Spatiotemporally nonlocal homogenization method for viscoelastic porous metamaterial structures

Abstract

The underlying size-dependent mechanism of viscoelastic porous metamaterial structures is still unclear, and the solution to their response using the high-fidelity numerical method is time-consuming, even prohibitive. This paper explores how the size-dependent effect of metamaterial structures emerges from the underlying nonlocal interactions in metamaterial microstructures, and then develops an accurate but efficient homogenization method for analyzing their size-dependent and time-dependent mechanical behaviors of viscoelastic porous metamaterial structures. By accounting for the nonlocal interaction between different representative volume elements and the history-dependent effect, a spatiotemporally nonlocal discrete element model is developed to analyze the mechanical behavior of viscoelastic porous metamaterial structures. With the help of the spatiotemporally nonlocal discrete element model, a spatiotemporally nonlocal homogenization method is proposed to accurately yet efficiently assess the size-dependent mechanical behavior of the porous metamaterial structure. The remarkable potential of the spatiotemporally nonlocal homogenization method is illustrated by simulating the stress relaxation of a viscoelastic porous metamaterial structure under axial strain. Results indicate that the size-dependent phenomenon can be significant, and the spatiotemporally nonlocal homogenization model can efficiently capture the size-dependent relaxation stress evaluated by the high-fidelity finite element model without loss of accuracy.