Spherically symmetric deformation of solids with nonlinear stress-state-dependent properties.

Existing experimental data demonstrate a significant stress-state sensitivity of the properties for a wide class of solids, including metals, rocks, plastics, and other structural materials. Conventional parameters used to describe the material stress state are the stress triaxiality and the Lode angle. However, only dependence of the fracture criteria on the type of stress state is often considered. In the present paper, a version of constitutive relations is proposed which allow to describe the stress-state dependence of the material properties for the entire deformation process and thus to provide a more accurate approach to the estimation of the stress–strain state of solids. The proposed approach is exemplified with the solutions of various spherically symmetry problems for physically nonlinear solids. It can be noticed that the stress-state sensitivity taken into account may result in essential deviations of the solutions obtained from the predictions of the classical models. Although the constitutive relations are essentially nonlinear, in some particular cases, an analytic solution of the problem can be obtained. The approach discussed in this paper provides a relatively simple but realistic continuum model able to describe complicated deformation features of materials. [ABSTRACT FROM AUTHOR]