A study on equivalence of nonlinear energy dissipation between first-order computational homogenization (FOCH) and reduced-order homogenization (ROH) methods

Abstract

Nowadays, studies on the mechanism of macro-scopic nonlinear behavior of materials by accumulation of micro-scopic degradation are attracting more attention from researchers. Among numerous approaches, multiscale methods have been proved as powerful and practical approaches in predicting macro-scopic material status by averaging and homogenizing physical information from associated micro-scopic material behavior. Usually in mechanical problem, the stress, consistent material modulus, and possible material state variables are quantities in interest through the upscaling process. However, the energy-related quantities are not studied much. Some initiative work has been done in the early year including but not limited to the Hill–Mandel condition in multiscale framework, which gives that the macro-scopic elastic strain energy density can be computed by volumetric averaging of that in the micro-scale. However, in the nonlinear analysis, the energy dissipation is an important quantity to measure the degradation status. In this manuscript, two typical multiscale methods, the first-order computational homogenization (FOCH) and reduced-order homogenization (ROH), are adopted to numerically analyze a fiber-reinforced composite material with capability in material nonlinearity. With numerical experiments, it can be shown that energy dissipation is the same for both approaches.