The publisher sent me the other day this new book by Audoly and Pomeau.  I haven’t gone through the book carefully, but a quick look has indicated that this is a very special book, well worth a close reading.  The book is beautifully written and well produced.  The authors have captured the recent excitement about thin elastic objects, such as rods, plates, and shells.  While existing books on plates and shells mostly focus on calculating critical loads for instability, this new book describes shapes produced by instability.  Examples include wrinkles in a leaf, ridges in a piece of crumpled paper, and curls of a hair.  The subject is photogenic, and the book contains a large number of delightful illustrations.  The book approaches the subject through physical phenomena, rather than mathematical formalisms.  The authors have intended it as a text for a course at the level of senior undergraduate students or beginning graduate students.         

At the invitation of Yonggang Huang, I’ll give 4-hour lectures at the NSF Summer Institute Course on the Mechanics of Soft Materials.   I attach the slides of the lectures, to be given on Monday, 10 May 2010.  An abstract of the lectures follows.

 Early this year Amazon sent me a recommendation of this book by Morton Gurtin, Eliot Fried, and Lallit Anand.  I pre-ordered this book, which arrived the other day.  The authors are active and distinguished scholars.  The publisher has done an excellent job in producing the book.  It is simply a joy to hold the book in your hands, and read. 

As you can see from the table of contents posted on Amazon, the book consists of 114 Sections.  Each section reads like an essay, focusing on a particular idea.  The book is concerned with formulating field theories, and is excellent for graduate students and researchers in mechanics, especially those interested in creating new theories and computational methods.  I have requested our library to order a copy. 

Professor Wolfgang Knauss, of the California Institute of Technology, is selected to receive the 2010 Timoshenko Medal.

I am writing on behalf of the Timoshenko Medal Committee: Zhigang Suo (Chair), Tayfun E. Tezduyar, Ares J. Rosakis, Kenneth M. Liechti, Lawrence A. Bergman, Daniel J. Inman, Krishnaswamy Ravi-Chandar, Thomas N. Farris, Wing Kam Liu, Mary C. Boyce, Sia Nemat-Nasser, Thomas Hughes, Ken Johnson, Grigory Barenblatt, Morton Gurtin.

Professor Nicolas Triantafyllidis, of Ecole Polytechnique and the University of Michigan, is selected to receive the 2010 Warner T. Koiter Medal.

I am writing on behalf of the Warner T. Koiter Medal Committee: Zhigang Suo (Chair), Tayfun E. Tezduyar, Ares J. Rosakis, Kenneth M. Liechti, Lawrence A. Bergman, Daniel J. Inman, Krishnaswamy Ravi-Chandar, Thomas N. Farris, Wing Kam Liu, Mary C. Boyce, Richard James, C.T. Sun, Pierre Suquet, Ray Ogden, Zenon Mroz.

Professor Rohan Abeyaratne, of Massachusetts Institute of Technology, is selected to receive the 2010 Daniel C. Drucker Medal.

I am writing on behalf of the Daniel C. Drucker Medal Committee: Zhigang Suo (Chair), Tayfun E. Tezduyar, Ares J. Rosakis, Kenneth M. Liechti, Lawrence A. Bergman, Daniel J. Inman, Krishnaswamy Ravi-Chandar, Thomas N. Farris, Wing Kam Liu, Mary C. Boyce, Thomas C.T. Ting, Albert Kobayyashi, Alan Needleman, Robert Taylor, Franck A. McClintock.

A body consists of two materials bonded at an interface. On the interface there is a crack. The body is subject to a load, causing the two faces of the crack to open and slide relative to each other. When the load reaches a critical level, the crack either extends along the interface, or kinks out of the interface.

Due in class, Tuesday, 4 May 2010

A crack pre-exists in a body. When the body is loaded, the two faces of the crack may simultaneously open and slide relative to each other. The crack is said to be under a mixed-mode condition. When the load reaches a critical level, the crack starts to grow, and usually kinks into a new direction. Subsequently the crack often grows along a curved path.

