Blog posts

Rubber or rubber-like materials, or generally elastomers, sustain large elastic deformations. The problems of such cases are non-linear, the non-linearity came from two sources, the first one due to materials, and the second is geomertrical non-linearity. Elastomers are, also, viscoelastic, i.e. time and temperature dependent.

Recently I received a message from the Cambridge University Press regarding a coming text on biomechanics entitled Introductory Biomechanics, From Cells to Organisms. by C. Ross Ethier and Craig A. Simmonds. I ordered an exam copy, went through, and found it very interesting. It covers cellular biomechanics, hemodynamics, circulatory system, ocular biomechanics, muscles and movement, and skeletal biomechanics. Each section has a significant number of problems. I examined closely the part on cellular biomechanics which is one of the main areas of my research and teaching interests, and enjoyed reading it. The cellular mechanics is presented in its interrelation to cell structure and biology (there are nice images of cells and their components to use for teaching). The main techniques of probing the cell, such as micropipette aspiration, AFM, optical tweezers, and magnetic cytometry, are considered. Models of the cytoskeleton (tensergity, foams) are also introduced. The math is limited to linear equations, one-dimensional or axisymmetric problems, but it seems appropriate for the introductory level. In addition, some results of computational (finite element) modeling are also included. I certainly expect that this textbook will be quite useful in my teaching. The web site http://www.cambridge.org/us/catalogue/catalogue.asp?isbn=9780521841122 has more details on the book.

As another celebration of March Journal Club of Mechanics of Flexible Electronics, this paper has just been submitted.

Abstract 

In one design of flexible electronics, thin-film islands of a stiff material are fabricated on a polymeric substrate, and functional materials are grown on these islands. When the substrate is stretched, the deformation is mainly accommodated by the substrate, and the islands and functional materials experience relatively small strains. Experiments have shown that, however, for a given amount of stretch, the islands exceeding a certain size may delaminate from the substrate. We calculate the energy release rate using a combination of finite element method and complex variable method. Our results show that the energy release rate diminishes as the island size or substrate stiffness decreases. Consequently, the critical island size is large when the substrate is compliant. We also obtain an analytical expression for the energy release rate of debonding islands from a very compliant substrate.