An incremental‐secant mean‐field homogenization model enhanced with a non‐associated pressure‐dependent plasticity model

This article introduces a, possibly damage-enhanced, pressure-dependent-based incremental-secant mean-field homogenization (MFH) scheme for two-phase composites. The incremental-secant formulation consists on a fictitious unloading of the material up to a stress-free state, in which a residual stress is attained in its phases. Then the secant method is performed in order to compute the mean stress fields of each phase. One of the main advantages of this method is the natural isotropicity of the secant tensors that allows defining the linear-comparison-composite (LCC). In this work, we show that this isotropic nature is preserved for a non-associated pressure dependent plastic flow, making possible the direct definition of the LCC. This model is thus able to represent the physics of real polymeric composites. The MFH scheme is then verified by testing its prediction capabilities in several cases, including cyclic and nonproportional loading involving perfectly elastic phases, elasto-plastic and damage-enhanced elasto-plastic phases in random representative volume elements (RVE) of uni-directional (UD) composites and of composites reinforced with spherical inclusions.