This lecture discusses the critical condition to initiate the growth, the direction of the kink, and the method to predict the curved path.

Due in class, Thursday, 22 April 2010

Lecture 1 introduced the crack bridging model. The model is also known as the cohesive-zone model, the Barenblatt model, or the Dugdale model. The model consists of two main ingredients:

Due in class, Thursday, 15 April 2010

Following Griffith (1921), we distinguish two processes: deformation in the body and separation of the body. Up to this point, the process of deformation has been described by field theories of various kinds, such as

Lecture 1 described the Begley-Landes experiment, and the blunting of a crack due to large deformation. Lecture 2 is motivated by the following considerations.

When a rubber containing a crack is loaded, before the crack extends, strain everywhere in the rubber can be large. By contrast, when a metal containing a crack is loaded, before the crack extends, strain in the metal is typically small, except near the tip of the blunted crack. Consequently, to analyze deformation in the metal, at a distance a few times the crack opening displacement away from the crack tip, we can use the field theory of infinitesimal deformation.

Due in class, Thursday, 8 April 2010

Decouple elastic deformation of the body and inelastic process of separation. Up to this point we have been dealing with the following situation. When a load causes a crack to extend in a body, a large part of the body is elastic, and the inelastic process of separation occurs in a zone around the front of the crack. Inelastic process of separation includes, for example, breaking of atomic bonds, growth of voids, and hysteresis in deformation.

For a crack in an elastic body subject to a load, the elastic energy stored in the body is a function of two independent variables: the displacement of the load, and the area of the crack. The energy release rate is defined by the partial derivative of the elastic energy of the body with respect to the area of the crack.

This definition of the energy release rate assumes that the body is elastic, but invokes no field theory. Indeed, the energy release rate can be determined experimentally by measuring the load-displacement curves of identically loaded bodies with different areas of the cracks. No field need be measured.

Due in class, Thursday, 1 April 2010

Fracture mechanics without invoking any field theory. In Lecture 1 on Fracture of Rubber, we considered the extension of a crack in an elastic body subject to a load. Following Rivlin and Thomas (1953), we regarded the elastic energy stored in the body as a function of two independent variables: the displacement of the load, and the area of the crack. The partial derivative of the elastic energy with respect to the area of the crack defined the energy release rate.

A rubber band can be stretched several times its original length. This large deformation may hide its brittleness: the strain to rupture can be markedly reduced by the presence of a crack. This lecture describes fracture mechanic of highly deformable materials, such as rubbers and gels.

Demonstrate in class the effect of a crack on a rubber band. Use a wide rubber band. Show the class that the rubber band can be stretched several times its original length. Then use scissors to cut a crack into the rubber band. Pull the rubber band to rupture. Note that the strain to rupture is markedly reduced by the crack. Pass the scissors and some rubber bands around. Invite every student to try.

A glass may withstand a static load for a long time (days, weeks, or years) and then, without warning, breaks suddenly. Here are salient empirical observations:

• The delay time depends on the magnitude of the load: The smaller the load, the longer the delay time.
• The phenomenon is environment-sensitive. Glass suffers delayed fracture in moisture, but not in vacuum. The lower the humidity, the longer the delay time.
• The phenomenon is thermally-activated. The lower the temperature, the longer the delay time.

The phenomenon occurs to all materials to some degree in some environments. The phenomenon is known variously as

Due in class, Thursday, 11 March 2010

Required reading. P.C. Paris, M.P. Gomez and W.E. Anderson, A rational analytic theory of fatigue. The Trend in Engineering 13, 9-14 (1961). I went online and found that the Trend in Engineering is the alumni newsletter of the College of engineering, of the University of Washington.  I could not find this paper online. John Hutchinson offered to write to Paul Paris for a copy of the paper, which Paris sent by airmail. A scanned copy of the paper is attached with this lecture. 

Due in class, Thursday, 4 March 2010