macromolecules, 28, 8759-8770, is an elastic beam model. Its successful modeling of DNA has been a triumph for entropic elasticity theory.

Review articles on surface energy

Due to interest in nanotechnologies, several researchers in the mechanics community have started focusing on surface energy effects. I found these two review articles (very long, >100 pages!) which provide decent tutorials and references on this subject suitable for training begining graduate students.

Elastic effects on surface physics, Surface Science Reports, Volume 54, Issues 5-8, August 2004, Pages 157-258Pierre Müller and Andrés Saúl

Surface thermodynamics revisited, Surface Science Reports, Volume 58, Issues 5-8, September 2005, Pages 111-239A.I. Rusanov

Thursday, January 26, 2006

Introduce A New Multiscale Method: Bridging Scale Method

By Albert C. To

In the last decade, great effort has been put forth to develop simulation methods which can resolve material behavior across the multiple length scales present in many physical systems (Liu et al., 2004). The bulk of this work has been motivated by new design paradigms that require an understanding of the phenomena at the continuum level brought on by the underlying micro- or nanoscale physics, for applications such as MEMS/NEMS devices or novel alloy design. Recently, attention has also been directed toward biological systems, many of which exhibit a strongly coupled hierarchical nature. In systems design, the traditional engineering simulation approach has made extensive use of continuum level modeling via empirical constitutive relations and numerical methods such as the Finite Element Method (FEM) while atomistic level methods such as molecular dynamics (MD) have been used to study detailed phenomena such as dislocation nucleation and propagation or the details of failure mechanisms.

Figure 1. Schematic of domain type considered in bridging scale method

Each of these approaches has limitations: in the case of FEM, the resolution is limited to the size of the continuum element for which the constitutive relation employed remains valid. For MD, the enormous number of degrees of freedom required for a continuum level simulation makes its use intractable for system sizes greater than hundred of nanometers. Thus, it is desirable to seek a method which can be used over large length scales, but maintain atomistic or near-atomistic resolution in regions of interest.

Figure 2. Bridging scale simulation of a Mode I crack propagation. (Left panel: bridging scale method; right panel: full molecular dynamics simulation) .

Figure 3. Bridging scale simulation of Mode II crack propagation. Center region with high resolution contains MD, lower resolution region denotes FEM only region. Note that the waves propagate naturally within the overlap region, however at the THK interface, the fine scale part is dissipated and the coarse scale propagates.

Bridging scale method is a dynamic multiscale method that couples atomic modeling with continuum modeling without introducing spurious reflections at the interface (Wagner and Liu 2003, Park et al 2005a, Park et al 2005b). The method assumes molecular dynamics and finite elements (FE) solutions exist in the whole domain, but MD is performed only in a small localized domain as shown in Fig. 1. By minimizing the Lagrangians of the MD and FE, a linear projector is derived to decompose the solutions into fine and coarse scale solutions. At each time step, the projector projects the fine scale part of the MD solutions to the FE region and is added to the FE solutions to obtain the total solutions. At the interface, a time history kernel is derived to filter out the high frequency content of outgoing phonons such that spurious reflections will be minimized. This approach has a distinct advantage that the continuum domain do not need to be meshed down to the atomic resolution near the atomistic/continuum interface, saving the need for special mesh design. The formulation also allows the finite element solutions to be run at much larger time step than at in MD, thus making the method computationally efficient. Bridging scale method has been used to simulate elastic wave propagation and dynamic brittle fractures and has shown very good performances compared to full molecular dynamics simulations (Wagner and Liu 2003, Park et al 2005a, Park et al 2005b).

Figure 4. Bridging scale simulation of a Mode II crack propagation. Left panel shows the final mesh distortion after the solid has completely fractured. Right panel shows the complete fracture.

Figure 2 shows a dynamic crack propagation in a brittle solid, and the results for bridging scale method and molecular dynamics simulation are almost identical. Figure 3 demonstrates the wave propagation/dissipation abilities of the THK interface. Notice that the coarse scale (long wavelength) waves propagate out of the high resolution region, while the fine scale (short wavelength) waves are dissipated at the interface such that there are no spurious reflections. Figure 4 demonstrates the ability for BSM to capture fracture without resorting to remeshing or special continuum fracture elements. This aspect is a unique strength of BSM. It is due to the use of a projection of interatomic forces in the FEM+MD overlap region to obtain the FEM internal forces. This projection avoids the computation of the deformation gradient or Jacobian for the finite elements in the overlap region, thus allowing mesh distortions that would not be possible in a standard FEM simulation.

The cited publications can be found in this webpage:

Wednesday, January 25, 2006

Friction and Fracture: a collection of online talks


Current Challenges in Mechanics of Materials

The Second Meeting of the Thin-Air Philosophical Society (TAPS), organized by Professor Demitris Kouris and sponsored by NSF, was held at the University of Wyoming in August of 2005. The presentations were posted on the website of the meeting.

The last morning of the meeting was devoted to a discussion of current challenges in the mechanics of materials. Topics include
• Applications of mechanics and materials
• Tools of the trade
• Mechanics of integrated small structures
• Genes, molecular architectures, and mechanical behaviors
• Integrating mechanics and chemistry
• Mechanics in the field of energy
• Sensing the world
• Multiscale simultaneous design
• Coupling of quantum mechanics with traditional mechanics at small scales; emergence of new computational tools and concepts
• Hierarchical top-down vs. Bottom-up engineering of models for complex systems: beyond multiscale modeling
• Continuum mechanics and thermodynamics

The participants did not aim for an exhaustive list of topics. Rather, examples were discussed, with sufficient diversity to reflect issues of general interest. Individual participants were then assigned to write paragraphs to describe these examples.

