Reduced order variational multiscale enrichment method for elasto-viscoplastic problems

This manuscript presents the formulation and implementation of a novel reduced order variational multiscale enrichment (ROVME) method for elasto-viscoplastic problems. This method provides a hierarchical model order reduction technique based on the eigenstrain concept to approximate the fine scale response resolved at subdomains of interest. By eliminating the requirement of direct fine scale discretization, the computational effort associated with the variational multiscale enrichment (VME) method is significantly reduced. The model order reduction is achieved in the scale-coupled inelastic problem by automatically satisfying the microscale equilibrium state through the eigenstrain concept and coarse discretization of inelastic strain fields within the microscale domain. The inelastic material behavior is idealized with coupled Perzyna type viscoplasticity and flow stress evolution based on the Johnson-Cook model. Numerical verifications are performed to assess the capabilities of the proposed methodology, against the direct VME method with detailed fine scale resolutions. The verification results demonstrate high accuracy and computational efficiency of the reduced order VME framework for elasto-viscoplastic problems with material heterogeneity.