Abstract

In this talk I assert that the usual interpretation of what one means by “elasticity” is much too insular and illustrate my thesis by introducing implicit constitutive theories that can describe the non-dissipative response of solids. I show that response which was hitherto untenable within the context of Cauchy or Green Elasticity are not only possible, they can explain phenomena that have thus far defied explanation. There is another important aspect to the introduction of such an implicit approach to the non-dissipative response of solids, namely the development of a hierarchy of approximations wherein, while the strains are infinitesimal or have a limiting value, the relationship between the stress and the linearized strain could be non-linear! Such approximations have been used but without a proper understanding of the basis for such theories (they would not be logically consistent within the context of explicit theories of Cauchy elasticity or Green elasticity).

Prof. K. R. Rajagopal is Distinguished Professor, Regents Professor and the Forsyth Chair in the Department of Mechanical Engineering at Texas A&M University. He is also a professor in the Department of Mathematics, the Department of Biomedical Engineering, the Zachry Department of Civil Engineering, and the Artie McFerrin Department of Chemical Engineering, and a senior research scientist for the Texas Transportation Institute. Prof. Rajagopal has been honoured internationally for his significant contributions to the world of continuum mechanics, computational mechanics, biomechanics and technology. Among these honours was his election to the international Hall of Fame for Engineering, Science and Technology. Rajagopal also has received patents for his continuum mechanics-related work in fields as divergent as biomechanics and granular material characterization to air brake control systems.