Advanced substrates for cell manipulation

In a recent review article W.F. Liu and C.S. Chen discuss how substrates can be functionalized to control chemical and mechanical cues transmitted to living cells.

See: Materials Today, December 2005, Vol. 8, Number 12, p. 28-35.

Monday, January 23, 2006

In Memoriam to Professor John H. Argyris: 19 August 1913--2 April 2004

By Thomas J. R. Hughes, J. Tinsely Oden, and Manolis Papadrakakis

( Note: This article was first published in 2004 in Computer Methods in Applied Mechanics and Engineering, Vol. 193, pp. 3763-3766. With the permission of the authors and CMAME, we share it with you here.)

A person with great vision, class and persuasion, who dramatically influenced Computational Engineering and Science and who will be long remembered as one of the great pioneers of the discipline in its formative years.

John H. Argyris passed away quietly on 2 April 2004 after respiratory complications. John rests in peace in Sankt Jorgens Cemetery in the city of Varberg, 60 km south of Goteborg, Sweden, near Argyris' summer house.

John was born on 19 August 1913 in the city of Volos, 300 km north of Athens, Greece into a Greek Orthodox family. His father was a direct descendant of a Greek Independence War hero, while his mother came from an old Byzantine family of politicians, poets and scientists, which included the famous mathematician Constantine Karatheodori, Professor at the University of Munich.

Volos, as it was during his childhood, remained very much alive in his memory, especially the house he grew up in. He vividly remembered, until the end, details of the room where, at the age two, he almost died from typhoid fever. In 1919 his family moved to Athens where he received his initial education at a Classical Gymnasium in Athens. After studying Civil Engineering for four years at the National Technical University of Athens, he continued his studies at the Technical University of Munich where he obtained his Engineering Diploma in 1936. Just after graduation he was employed by a private consulting organization working on the leading-edge technical design of highly complex structures. One of these early engineering accomplishments was that of designing a 320 m high radio transmitter mast with a heavy mass concentrated at the top.

With the outbreak of World War II, John was in Berlin continuing his studies at the Technical University of Berlin. Just after the German invasion of Greece, John was arrested and led to a concentration camp, on the accusation of transferring research secrets to the Allies. His savior turned out to be the eminent German Admiral Kanaris, of Greek descent, who arranged his escape by informing the guards that the prisoner would be executed outside the camp. In 1944, Kanaris himself was tragically executed as one of the leaders of the assassination attempt against Hitler. Following his escape from prison, John managed to leave Germany soon thereafter in a very dramatic manner. He swam across the Rhine River during a midnight air raid, holding his passport in his teeth. He managed to reach Switzerland where he completed his Doctoral degree at ETH of Zurich in 1942 in Aeronautics. In 1943 he moved to England and worked as a technical officer at the Engineering Department of the Royal Aeronautical Society of London.

John could never derive any pleasure in ordinary day-to-day work and was only attracted to problems that seemed unsolvable. Even when working in industry, his directors soon realized that the best policy towards John Argyris was to entrust him with intractable problems. At the same time he was fascinated by the properties of triangular and tetrahedral components that appeared to him as ideal elements to build up an engineering system. He could never sympathize with Cartesian analytical geometry that he found most inelegant. During the war, he wrote three classic papers in Reports and Memoranda of the then Aeronautical Research Council. These were concerned with the diffusion of loads into stringer-reinforced stressed skin structures of wings and fuselages. He developed a theory using his intuition that combined differential equations and finite difference calculus that was immediately successful and later confirmed by experiments and applied with great success to British fighter and bomber aircraft during the war. However, the real break-through in his way of thinking and approach to technical problems of solid mechanics was achieved when the first electro-mechanical computing devices emerged in 1944 in Britain at the National Physical Laboratory and in the United States at Harvard University.

In those days aeronautical engineers were trying to build the first combat jet aircraft whose speed required swept-back wings. One such example was the flawed German fighter ME262, proof of its designers' failure to develop a reliable method of analyzing the non-orthogonal geometry of wings. In August of 1943 John spent three whole days and nights in a bold attempt to solve that particular problem. His only help was a rudimentary computing device capable of solving a system of up to 64 unknowns. It took one sudden moment of clarity, on the third evening of his brainstorming session for him to realize that the answer could be the application of triangular elements. Here his dislike of orthogonal Cartesian geometry found an ideal field. Astonishingly enough the deviation from preceding experimental test results proved less than 8%. This was the birth of the matrix force and displacement methods, the finite element method, as later named. Immediately, all publications on this method were declared secret. Within the triangular element philosophy, John did not use Cartesian direct and shear stresses and strains, but a novel definition of stresses, expressed in terms of these direct stresses and strains, measured parallel to the three sides of each triangle. This new definition of stresses and strains led to the formulation of the Natural Approach which possessed great computational advantages and allowed a simple and elegant generalization to large displacements.

In 1949 John joined the Imperial College of the University of London as a Senior Lecturer and in 1955 became a Full Professor and Director of the Sub-department of Aeronautical Studies until 1975. After becoming an Emeritus Professor he continued his collaboration with Imperial College as a Visiting Professor until 1980. In 1959 he accepted an offer from the University of Stuttgart and became Director of the Institute for Statics and Dynamics of Aerospace Structures. He created the Aeronautical and Astronautical Campus of the University of Stuttgart, a focal point for applications of digital computers and electronics. After becoming an Emeritus Professor at the University of Stuttgart he continued to work until the age of 88 with the same vigor, writing books and scientific papers with a compelling vitality and creative thinking.

