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

0504439 - ÚGN 2020 RIV US eng J - Journal Article
Čermák, Martin - Sysala, Stanislav - Valdman, Jan
Efficient and flexible MATLAB implementation of 2D and 3D elastoplastic problems.
Applied Mathematics and Computation. Roč. 355, August 2019 (2019), s. 595-614. ISSN 0096-3003. E-ISSN 1873-5649
R&D Projects: GA MŠMT LQ1602
Institutional support: RVO:68145535 ; RVO:67985556
Keywords : MATLAB code vectorization * elastoplasticity * finite element method * tangential stiffness matrix * semismooth Newton method
OECD category: Applied mathematics; Applied mathematics (UTIA-B)
Impact factor: 3.472, year: 2019
Method of publishing: Limited access
https://www.sciencedirect.com/science/article/pii/S0096300319301584

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.
Permanent Link: http://hdl.handle.net/11104/0296072