New self-consistent approach for inelastic materials based on translated fields

Abstract

In real heterogeneous materials, the simultaneous presence of instantaneous mechanisms (elasticity) and time dependent ones (non linear visco-plasticity) leads to a complex space-time coupling between the mechanical fields, difficult to represent in a simple and efficient way. In this work, a new micro-macro model is proposed, starting from the integral equation and translated strain rate fields. The chosen translated field is the (compatible) viscoplastic strain rate of the (fictitious) viscoplastic heterogeneous medium submitted to a uniform (unknown) boundary condition. The self-consistency condition allows to define these boundary conditions so that a relative simple and compact strain rate concentration equation is obtained. The model is first applied to the case of a two-phase composite with isotropic, linear and incompressible visco-elastic properties. In that case, an exact self-consistent solution using the Laplace-Carson transform is available. The agreement between both approaches appears quite good. Results for elastic-viscoplastic FCC polycrystals are also presented and compared with those obtained from other models.