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

• Published in: Computational mechanics Vol. 68; no. 2; pp. 295 - 310
• Main Authors: Geelen, Rudy, Plews, Julia, Dolbow, John
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2021; Springer; Springer Nature B.V
• Subjects: Analysis; Classical and Continuum Physics; Computational Science and Engineering; Elastodynamics; Engineering; extended/generalized finite element methods; Finite element analysis; Finite element method; Lumping; MATERIALS SCIENCE; Mathematical analysis; Methods; multiscale problems; Original Paper; phase-field; scale-bridging; Shape functions; Theoretical and Applied Mechanics; Time integration; time-dependent shape functions; transient dynamics; variational fracture modeling; Wave propagation; Scale-bridging; Time-dependent shape functions; Multiscale problems; Extended/generalized finite element methods; Phase-field; Transient dynamics; Variational fracture modeling
• ISSN: 0178-7675; 1432-0924
• DOI: 10.1007/s00466-021-02032-2

This paper presents an extended/generalized finite element method for bridging scales in linear elastodynamics in the absence of scale separation. More precisely, the GFEM gl 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.