In 1956 John addressed the problem of stress analysis of aircraft fuselages with many cut-outs, openings and severe irregularities. Computers then were not capable of enabling a global application of the finite element method. John, again following his intuition, realized that the problem could be solved by a new physical device involving the application of initial stresses and strains and an extension of matrix methods to a higher level. This was presented at the IUTAM Congress in Brussels in 1956 and created a great upheaval, because the whole derivation involved only 20 lines of physical argument and four lines of advanced matrix algebra. Most experts in the United States and Europe said that the theory must be wrong on the grounds of its simple derivation and they did not even accept the evidence of the computational results obtained by John that proved the correctness of this derivation. Somewhat later, however, a Ph.D. Thesis from Sydney, Australia was sent to John in which the candidate proved in 124 pages of close mathematical argument that the formula of John Argyris was indeed correct. This approach was also extensively applied to the design of the Boeing 747 as early as 1960. In the 1960s and 1970s John had applied the finite element method with great success in Aerodynamics, Optimization, Combustion Problems, Nonlinear Mechanics and other fields of research and industrial interest, among them the suspension roof of the Munich Olympic Stadium in the late 1960s. Around that period NASA sought his knowledge on the thermal shielding of the Apollo spacecraft. He suggested covering the fuselage with specially formulated substances that, upon reentry into the atmosphere, would evaporate and cool its surface. In 1976 John was concerned with the theory of Chaos and introduced these theories in studying the turbulence flow around the European Space Vehicle Hermis.

It is difficult to summarize the impressive accomplishments of John Argyris. Among his writings were over 10 books, including three important textbooks: Introduction to the Finite Element Method, Vols. I, II and III, 1986–88; Dynamics of Structures, 1991; An Explanation of Chaos, 1994. The latter was printed in English and German and in Germany alone was published three times in one year, a rare achievement for a scientific publication of this kind. In addition to these writings, he published over 500 extended scientific articles in major international journals and lectured extensively both within Europe and abroad. His textbooks and extensive journal publications are essential reading material for students, practicing engineers and researchers around the world and have become benchmarks for later treatises on Computational Mechanics.
One of his most important contributions in the engineering community was the founding and editorship of the journal Computer Methods in Applied Mechanics and Engineering, a publication that has provided much of the lifeblood of Computational Methods in Applied Mechanics and Engineering for more than three decades. John Argyris took great interest and pride in this venture and insisted on running the journal meticulously and diligently, thus succeeding in making it one of the leading journals in Computational Mechanics available today.

John received many honors including 18 Doctorate Degrees, "Honoris Causa", three honorary professorships and six academy memberships from universities and academies all over the world, and more than 25 other awards and distinctions, among them the Gauss–Newton Award from IACM, the von Karman Medal from ASCE, the Timoshenko Medal from ASME, the Laskowitz Gold Medal from the Academy of Science of New York for "the invention of the Finite Element Method", the Prince Philip Gold Medal of the Royal Academy of Engineering, the Grand Cross of Merit of the Federal Republic of Germany and the Einstein Award from the Einstein Foundation for his "momentous work on the Finite Element Method and Chaos Theory". He was also Fellow of the Royal Society of London, Honorary Member of the Executive Council of IACM and Honorary President of GACM.

John was blessed with many talents, making him a true modern Renaissance man; he was a scholar, a thinker, a teacher, a visionary, an orator, an elegant writer, a linguist. Deeply cultivated, a man with rare principles and a passionate patriot, he was also unique in blending his Mediterranean temperament with Western European rationalism.

In the paper which coined the name "Finite Element Method", published in 1960, the world-renowned author Ray Clough refers to the finite element method as "the Argyris Method". Von Karman's prophetic statement that Argyris' invention of the Finite Element Method entailed one of the greatest discoveries in Engineering Mechanics and revolutionized our thinking processes more than 50 years ago was proven to be absolutely true. Indeed, the Finite Element Method, based on John Argyris' fundamental and far-reaching contribution, has truly revolutionized today's engineering and scientific environments. He had the vision and intellectual capacity to develop the basic steps of the Finite Element Method and to make numerous contributions in the development of the method. His early work "Energy Theorems of Structural Analysis", published in 1954, is considered to be the most important series of papers ever published in the field of Structural Mechanics.

During the early years at Imperial College he met his wife Inga-Lisa who provided him with unshakable support throughout all the difficult moments of his life. John was also fortunate to see his son Holger follow a successful career in engineering and bring into the world, with his wife Carina, two adorable grandchildren who brightened his final years.

John, in accordance with Herakleitos' aphorism of “ ”, has joined the Pantheon of those enlightening personalities who, with their revolutionary ideas and contributions, have changed the scientific world in the 20th Century. His geometrical spirit, the elegance of his writings, his deep appreciation and understanding of classical ideas, his creativity and his epochal vision of the future initiated and defined the modern era of Engineering Analysis and set us all on life's path of discovery. Our Computational Mechanics Community has lost the most eminent member and for many of us, a devoted friend. He will be deeply missed, but his legacy will empower generations.

Sunday, January 15, 2006

Mechanics of Nanoscale and Hierarchical Structures of Biological Materials: Flaw Tolerant Strategies in Nature

Professor Huajian Gao, who had served as a director at the Max Planck Institute for Metals Research during the last 5 years and is now moving to the Division of Engineering of Brown University, has been working with collaborators on mechanics of bottom-up designed nanocale and hierarchical structures of biological materials such as bone and gecko . This research has revealed several key mechanics concepts and principles that underline a wide variety of biological systems. The following is a report of his research on bio-inspired flaw tolerant strength theory.

