A study on the isothermal elastic response of inhomogeneous materials for certain classes of boundary value problems

Abstract

In this work, a systematic study of the solution to classes of boundary value problems when the body is inhomogeneous is undertaken. Within the framework of field theories, the non-linear equations, describing the isothermal elastic response of the material, are the focus of the study. In this framework, a material is considered to be inhomogeneous if the strain energy and/or density depends explicitly on position. For such a material, the possibility of homogeneous deformation and uniform stress fields is explored. Then, solution to boundary value problems corresponding to family one, two, three and four are extended to inhomogeneous materials whose strain energy depends explicitly only on a particular spatial coordinate. The study helped to identify the responses that are characteristic of inhomogeneous materials. This provides a means for identifying these materials. Next, the necessity to model inhomogeneous materials using inhomogeneous models is established. Finally, a few issues concerning the development of inhomogeneous models and experimental identification of these, is addressed.