Viscoelastic-viscoplastic polymer composites: Development and evaluation of two very dissimilar mean-field homogenization models

Abstract This paper deals with the micromechanical modeling of polymer composites with viscoelastic-viscoplastic (VE-VP) constituents. Two mean-field homogenization (MFH) models based on completely dissimilar theoretical approaches are extended from elasto-viscoplasticity (EVP) to VE-VP and assessed. The first approach is the incremental-secant method. It relies on a fictitious unloading of the composite at the beginning of each time step. Then, a thermoelastic-like Linear Comparison Composite (LCC) is constructed from the computed residual state directly in the time domain. The method provides naturally isotropic per-phase incremental-secant operators for isotropic VE-VP constituents. It takes into account both the first and the second statistical moment estimates of the equivalent stress micro-field. The second approach is the integral affine method. It starts by linearizing the rates of viscoplastic strain and internal variables. The linearized constitutive equations are then recast in a hereditary integral format to which the Laplace-Carson (L-C) transform is applied. A thermoelastic-like LCC is built in the L-C domain, where MFH is carried out. Finally, the composite’s response in the time domain is recovered by numerical inversions of L-C transforms. The method is able to overcome the issue of heterogeneous viscous stresses encountered by time domain MFH models. The two proposed MFH formulations are able to handle non-monotonic, non-proportional and multi-axial loading histories. Their accuracy was assessed against full-field finite element (FE) results for different microstructures and loadings. The computational cost of both methods is negligible compared to FE analyses. Overall, the incremental-secant approach is much simpler mathematically and numerically than the integral affine formulation, its accuracy ranges from acceptable to excellent, and important improvements can be expected in the future by controlling the virtual unloading time increment.