Adaptation of the Microplane Constitutive Model for Brittle-Plastic Glassy Polymers

Abstract

This paper presents a microplane constitutive model for the tensile and compressive damaging behavior of brittle-plastic glassy polymers. The model is formulated and validated using experimental data on such polymers and is an adaptation of the previous microplane model formulation developed for concrete. The model considers a material point as a Gaussian approximation of a unit sphere, discretized into several “microplanes”. The macroscopic strain tensor is projected onto these microplanes yielding various micro-strain vectors. The various damage mechanisms such as tensile microcracking, shear microplasticity, and micro-crack friction are formulated in terms of the microplane level strain vectors, yielding corresponding stress vectors. These are then homogenized via the principle of virtual work yielding the macroscopic stress tensor. One of the salient features of the present adaptation includes a volumetric-deviatoric (V-D) split in the microplane level stresses and strains. This enables properly capturing a Poisson’s ratio greater than 0.25, which happens to be the case with most polymers. On the other hand, a normal stress comparison algorithm is implemented to alleviate the overestimation of stresses which can happen due to the V-D split. The proposed adaptation is validated using experimental data from uniaxial tension and compression tests on two different polymers, which includes post-peak inelastic behaviors such as hardening and softening or both. The model shows excellent agreement with the experimental data, demonstrating its ability and applicability to accurately capture the various damage mechanisms in brittle-plastic glassy polymers. The results presented here are at the material point level, and the application to structure level problems via a user material subroutine in a finite element software is in progress.