An adaptive manifold- and discrete empirical interpolation method-based reduced order model for nonlinear solids

Abstract

Predicting the multiscale nonlinear behavior of heterogeneous materials is critical to many engineering fields but requires computationally intensive techniques such as Computational Homogenization (CH). Reduced Order Model (ROM) surrogates have been developed to address the demands of multiscale modeling, but most are limited to single-scale or linear behavior. To this end, we propose a novel form of ROM that bypasses the associated computational requirements of scale and nonlinearity. The ROM is constructed within a CH framework and reduces irreversible processes at the fine scale. Reduction of Partial Differential Equations (PDEs) for geometric nonlinearities is accomplished using a Manifold-based Nonlinear Reduced Order Model (MNROM) which can interpolate microscopic fields from principal components. Reduction of Ordinary Differential Equations (ODEs) for material nonlinearities is accomplished using the Adaptive Discrete Empirical Interpolation Method (ADEIM) with adaptive sampling, which can project evolving field data globally from a few locally modeled points. Both PDE and ODE schemes are joined together using operator splitting and scale transition relationships to tackle coupled problems. We demonstrate the coupled ROM by examining elastoviscoplastic behavior in a particulate composite with a nearly incompressible binder. This is done for a complex 2D microstructure over a large range of strains and plastic deformations.