Computationally efficient higher-order three-scale method for nonlocal gradient elasticity problems of heterogeneous structures with multiple spatial scales

Abstract

In this work, an innovative higher-order three-scale (HOTS) computational approach is developed, which can handle and simulate the nonlocal strain-stress gradient elasticity model of heterogeneous structures with multiple spatial scales. The significant characteristics of this study are: (i) the raw fourth-order nonlocal gradient elasticity equations with three-scale structural characteristics are decoupled as the new multi-scale second-order equations for reducing the continuity requirements for multi-scale computational method. (ii) a new micro-meso-macro coupled HOTS computational model for accurately analyzing the nonlocal gradient elasticity behaviors of heterogeneous structures with three-scale structural configurations is rigorously devised by virtue of multi-scale asymptotic analysis. (iii) the small-scale approximate performance of HOTS solutions is derived in the pointwise sense, that illustrates the crucial indispensability of establishing the HOTS solutions for capturing the micro-scale, meso-scale and macro-scale gradient elasticity behaviors of the heterogeneous structures accurately. (iv) the efficient three-scale numerical algorithm on the basis of finite element method (FEM) is presented at length. Finally, several numerical experiments are carried out to validate the applicability of the established HOTS computational methodology, presenting not only the excellent numerical accuracy, but also the advanced computational efficiency. This work provides a unified three-scale computational framework which enables the accurate analysis and efficient simulation of nonlocal strain-stress gradient elasticity problems of heterogeneous structures with multiple spatial scales, and provides a potential application for practical engineering computation.