Inverse problem of inclusions of polynomial eigenstress

Abstract

Based on a geometric approach, the Markenscoff result [J. Elast. 49 163 (1998); J. Mech. Phys. Solids 46 2297 (1998)], that the shape classes of inclusions of constant eigenstrain and constant eigenstress form a 9-dimensional manifold, is extended to determine the class of shapes of inclusions of constant eigenstrain and eigenstress, which is a polynomial function. It is found that, in the case of linear stress dependence, it forms a 16-dimensional manifold in 3-D. The approach also allows for a possible numerical determination of the shape of the inclusion. In 2-D, the shape of the perturb domain, from a circle that maintains a linear stress dependence, is determined.