On the hierarchical biomechanics of bone, Gao has aimed to gain some understanding of the hierarchical nanocomposite structures of hard biological tissues such as bone, tooth and shells. At the most elementary level of structural hierarchy, bone and bone-like materials exhibit a generic structure on the nanometer length scale consisting of hard mineral platelets arranged in a parallel staggered pattern in a soft protein matrix. Gao has posed the following questions of interest to mechanics: (1) The length scale question: why is nanoscale important to biological materials? (2) The stiffness question: how does nature create a stiff composite containing a high volume fraction of a soft material (protein)? (3) The toughness question: how does nature build a tough composite containing a high volume fraction of a brittle material (mineral)? (4) The strength question: how does nature balance the widely different strengths of protein and mineral ? (5) The optimization question: Can the generic nanostructure of bone and bone-like materials be understood from a structural optimization point of view? If so, what is being optimized? What is the objective function? (6) The buckling question: how does nature prevent the slender mineral platelets in bone from buckling under compression? (7) The hierarchy question: why does nature always design hierarchical structures?

What is the role of structural hierarchy? Anyone who is interested in these questions can read Gao’s papers on this subject. They may not necessarily agree with his points of view, but these questions can serve as a good starting point and motivation for someone with a solid mechanics background and a serious interest in mechanics of biological systems. Gao believes that a complete analysis of these questions taking into account the full biological complexities requires collaborative effort of a whole community. In the published papers by Gao and coworkers, the length scale question is addressed based on the principle of flaw tolerance which, in analogy with related concepts in fracture mechanics, indicates that the nanometer size makes the normally brittle mineral crystals insensitive to cracks-like flaws. Below a critical size on the nanometer length scale, the mineral crystals fail no longer by propagation of pre-existing cracks, but by uniform rupture near their limiting strength. The robust design of bone-like materials against brittle fracture certainly provides an interesting analogy between Darwinian competition for survivability and engineering design for notch insensitivity. Gao’s analysis with respect to the questions on stiffness, strength, toughness, stability and optimization of the biological nanostructure provides further insights into the basic design principles of bone and bone-like materials. For example, the staggered nanostructure of bone is shown to be an optimized structure with the hard mineral crystals providing structural rigidity and the soft protein matrix dissipating fracture energy. To understand the question on structural hierarchy, Gao proposed a “fractal bone” model with multiple levels of self-similar “hard-soft” composite structures mimicking the nanostructure of bone. The theoretically constructed fractal bone is a truly hierarchical material with different properties at different length scales and can be designed to tolerate crack-like flaws at multiple length scales.

With similar philosophy, Gao and coworkers have also been conducting research on the hierarchical biomechanics of adhesion structures of gecko. Gecko and many insects have evolved specialized adhesive tissues with bottom-up designed hierarchical structures that allow them to maneuver on vertical walls and ceilings. The adhesion mechanisms of gecko must be robust enough to function on unknown rough surfaces and also easily releasable upon animal movement. How does nature design such macroscopic sized robust and releasable adhesion devices? How can an adhesion system designed for robust attachment simultaneously allow easy detachment? These questions have motivated Gao to develop a mechanics theory of robust and releasable adhesion in biology. On the question of robust adhesion, Gao introduces a fractal gecko hairs model, somewhat similar to his fractal bone model, with self-similar fibrillar structures at multiple hierarchical levels. Gao and coworkers have shown that structural hierarchy again plays a key role in robust adhesion: it allows the work of adhesion to be exponentially enhanced with each added level of hierarchy. Gao shows that, barring fiber fracture, the fractal gecko hairs can be designed from nanoscale and up to achieve flaw tolerant adhesion at any length scales. However, consideration of crack-like flaws in the hairs themselves results in an upper size limit for flaw tolerant design. On the question of releasable adhesion, Gao has shown that the asymmetrically aligned seta hairs of gecko form a strongly anisotropic material with adhesion strength strongly varying with the direction of pulling. This orientation-dependent pull-off force enables robust attachment in the stiff direction of the material to be released by pulling in the soft direction. This strategy, which Gao succinctly termed as a “stiff-adhere, soft-release” principle, can be understood in a simple way as follows. When pulled in the stiff direction, less elastic energy can be stored in the material (much like a stiff spring can store less energy compared to a soft spring), leading to lower energy release rate to drive random crack-like flaws induced by surface roughness. On the other hand, much more elastic energy can be stored in the material when pulled in the soft direction, especially when the material is strongly anisotropic, leading to much higher energy release rate to drive the roughness induced crack-like flaws.

Professor Grigory I. Barenblatt received the 2005 Timoshenko Medal

In recognition of his many contributions in applied mechanics, Professor Grigory I. Barenblatt is the recepient of the 2005 Timoshenko Medal.
During his distinguished career, Professor Barenblatt has made seminal contributions to many areas of solid and fluid mechanics, which include cohesive fracture mechanics, turbulence modeling, non-local damage theory, stratified flows, flame, flows in porous media, and the theory and application of intermediate asymptotics.

The following is his Timoshenko Medal Lecture delivered at the Applied Mechanics Division's annual dinner meeting last November.

Applied Mechanics: an age old science perpetually in rebirth

By Grigory I. Barenblatt

Mr. Chairman, Colleagues, Ladies and Gentlemen:
I want to express my gratitude to the Executive Committee of the Applied Mechanics Division of the American Society of Mechanical Engineers for nominating me for the Timoshenko Medal, and to the Board of Governors for awarding me the Medal on behalf of ASME.

