Modelling the response of elastic materials that are under stress #

Art Gower

14:10 Monday in 4Q05.

Part of the Solid mechanics session.

Abstract #

Typically in elasticity, the free energy W is considered to be a function of the strain of an elastic deformation W := W(F). However, to choose a strain energy, and write it out explicitly, we usually consider that the reference is stress free, or just assume that the material response is isotropic to deformations.

In this talk I will show how to model the free energy, and the stress, of a material that is already under stress. The key challenge here is that we do not know a stress free configuration to use as a reference. And without a stress free reference the form of the energy W becomes more complicated. Fortunately, a restriction called Initial Stress Reference Independence (ISRI) has to be satisfied which reduces the forms of the energy. Since its introduction, there has been some debate about ISRI, and its applications. In this talk I will clarify in a simple way the assumptions and consequences of ISRI.