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

Journal Article (Journal Article)

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.

Full Text

Duke Authors

Cited Authors

  • Geelen, R; Plews, J; Dolbow, J

Published Date

  • August 1, 2021

Published In

Volume / Issue

  • 68 / 2

Start / End Page

  • 295 - 310

Electronic International Standard Serial Number (EISSN)

  • 1432-0924

International Standard Serial Number (ISSN)

  • 0178-7675

Digital Object Identifier (DOI)

  • 10.1007/s00466-021-02032-2

Citation Source

  • Scopus