The personality and name of Stepan Prokofievich Timoshenko (Stephen P. Timoshenko as he is called in this country) is very special for me. When I was a beginning student at Moscow High Technical School, where I studied before entering the Mathematics Department at Moscow State University. I purchased his book “The theory of elasticity”: in fact, this was the first technical book in my personal library. The clarity and depth of the presentation of this difficult subject wits then and remains now for me an unsurpassed standard. Something in this book astonished me, and I addressed a question to my maternal grandfather, an eminent Professor of Differential Geometry at Moscow State University. (I was raised by his family after my mother, one of the first virologists, perished preparing a vaccine against encephalitis.) The question wits: the author is definitely a Russian (at that time in our circles nobody noticed the difference between Russians, Byelorussians, and Ukrainians). Why did his book appear in translation from English? Grandfather explained - Timoshenko emigrated after the Revolution (such people were unpopular in the Soviet Union in the late forties) - however, with a kind smile he took from his library and presented me with Timoshenko’s course on elasticity in two volumes, published in Russian in 1914 and 1916 by the Sanct Petersburg Institute of Railways Transportation, and presented to him by the author. SP got the chair at this Institute after some period of unemployment: before that he was Dean at Kiev Polytechnic Institute and was fired by the Minister of Education for substantial exceeding the number of admitted Jewish students allowed by explicitly formulated (this was important) norms. Visiting my family in Moscow last summer after learning about the award, I wanted to bring these volumes to this country, but I was warned that strict rules concerning old books would not allow it. When I already was a young scientist, I was introduced to SP during his visit to Moscow. Also, I was proud when I had seen that SP and James P. Goodier mentioned my work concerning fracture in their book.

Much later when, by the initiative of Joseph B. Keller and Milton D. Van Dyke, Dean Thomas Hughes nominated me for the Timoshenko Professorship at Stanford University I spent many happy hours working in the Timoshenko Room at the Durand Applied Mechanics Building where there is exhibited a remarkable portrait of Stepan Prokofievich. I am deeply grateful to all of them for granting me this unique experience. My collaboration with my eminent colleague and now close friend Alexandre J. Chorin started shortly before that at Berkeley and continues to this day. Alexandre visited me for working together at Stanford; therefore in one of our joint works my affiliation is Stanford University.

Mechanical Engineering and Applied Mechanics, as its part, are among the first and greatest intellectual achievements of mankind. The names of Archimedes and Galileo are known to everybody. I am sad to say that nowadays these disciplines are not popular among bright young people choosing their career. And this tendency is not a new one: it started rather long ago, apparently in the twenties. As you know, G.I. Taylor, one of the first winners of the Timoshenko Medal, worked all his life at Cavendish Physical Laboratory in Cambridge. J .J. Thompson, Lord Ernest Rutherford, Sir Lawrence Bragg, great men of science, all of them Nobel Prize winners, were the Directors of the Cavendish Laboratory during G.I.’s time. According to E.N. da C. Andrade, brilliant physicists at Cavendish who created at these times pioneering works, such as ‘smashing’ the atom, discovering X-ray radiation coming from stars, researching the structure of hemoglobine and mioglobine and, finally founding the double spiral, expressed their astonishment at how such a brilliant person as G.I. Taylor could spend his life dealing with such dull and old stuff as applied mechanics. I want to give a definitive answer. Yes, mechanical engineering and applied mechanics are old art and science. But they are also young because they are eternal art and science. It is very sad that the attitude towards mechanical engineering and applied mechanics as something of secondary interest entered the consciousness of a large and influential part of society, and this attitude cannot leave their children - future students - unaffected.

Allow me another instructive example. Years ago when I had to renew my American visa, I visited the American Consulate in Rome. Strong letters in support of my application preceded my visit to the Consulate, and I was told that the American Consul decided to process my application personally - a rare distinction. So, I was escorted to the Consul immediately and I was shocked: the Consul happened to be a rare beauty in her flourishing age: blue eyes, luxurious black hair, a truly unforgettable impression ... She understood that I was impressed, and she waited a little in asking ordinary questions, and did her job. When only a small, purely technical part of the job remained, she asked her secretary to do it, and said: ”Professor, now we have 5-10 minutes. Could you tell me what you have done in your science to deserve such letters of support?” At that time our group (Professor A.J. Chorin, Dr. V.M. Prostokishin and myself) were working intensively on investigating the scaling laws for turbulent flows in pipes and other shear flows. We came to the conclusion that the fundamental universal logarithmic law which was in use for several decades is not quite correct, and should be abandoned and replaced by a different Reynolds- number-dependent scaling law. I have to admit that many people at that time, and some of them up to now, consider our results as controversial. However, the formulae and all available experiments definitely speak in our favor. I remind you that many similar situations have occurred in the history of science, and not only in science. For instance, when an essay of Maurice Maeterlinck, who won the Nobel Prize for his ‘Blue Bird’, was included in the Index Prohibitorum by the Catholic Church, Maeterlinck wrote “At every crossing the road that leads to the future, each progressive spirit is opposed by a thousand men appointed to guard the past.” In our case, these men can also be understood: if we are right, text-books and lecture courses should be changed and you have to bear in mind that the universal logarithmic law is taught every year in a thousand universities and polytechnic institutes. We continued to defend the truth in our seminars, lectures and publications. I had no choice: my great mentor Andrey Nikolaevich Kolmogorov, whose name is known to everybody in this audience, said: “I have lived being guided by a principle that the truth is a blessing, and our duty is to find it and to guard it.”

I return to the unforgettably charming lady Consul. I decided: obviously the elegant lady who starts and finishes her days by using the flow in pipes should be interested in such work. And I did my best to present our results in the short time given to me. The Beauty - Consul - looked at me (with her wonderful dark blue eyes!) and said: “Professor, of course, what you said is interesting, even exciting. However, frankly speaking, I am astonished. When we have some
problems with pipes, we address a plumber, not a professor with a world-wide reputation!” I was ashamed, and up to now I have a feeling of personal guilt. Indeed, now we know the structure of remote stars better than the strength of a shuttle or a dam and contrary to astronomers and astrophysicists how little we do to explain in particular to younger generations the fundamental depth and beauty of our profession and to popularize it.

Money is not yet wealth. And the leading nations of the XXI century will not necessarily be the countries having more money than others. These will be the nations where great national and global problems will be understood and appreciated by the majority of their populations. The heroes of these nations will be engineers and scientists of great vision and ability to select and explain the problems of primary importance, and to achieve the support, governmental and private, necessary to solve these problems, leading to engineering achievements that bless society.

