Non-linear space-time elasticity

S. Schuss, Silke Glas, Hesch*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)
5 Downloads (Pure)

Abstract

In this contribution we introduce a novel space-time formulation for non-linear elasticity, able to calculate large deformations and displacements with high efficiency using structured and unstructured meshes in the space-time cylinder without changing the required regularity and thus, enabling the use of Lagrangian shape functions including tetrahedron and hypertetrahedron or tesseract elements. The common and indiscriminate treatment of spatial and temporal directions allows us to remove one of the major bottlenecks in parallel computations: The design of time-stepping schemes, which can neither been parallelized efficiently in time nor allow for local refinements as no information transfer backwards in time is possible. Moreover, stability of time-stepping schemes depend on the accumulation of local approximation errors in each time-step, in contrast to space-time formulation, characterized by enhanced stability and robustness. Eventually, we will demonstrate superiority in the convergence against classical time-stepping schemes using various examples including highly sensitive systems in the context of non-linear elasticity.
Original languageEnglish
Pages (from-to)1965-1990
Number of pages26
JournalInternational journal for numerical methods in engineering
Volume124
Issue number9
Early online date3 Jan 2023
DOIs
Publication statusPublished - 15 May 2023

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