Overlapped-coupling between spherical discrete elements and micropolar finite elements in one dimension using a bridging-scale decomposition for statics

Abstract

Purpose – The purpose of this paper is to develop a concurrent multiscale computational method for granular materials in the quasi-static loading regime. Design/methodology/approach – Overlapped-coupling between a micropolar linear elastic one-dimensional (1D) mixed finite element (FE) model and a 1D chain of Hertzian nonlinear elastic, glued, discrete element (DE) spheres is presented. The 1D micropolar FEs and 1D chain of DEs are coupled using a bridging-scale decomposition for static analysis. Findings – It was found that an open-window DE domain may be coupled to a micropolar continuum FE domain via an overlapping region within the bridging-scale decomposition formulation for statics. Allowing the micropolar continuum FE energy in the overlapping region to contribute to the DE energy has a smoothing effect on the DE response, especially for the rotational degrees of freedom (dofs). Research limitations/implications – The paper focusses on 1D examples, with elastic, glued, DE spheres, and a linear elastic micropolar continuum implemented in 1D. Practical implications – A concurrent computational multiscale method for granular materials with open-window DE resolution of the large shearing region such as at the interface with a penetrometer skin, will allow more efficient computations by reducing the more costly DE domain calculations, but not at the expense of generating artificial boundary effects between the DE and FE domains. Originality/value – Open-window DE overlapped-coupling to FE continuum domain, accounting for rotational dofs in both DE and FE methods. Contribution of energy from micropolar FE in overlap region to underlying DE particle energy.