Number of the records: 1

Efficient and flexible MATLAB implementation of 2D and 3D elastoplastic problems

SYSNO ASEP	0504439
Document Type	J - Journal Article
R&D Document Type	Journal Article
Subsidiary J	Článek ve WOS
Title	Efficient and flexible MATLAB implementation of 2D and 3D elastoplastic problems
Author(s)	Čermák, Martin (UGN-S) Sysala, Stanislav (UGN-S)_{RID, ORCID} Valdman, Jan (UTIA-B)_{RID, ORCID}
Number of authors	3
Source Title	Applied Mathematics and Computation. - : Elsevier - ISSN 0096-3003 Roč. 355, August 2019 (2019), s. 595-614
Number of pages	20 s.
Publication form	Online - E
Language	eng - English
Country	US - United States
Keywords	MATLAB code vectorization ; elastoplasticity ; finite element method ; tangential stiffness matrix ; semismooth Newton method
Subject RIV	BA - General Mathematics
OECD category	Applied mathematics
Subject RIV - cooperation	Institute of Information Theory and Automation - General Mathematics
R&D Projects	LQ1602 GA MŠMT - Ministry of Education, Youth and Sports (MEYS)
Method of publishing	Limited access
Institutional support	UGN-S - RVO:68145535 ; UTIA-B - RVO:67985556
UT WOS	000464930500044
EID SCOPUS	85063371842
DOI	10.1016/j.amc.2019.02.054
Annotation	Fully vectorized MATLAB implementation of various elastoplastic problems formulated in terms of displacement is considered. It is based on implicit time discretization, the finite element method and the semismooth Newton method. Each Newton iteration represents a linear system of equations with a tangent stiffness matrix. We propose a decomposition of this matrix consisting of three large sparse matrices representing the elastic stiffness operator, the strain-displacement operator, and the derivative of the stress-strain operator. The first two matrices are fixed and assembled once and only the third matrix needs to be updated in each iteration. Assembly times of the tangent stiffness matrices are linearly proportional to the number of plastic integration points in practical computations and never exceed the assembly time of the elastic stiffness matrix. MATLAB codes are available for download and provide complete finite element implementations in both 2D and 3D assuming von Mises and Drucker–Prager yield criteria. One can also choose several finite elements and numerical quadrature rules.
Workplace	Institute of Geonics
Contact	Lucie Gurková, lucie.gurkova@ugn.cas.cz, Tel.: 596 979 354
Year of Publishing	2020
Electronic address	https://www.sciencedirect.com/science/article/pii/S0096300319301584

Number of the records: 1