On the superlinear convergence in computational elasto-plasticity

Sauter, Martin; Wieners, Christian

doi:10.1016/j.cma.2011.08.011

Cited by 24 publications

(25 citation statements)

References 35 publications

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“…The semismoothness of constitutive operators in elastoplasticity has been studied e.g. in . Namely in , one can find an abstract framework for how to investigate the semismoothness of operators in an implicit form.…”

Section: Preliminariesmentioning

confidence: 99%

Subdifferential‐based implicit return‐mapping operators in computational plasticity

et al. 2016

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The paper is devoted to the numerical solution of elastoplastic constitutive initial value problems. An improved form of the implicit return-mapping scheme for nonsmooth yield surfaces is proposed that systematically builds on a subdifferential formulation of the flow rule. The main advantage of this approach is that the treatment of singular points, such as apices or edges at which the flow direction is multivalued involves only a uniquely defined set of non-linear equations, similarly to smooth yield surfaces. This paper (PART I) is focused on isotropic models containing: a) yield surfaces with one or two apices (singular points) laying on the hydrostatic axis; b) plastic pseudo-potentials that are independent of the Lode angle; c) nonlinear isotropic hardening (optionally). It is shown that for some models the improved integration scheme also enables to a priori decide about a type of the return and investigate existence, uniqueness and semismoothness of discretized constitutive operators in implicit form. Further, the semismooth Newton method is introduced to solve incremental boundary-value problems. The paper also contains numerical examples related to slope stability with available Matlab implementation.

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Section: Preliminariesmentioning

confidence: 99%

Subdifferential‐based implicit return‐mapping operators in computational plasticity

et al. 2016

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“…There has been considerable progress in the analysis of return algorithms for models of classical plasticity. More recent work [70,161] has been based on results for semismooth Newton methods -by this approach the authors have been able to show superlinear convergence of the return mapping algorithm.…”

Section: Computation Of the Closest-point Projectionsmentioning

confidence: 99%

Plasticity

Han

Reddy

2013

Interdisciplinary Applied Mathematics

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“…There is a great deal of literature on such problems. The best and most efficient ways to deal with the plastic behavior are typically variants of Newton's method; see, for example, [17][18][19][20][21][22][23]. Recently, a total finite element tearing and interconnect (TFETI) domain decomposition solver was introduced in [24].…”

Section: Introductionmentioning

confidence: 99%

Efficient numerical methods for the large‐scale, parallel solution of elastoplastic contact problems

Frohne

Heister

Bangerth

2015

Numerical Meth Engineering

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Abstract. Elastoplastic contact problems with hardening are ubiquitous in industrial metal forming processes as well as many other areas. From a mathematical perspective, they are characterized by the difficulties of variational inequalities for both the plastic behavior as well as the contact problem. Computationally, they also often lead to very large problems. In this paper, we present and evaluate a set of methods that allows us to efficiently solve such problems. In particular, we use adaptive finite element meshes with linear and quadratic elements, a Newton linearization of the plasticity, active set methods for the contact problem, and multigrid-preconditioned linear solvers. Through a sequence of numerical experiments, we show the performance of these methods. This includes highly accurate solutions of a benchmark problem and scaling our methods to 1,024 cores and more than a billion unknowns.

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On the superlinear convergence in computational elasto-plasticity

Cited by 24 publications

References 35 publications

Subdifferential‐based implicit return‐mapping operators in computational plasticity

Subdifferential‐based implicit return‐mapping operators in computational plasticity

Plasticity

Efficient numerical methods for the large‐scale, parallel solution of elastoplastic contact problems

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