Model error estimation in surrogate models of failure for composite materials

Abstract

Failure theories in amorphous polymer utilize critical values of stress or strain invariants to determine the onset of damage. In polymer matrix fiber composite materials these theories have been extended to identify the location of failure. Some of these models use homogenization methods that render average values of stress and strain fields that do not represent the actual value of the fields neither in the fiber nor the matrix. The micromechanical enhancement method, MME, is able to approximate local values of strain fields to estimate failure location from homogenized strain fields by assuming a regular arrangement of fibers. In this work we study the error in the MME model in the determination of the critical strain invariants when compared to simulations that take explicitly into account non-regular fiber arrangements. Our results indicate the need to shift from deterministic simulations towards methods that quantify local variations of the microstructure such as fiber volume fraction distributions to determine the tails in the distribution of maximum strain invariant. Bayesian analysis shows that large variations in the fiber distribution have a negative impact in the MME model predictions.