Subdifferential-based implicit return-mapping operators in computational plasticity

0465667 - ÚGN 2017 RIV DE eng J - Journal Article
Sysala, Stanislav - Čermák, Martin - Koudelka, T. - Kruis, J. - Zeman, J. - Blaheta, Radim
Subdifferential-based implicit return-mapping operators in computational plasticity.
ZAMM-Zeitschrift fur Angewandte Mathematik und Mechanik. Roč. 96, č. 11 (2016), s. 1318-1338. ISSN 0044-2267. E-ISSN 1521-4001
R&D Projects: GA MŠMT LQ1602; GA ČR GA13-18652S
Institutional support: RVO:68145535
Keywords : elastoplasticity * nonsmooth yield surface * multivalued flow direction * implicit return-mapping scheme * semismooth Newton method * limit analysis
Subject RIV: BA - General Mathematics
Impact factor: 1.332, year: 2016
http://onlinelibrary.wiley.com/doi/10.1002/zamm.201500305/full

In this paper we explore a numerical solution to elastoplastic constitutive initial value problems. An improved form of the implicit return-mapping scheme for nonsmooth yield surfaces is proposed that systematically builds upon a subdifferential formulation of the flow rule. The main advantage of this approach is that the treatment of singular points – apices or edges at which the flow direction is multivalued – only involves a uniquely defined set of non-linear equations, similarly to smooth yield surfaces. This paper focuses on isotropic models containing: a) yield surfaces with one or two apices (singular points) on the hydrostatic axis, b) plastic pseudo-potentials that are independent of the Lode angle, and c) possibly nonlinear isotropic hardening. We show that for some models the improved integration scheme also enables us to a priori decide about a type of the return and to investigate the existence, uniqueness, and semismoothness of discretized constitutive operators. The semismooth Newton method is also introduced for solving the incremental boundary-value problems. The paper contains numerical examples related to slope stability with publicly available Matlab implementations.
Permanent Link: http://hdl.handle.net/11104/0264115