Such engineers and scientists of great vision and organizing abilities do exist; they are among us. In due time and favorable circumstances they appear and make steps of historic importance. It is enough to remember here John Rockefeller, Thomas Aha Edison, Henry Ford, Robert Oppenheimer, Howard Hughes, and more recently W.R. Hewlett, D. Packard, and William Gates.

A remarkable example, less known, is Leo Szillard, an American physicist of Hungarian origin. It was he who recognized the practical necessity of designing the atomic bomb. He prepared the text of the letter to President Franklin D. Roosevelt, where the crucial importance of immediately starting work on the construction of the atomic bomb was emphasized in strong terms. This text was signed (not very enthusiastically) by Albert Einstein. Roosevelt decided to
decline Einstein’s proposal (it is difficult to believe now, but it is possible to understand FDR: the country at that time had to carry the tremendous burden related to supplying the American Army and Allies by ordinary weapons and ammunition). When Szillard learned about the negative decision in preparation, he found a personal friend of FDR, explained to him the problem, its importance and urgency, and persuaded him to interfere. The friend visited FDR, and after dinner asked him only one question: “Frank, do you think, if in 1812 Napoleon had not turned down Fulton, the inventor of the steamer, the world map would be nowadays the same?” And FDR gave the order to start the work. The scale and value of this work - the Manhattan Project - is well known.

However, the common opinion of the layman, even scientific and engineering laymen, is that nowadays there are no such problems of the scale of the Manhattan Project whose importance for the nation and the world is understood by everybody. This is deeply wrong! Such problems do exist, and they can be understood by everybody. First of all, among these problems are large-scale natural disasters, and energy problems. I will present several examples.
Tropical hurricanes. The scales of these disasters are huge, and the morale and material losses are formidable. I want to emphasize here that in fact hurricanes present a fascinating problem of applied mechanics. And, in general, Sir James Lighthill, one of the first winners of the Timoshenko Medal, considered natural disasters, in particular, hurricanes, as problems of first importance for applied mathematics and mechanics.

As far as hurricanes are concerned, the situation is as follows. As a preliminary note, I want to mention a simple calculation, by which A.N. Kolmogorov started his course on turbulence at Moscow State. He asked the listeners: What will the velocity be at the surface of the river Volga in Russia (close by its parameters to the Mississippi in this country) if by some miracle it becomes laminar ? The answer was striking: hundreds of thousands of miles per hour! Why then is it kept so slow ? The reason is that the flow is turbulent: it is stuffed with turbulent vortices, and these vortices play the role of brakes, slowing the flows. An analogy: moving along mountain slopes, drivers use chains to cover the wheels - the vortices play the role of such chains.

Sir James Lighthill proposed, on the basis of many observations, a “sandwich model” of hurricanes. According to this model in the ocean during a hurricane there exist three layers: air, sea, and “ocean spray” between them, where “the third fluid” is contained; in fact, air suspension of droplets, sometimes sufficiently large, tens of microns in diameter.

Our group (Professor A.J. Chorin, Dr. V.M. Prostokishin and myself) considered, under some natural assumptions, turbulent flow of ocean spray. The general theory of turbulent flows carrying heavy particles, developed earlier by A.N. Kolmogorov and myself, at that time his graduate student, was used in this consideration. It happened that the droplets reduce turbulence intensity, because turbulent vortices spend a significant part of their energy for suspension of droplets. Returning to the analogy with wheel chains - the chains that are worn out become weaker. The flow accelerates under the same pressure drop. Our calculations showed that this acceleration can be very large, reaching velocities of large tropical hurricanes.

I note that the same mechanism of acceleration of turbulent flows by heavy particles was noticed earlier in the great Chinese rivers Yangtze and the Yellow River, carrying a large amount of sediment, and in dust storms, both terrestrial and Martian. And the basic question arises: is it possible to prevent, or at least reduce the strength of tropical hurricanes? Our answer is affirmative, but it requires the serious large scale work of the mechanical community. The technical problem is to suppress the formation of droplets. In principle it can be done by pouring oil on the surface of the sea. By the way, such practice is known from ancient times when on the decks of vessels several barrels of oil were reliably strengthened, and in critical circumstances the oil was poured overboard. It was noticed that the intensity of the squall was quickly reduced. There exist several attempts to explain this phenomenon, but according to our viewpoint the basic effect is the suppressing of the formation of droplets. By the way, up to now the recommendations for sailors on small boats to pour oil are routinely proposed in the literature. Of course, the oil (or some detergents which also are recommended for using under such circumstances) should be safe. There are several candidates for such materials. And I repeat - a group of enthusiasts headed by young, energetic leaders can solve this problem and do it in real time - the witches like the recent Katrina should never threaten New Orleans and
other remarkable cities.

Our paper was published in PNAS a month before Katrina, and it attracted the attention of PR. I was interviewed by TV - after a preliminary make up - and when the lady, senior in the team, was asked by someone who was present, when this interview would be aired, the answer was instructive: “We have to wait for a good hurricane, then more people will pay attention.’’

The problem of forest fires, also very sensitive for the world (remember, e.g., Portugal this summer), bears some similarity to hurricanes. During a forest fire a dark layer is formed above the trees where the debris and soot are moving. They suppress turbulence in the same way as droplets in ocean spray: that is apparently the reason for strong winds and even firestorms.

