Reduced order homogenization models for failure of heterogeneous materials

Abstract

This dissertation presents a reduced order multiscale computational model for simulating failure and damage propagation in brittle composite materials. The model builds on the eigendeformation-based reduced order homogenization approach. The reduced order models (ROM) are obtained by (1) conducting an optimization study to identify the best ROM among all possible models within the model space, and (2) by devising a new strategy to efficiently identify reduced order models with excellent accuracy characteristics. The identification problem is first posed as an integer optimization problem to identify the optimal reduced order and the genetic algorithm method is used to evaluate the optimization problem. Numerical simulations conducted using unidirectionally reinforced microstructures reveal that the optimal reduced order models identified through this process accurately describe the response characteristics of the composite material for a wide range of loading conditions. The second approach investigated is the method of failure paths, in which the representative volume element (RVE) is subjected to various loading states until damage is induced on the microstructure and selecting the failure modes associated with the load states as the basis of the model reduction. To further reduce the computational cost these potential failure modes are allowed to overlap. Lastly, to alleviate the spurious post failure residual stresses observed and to improve the accuracy of the reduced order model, a novel `zero mode' impotent eigenstrains are incorporated into the constitutive framework. The zero mode eigenstrains successfully eliminate the spurious residuals with minimal added computational effort.