Validation of an interaction law for the Eshelby inclusion problem in elasto-viscoplasticity

The nonlinear Eshelby problem is considered for an elastic viscoplastic inclusion. An approximate solution has been proposed by [Molinari et al., 1997. On the self-consistent modelling of elastic–plastic behavior of polycrystals. Mech. Mater. 26, 43–62] who have postulated a simplified interaction law. With this interaction law, the average strain rate in the inclusion can be related to the far field loading prescribed in the matrix. In the present work, the matrix and the inclusion have elastic-viscoplastic behavior described by a nonlinear Maxwell law. Comparisons between predictions derived from the interaction law and finite element results are performed. It is observed that the approximate solution is in good agreement with numerical results as far as average strain rates and stresses are considered in the inclusion. Various inclusion shapes, material parameters and loading conditions are taken into account.