Microplane Constitutive Model for Tension–Compression Asymmetry and Pressure-Sensitive Damage in Polymers

Abstract

The multiaxial damage behavior of brittle polymers is highly complex, involving a stark tension–compression asymmetry and strong pressure sensitivity. These aspects are challenging to predict via phenomenological tensor-based damage models. Recognizing that these behaviors stem from various microscale damage mechanisms, this work presents a novel adaptation of the microplane constitutive model for these materials. The salient feature of the model is the semi-multiscale architecture consisting of “microplanes,” which are imagined planes of various orientations within the material microstructure. Various tensile and compressive damage mechanisms are formulated in terms of stress–strain vectors acting on these microplanes. The homogenized macroscale stress tensor is obtained via the principle of the virtual work. This multiscale arrangement allows simple, intuitive, and physically based formulations of microscale damage mechanisms as well as easy distinction of tension and compression. The mechanisms considered here include tensile microcracking, shear-driven plastic-frictional damage, and far postpeak compression hardening. The formulation involves splitting the volumetric and deviatoric components of stresses, which enables properly capturing Poisson ratios greater than 0.25. It also includes a normal strain dependence of the microplane strain limits governing frictional damage evolution. The model is calibrated and successfully validated against experimental data on several polymers under uniaxial tension, compression, and triaxial compression. The model is demonstrated to capture the tension–compression asymmetry of the inelastic behavior, as well as the pressure-sensitive nonlinear behavior under triaxial compression, in excellent agreement with experiments. Notably, the predictions under triaxial compression are found to outperform the Drucker Prager model, thus highlighting the superior potential of the microplane modeling approach for multiaxial damage in polymers.