Scale-bridging with the extended/generalized finite element method for linear elastodynamics

TitleScale-bridging with the extended/generalized finite element method for linear elastodynamics
Publication TypeJournal Article
Year of Publication2021
AuthorsR Geelen, J Plews, and J Dolbow
JournalComputational Mechanics
Volume68
Start Page295
Issue2
Pagination295 - 310
Date Published08/2021
Abstract

This paper presents an extended/generalized finite element method for bridging scales in linear elastodynamics in the absence of scale separation. More precisely, the GFEMgl framework is expanded to enable the numerical solution of multiscale problems through the automated construction of specially-tailored shape functions, thereby enabling high-fidelity finite element modeling on simple, fixed finite element meshes. This introduces time-dependencies in the shape functions in that they are subject to continuous adaptation with time. The temporal aspects of the formulation are investigated by considering the Newmark-β time integration scheme, and the efficacy of mass lumping strategies is explored in an explicit time-stepping scheme. This method is demonstrated on representative wave propagation examples as well as a dynamic fracture problem to assess its accuracy and flexibility.

DOI10.1007/s00466-021-02032-2
Short TitleComputational Mechanics