A nonuniform transformation field analysis for composites with strength difference effects in elastoplasticity

Abstract

Many composites and their constituents exhibit strength difference (SD) effects. To reduce the computational cost associated to twoscale simulations, the theory of nonuniform transformation field analysis (NTFA, originally proposed by Michel and Suquet, 2003) is extended to consider a general case of SD effects in elastoplasticity, containing several well-known plasticity models like von Mises or Drucker and Prager as special cases. A space-time decomposition is done separately for volumetric and deviatoric inelastic strain fields, thus leading to two sets of plastic modes with different charateristics. Localization rules are deduced from superposition principles for the microscopic strain and stress fields, which are then homogenized to obtain the effective response. A coupled model governing the evolution of the resulting reduced variables is proposed based on some dissipative considerations. A convenient matrix formulation for an FE-based implementation is presented in detail. The proposed coupled model is shown to be exact for homogeneous cases and sufficiently accurate for three-dimensional heterogeneous microstructures. Finally, an efficient structural analysis is performed by using corresponding algorithmic consistent tangent operators.