Another very important matter. I think that an honest analysis, deeply based on scientific consideration of natural and technogenic disasters can be not less but very often more exciting and important than great projects like Manhattan and all these cosmology and particle acceleration enterprises. There is a difference. Money, and even Big Money, cannot prevent such analysis. But Very Big Money plus politics can do it, and in these cases a chain reaction of disasters started. An example: “Titanic”. In 1913 fundamental engineering and scientific analysis of this disaster was not performed; only much later it was understood what had happened there - the temperature was lower than the temperature of the steel embrittlement, and the vessel’s body became brittle. Twenty-seven years later: 24 May 1941 at 5:52 a.m. the HMS battle-cruiser “Hood”, the flagship of the fleet chasing the German battleship “Bismarck” made a first volley. “Bismarck” answered by a shot of a small antiaircraft gun. And at 6:00 a.m. “Hood” sank; fifteen hundred people perished, only four were saved! (The steel was supplied by the same firm as for the “Titanic” .) Thinking about this case I was astonished: 24 May, spring - it should not be cold! But read Volume I11 of Churchill’s “The Second World War” - 24 May was an extremely cold day at the place.. .clearly the temperature of embrittlement again was crossed. And again: no competent engineering and scientific analysis! Only later when the welded “Liberty” ships started to break in two halves in the North Sea (tens of thousands of people perished), such analysis was performed, and Fracture Mechanics was created. George Irwin, later a Timoshenko Medal winner, was the leader. I also participated in this work. Fracture Mechanics is now as a charming lady in her forties: a remarkable past and a lot in the future. A wonderful branch of mechanical engineering and applied mechanics! Each fracture surface can tell you a lot about both the material and the loading: those who are really interested in what happened can achieve it (of course, only if they will be allowed to obtain the fractographs!)!

I want to tell you about one more field, fully deserving the attention of mechanical engineers, and able to create a first class large scale project. Nowadays when the price of gas reliably crossed the $3/gallon line the problems of energy resources is of interest to every layman. The time when I got my Ph.D. degree was difficult for people of my ethnical origin, and after many attempts I got an offer from the Institute of Petroleum of the Academy of Sciences. I was very lucky to get this job, and since that time Petroleum Engineering is also my profession. It is very important practically - this is trivial to say. But I want to emphasize that it is remarkable as an object of applied mechanics. Many ideas which reveal themselves in such fields as gas dynamics, boundary layer theory, etc., as vague models appear in petroleum engineering as exact mathematical formulations - it is an enjoyment to deal with them. What is most important - every new oil and gas deposit presents a new scientific problem, very often leading to good mathematics. The practical problem of highest importance is to enhance oil recovery. Now the legal figure is 30 percent, so it is considered as normal if we leave in the rocks 70 percent of an irrecoverable gift of nature. But take the deposits of Southern California: Lost Hills, Bellridge. The oil there lies in diatomites: rocks of very high porosity, low strength and practically zero permeability. The exploitation of such deposits by ordinary methods, including ordinary hydraulic fracture, leads to huge losses. The oil recovery is low. To find the proper way of development of such deposits means a reliable way to reduce the energy crisis. It cannot be done without the active participation of mechanical engineering and applied mechanics - what I am saying is based on my old and recent experience. The same is true for huge gas deposits in
so-called tight sands available in this country - recently I presented a lecture about this subject.

Ladies and gentlemen, colleagues, I come to my conclusion. Sir Winston Churchill, the greatest man of the last century said: “If the human race wishes to have a prolonged and indefinite period of material prosperity, they have only got to behave in a peaceful and helpful way towards one another, and science will do for them all that they wish and more than they can dream. “Nothing is final. Change is unceasing and it is likely that mankind has a lot more to learn before it comes to its journey’s end.. . .” I want to finish my speech by saying that in this future development of mankind our field, mechanical engineering and applied mechanics will play a decisive and governing role. Many fields of science and engineering will appear, become fashionable and disappear, but our branch of activity will always shine because it is eternal and perpetually renewing.

Saturday, January 14, 2006

Applied Mechanics News: Kyung-Suk Kim won Ho-Am Prize of $200,000

Applied Mechanics News: Kyung-Suk Kim won Ho-Am Prize of $200,000

Professor Carl T. Herakovich won the 2005 Applied Mechanics Award

At the Annual Dinner of the Applied Mechanics Division last November, in Orlando, Florida, Professor Carl T. Herakovich was presented the 2005 Applied Mechanics Award, in recognition of his distinguished contributions to mechanics of fibrous composite materials, and his distinguished service to the mechanics and engineering science community. The text of his acceptance speech follows.

Acceptance Speech
The 2005 Applied Mechanics Division Award
Carl T. Herakovich

Thanks Wing, it is indeed a great honor and pleasure to be recognized by the Applied Mechanics community.

I hold the mechanics community in the highest regards and with the utmost respect. I am always so impressed by the intelligence of the people in this community, their honesty and their candor.

And I can really enjoy being around mechanicians in a social setting. Give them a little wine at dinner and it can be quite a party. I really do enjoy the people in this community. I feel very much at home. (Comment briefly on the dinner in Warsaw at the International Congress in August 2004, and the dinner in DC in Sept. 2005.)

As it happens, you have given me a very nice 50th Anniversary gift. It was 50 years ago, September 1955, that I entered Rose Polytechnic Institute in Terre Haute, Indiana (now Rose-Hulman Institute of Technology) to begin my studies in engineering.

How did I end up spending 50 years in mechanics? Several people had a major impact on my decisions along the way. Professor Richard H. F. Pao at Rose was undoubtedly the first person that peaked my interest in the field. The first class I had from Prof. Pao was in fluid mechanics and my oldest memory of him is the time that I fell asleep in his 8 o’clock fluids class one wintry day while sitting next to a hot radiator with my heavy coat still on. Pao woke me up and left no question that I had embarrassed him by falling asleep in his class. That had a major impression on me, as I never like it when students fell asleep in my class in later years. The class that really made me realize that there was this field called mechanics was an elective that I took from Prof. Pao in the second semester of my senior year. The course was on Advanced Mechanics of Materials out of the old Seely and Smith book.

