Evaluation of the energy change due to presence of multiple irregularly shaped inclusions in hyperelastic solids

In this paper, an M_c-integral is presented for evaluation of the energy change due to presence of multiple irregularly shaped inclusions in 2-D hyperelastic solids. The integral is shown to be path-independent and so can be accurately evaluated by using finite elements. The formulation is considered to be feasible for problems subjected to large deformation. The energy change can be exactly evaluated by M_c when the hyperelastic solids are homogeneously stressed (i.e. the material characteristic), and effectively approximated when the solids are nonhomogeneously stressed (i.e. the structural characteristic). It is thus suggested that M_c be used as an energy parameter that quantitatively measures the change of material and/or structural integrity due to presence of the inclusions. The applicability of the proposed integral is illustrated by using it for identifying the associated effective material properties.