On vectorized MATLAB implementation of elastoplastic problems

0536400 - ÚTIA 2021 RIV US eng C - Conference Paper (international conference)
Čermák, Martin - Sysala, Stanislav - Valdman, Jan
On vectorized MATLAB implementation of elastoplastic problems.
AIP Conference Proceedings, Volume 2293, Issue 1 : INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2019. Melville: AIP Publishing, 2020, č. článku 330003. ISBN 978-0-7354-4025-8. ISSN 0094-243X.
[INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2019. Rhodos (GR), 23.09.2019-28.09.2019]
R&D Projects: GA ČR GA17-04301S; GA ČR(CZ) GA19-11441S
Grant - others:GA MŠk(CZ) LO1404
Institutional support: RVO:67985556 ; RVO:68145535
Keywords : MATLAB * tangent stiffness matrices * vectorizations
OECD category: Applied mathematics
http://library.utia.cas.cz/separaty/2020/MTR/valdman-0536400.pdf

We propose an effective and flexible way to assemble tangent stiffness matrices in MATLAB. Our technique is applied to elastoplastic problems formulated in terms of displacements and discretized by the finite element method. The tangent stiffness matrix is repeatedly assembled in each time step and in each iteration of the semismooth Newton method. We consider von Mises and Drucker-Prager yield criteria, linear and quadratic finite elements in two and three space dimensions. Our codes are vectorized and available for download. Comparisons with other available MATLAB codes show, that our technique is also efficient for purely elastic problems. In elastoplasticity, the assembly times are linearly proportional to the number of integration points.
Permanent Link: http://hdl.handle.net/11104/0314169