The next person who influenced my studies in mechanics is clearly my wife Marlene. We met in Terre Haute in Sept. 1957, and married not quite three years later in April 1960. In August 1960, we were preparing to go to Colorado where we both were to have jobs. I then saw an announcement that assistantship were available in Mechanics at The University of Kansas. Now, even though we had only been married about three months and Marlene was about 2.5 months pregnant, she agreed to my wild, out-of-the-blue suggestion that we forego the jobs and go to Kansas so I could study mechanics in graduate school. There had been no previous indication that I would ever want to pursue graduate education. (This change in attitude was undoubtedly influenced by my job at the time working for the Indiana Highway Department.)

After two years in Kansas and two more back at Rose teaching and coaching, I again decided that I would like to go back to graduate school to study more mechanics. Again, Marlene agreed even though we now had two sons. Thus, we ended up in at IIT Chicago (very near our homes in Northern Indiana). There I met Prof. Phil Hodge who became my PhD advisor and mentor. He is a great role model and one who has been very active in AMD, serving on the Executive Committee and as Editor of JAM. He was also active in ASME boards and committees as well as the U. S. National Committee on Theoretical and Applied Mechanics. I have followed in his footsteps in many of these activities.

I have had the good fortune to know and interact with a number of the people who have made a significant impact on mechanics in general and this Division in particular. In addition to Hodge at IIT, fellow students were Ted Belytschko and Bill Saric, both former members of the AMD EC.

During my tenure on the Executive Committee, I was privileged to work with David Bogy, Ben Freund, John Hutchinson, Tom Cruse, Stan Berger, Lallit Anand, Alan Needleman and Tom Hughes. This was a very active time for the EC as we initiated two new ASME medals, the Koiter Medal and the Drucker medal. I had the privilege of informing both Professor Koiter and Professor Drucker that a medal was established in their honor and that they were to be the first recipients.

During my term as ASME Vice President of Basic Engineering, I had the opportunity to work with AMD Chairs Dusan Krajcinovic, Stelios Kyriakides, Pol Spanos and Mary Boyce.

On the USNC/TAM, I have had the good fortune to work with Tinsley Oden, Jan Achenbach, Bruno Boley, Andy Acrivos, Hassan Aref, Zdenek Bazant, Dan Drucker, George Dvorak, Wolfgang Knauss, and K. Ravi-Chandar, and many others.

Other mechanicians I have known, and on occasion worked with, include: Bernard Budiansky, Mike Carroll, Dick Christensen, Steve Crandall, Jim Dally, Frank Essenburg, Bob McMeeking, Paul Naghdi, Bob Plunkett, Chuck Taylor, Nick Hoff and Sea Nemat-Nasser. I have met Julius Miklowitz, William Prager, Eli Sternberg, Morton Gurtin and Warner Koiter. (Comment on Gurtin giving a lecture at IIT when I was a graduate student. Gurtin is in the audience.)

I hope it is obvious that I feel very lucky to be able to say that I have rubbed elbows with some of the giants of mechanics and the Applied Mechanics Division.

I owe a debt of gratitude to Dan Pletta who hired me at Virginia Tech, Dan Frederick who served as my chairman there for many years, and Ed Starke who hired me at the University of Virginia. And, of course, to Marlene who has always been there, and allowed me to follow what were at times, capricious whims.

In closing, I would like to comment briefly on some beliefs that I have arrived at after 50 years in the field. I believe that the sustainable future of mechanics is in the fact that it is a science. While we in the US tend to think of mechanics as an engineering discipline, if you read the literature on the establishment of the International Union of Theoretical and Applied Mechanics, our field was, and is, clearly considered a science.

There are several Engineering Science and Mechanics departments in the US that have maintained strength and vitality while other mechanics departments without Science in the name have floundered. Advances in engineering, in particular computational engineering, have radically changed the practice of engineering during my professional lifetime. We are now more science oriented in our approach to traditional engineering problems as well as the types of new problems that we are investigating.

Further, it is evident that science receives the lion’s share of research funding in the US. This was brought home to the USNC/TAM last spring when we had presentations from congressional staff members. The message was: if you hope to increase funding for mechanics, emphasize the science of mechanics. Indeed, the USNC/TAM is considering a name change that would include the word science. Your collective input to a more modern name for the US Committee would be most welcome.

In my role as Secretary of the USNC/TAM, I want to encourage all of you to submit proposals to host an IUTAM Symposium. These international symposia are opportunities to bring together an international assemblage of experts in a specific field of mechanics. They can have a major impact on the field as well as your local institution. The US has been somewhat lax in proposing IUTAM symposia recently and I encourage you to consider submitting a proposal. All pertinent information can be found on the USNC/TAM web site at USNCTAM.org. The two-page proposals are due in early January 2006.

Again, I thank all of you for honoring me as you have.

Monday, January 09, 2006

2005 AMD Honors and Awards

George Haller
For seminal contributions to nonlinear dynamics, including the development of analytic theories for chaos near resonance and for unsteady separation in fluid flows

L. Mahadevan
For significant research contributions to the exploration of nonlinear and nonequilibrium phenomena in continuum mechanics using geometry, analysis and scaling ideas in close conjunction with experiments

Carl T. Herakovich
In recognition of his distinguished contributions to mechanics of fibrous composite materials, and his distinguished service to the mechanics and engineering science community

Robert L. Taylor
For pioneering contributions to computational solid mechanics and, in particular, for the development of methods and software used worldwide for the calculation of inelastic response of structures

Raymond W. Ogden
For seminal contributions to nonlinear elasticity, its mathematical foundations and its applications

Grigory I. Barenblatt
For seminal contributions to almost every area of solid and fluid mechanics,including fracture mechanics, turbulence, stratified flows, flames, flow in porous media, and the theory and application of intermediate asymptotics