An interior‐point algorithm for elastoplasticity

Krabbenhøft, K.; Lyamin, A. V.; Sloan, Scott W.; Wriggers, Peter

doi:10.1002/nme.1771

Cited by 119 publications

(133 citation statements)

References 71 publications

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“…For associated materials, it is possible to define a (global) minimization problem for which (2.11) are just the optimality conditions. Then, powerful methods from optimization are available, e.g., SQP methods (Wieners, 2007(Wieners, , 2008, interior point methods (Krabbenhoft, Lyamin, Sloan, and Wriggers, 2006), and augmented Lagrange methods (Sauter, 2010). For these methods, global convergence can be guaranteed.…”

Section: Discretization By the Finite Element Methodsmentioning

confidence: 99%

“…A specific feature of the Drucker-Prager model is the non-differentiability of the yield function at the boundary of the elastic domain. This is often seen as a drawback and we also consider a smoothed variant (Krabbenhoft et al, 2006;Miehe and Lambrecht, 1999), which renders the yield function smooth at the expense that it is no longer possible to write down the response function explicitly.…”

Section: Drucker-prager Plasticitymentioning

confidence: 99%

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On the superlinear convergence in computational elasto-plasticity

Sauter

Wieners

2011

Computer Methods in Applied Mechanics and Engineering

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We consider the convergence properties of return algorithms for a large class of rate-independent plasticity models. Based on recent results for semismooth functions, we can analyze these algorithms in the context of semismooth Newton methods guaranteeing local superlinear convergence. This recovers results for classical models but also extends to general hardening laws, multi-yield plasticity, and to several non-associated models. The superlinear convergence is also numerically shown for a large-scale parallel simulation of Drucker-Prager elasto-plasticity.

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Section: Discretization By the Finite Element Methodsmentioning

confidence: 99%

Section: Drucker-prager Plasticitymentioning

confidence: 99%

On the superlinear convergence in computational elasto-plasticity

Sauter

Wieners

2011

Computer Methods in Applied Mechanics and Engineering

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“…This was the basis of the mathematical programming approach to elasticplastic structural analysis pioneered by Maier and and coworkers (see, for example, [7,8]). More recently, Krabbenhoft et al [9] have developed an interior point algorithm for the incremental update of the structural state in elastic-plastic models. Variational update at the element level has been applied, for example, by Comi [10].…”

Section: Introductionmentioning

confidence: 99%

Numerical collapse simulation of large‐scale structural systems using an optimization‐based algorithm

Sivaselvan

Lavan

Dargush

et al. 2009

Earthq Engng Struct Dyn

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SUMMARYA new algorithm for nonlinear dynamic simulation of structures is presented. The algorithm is based on a mixed Lagrangian approach described by Sivaselvan and Reinhorn (J. Eng. Mech. (ASCE) 2006; 132(8):795-805). The algorithm developed in this paper is for the simulation of large-scale structural systems. The algorithm is applicable to a wide class of structural systems whose constituent material or component behavior can be derived from a stored energy function and a dissipation potential. The algorithm is based on the fact that for such systems, when using a certain class of time-discretization schemes to numerically compute the system response, the incremental problem of computing the system state at the next sample time knowing the current state and the input is one of convex minimization. As a result, the algorithm possesses excellent convergence characteristics. It is also applicable to geometric nonlinear problems. The implementation of the algorithm is described, and its applicability to the collapse analysis of large-scale structures is demonstrated through numerical examples.

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“…Since then, most 54 H. W. CHANDLER AND C. M. SANDS computational models have been developed by either ignoring the excessive dilation (e.g. [2]) or by specifying the yield surface and flow rule independently (e.g. [3]).…”

Section: Introductionmentioning

confidence: 99%

Including friction in the mathematics of classical plasticity

Chandler

Sands

2009

Num Anal Meth Geomechanics

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SUMMARYIn classical plasticity there are clear mathematical links between the dissipation function and the consequent yield function and flow rule. These links help to construct constitutive equations with the minimum of adjustable parameters. Modelling granular materials, however, requires that the dissipation function depends on the current stress state (frictional plasticity) and this changes the mathematical structurealtering the links and invalidating the associated flow rule. In this paper we show, for a large family of dissipation functions, how much of the structure remains intact when frictional dissipation is included. The surviving links are examined using straightforward physically based graphical insight and well-established mathematical techniques leading to a central result, which provides a mathematical justification for the procedural features of hyperplasticity. This should allow hyperplasticity to be used more widely and certainly with increased confidence.As an example of the effectiveness of the general method, two specific dissipation functions are constructed from the simple physical concepts of sliding friction and granule damage. One is based on a Drucker-Prager cone and the other a Matsuoka-Nakai cone, both incorporate kinematic hardening and a compactive cap. In each Case a single smooth yield function with consistent flow rules is produced. The computational usefulness of an inequality derived in the paper is demonstrated in the generation of the figures showing yield surfaces and flow directions by means of a simple maximization procedure.

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An interior‐point algorithm for elastoplasticity

Cited by 119 publications

References 71 publications

On the superlinear convergence in computational elasto-plasticity

On the superlinear convergence in computational elasto-plasticity

Numerical collapse simulation of large‐scale structural systems using an optimization‐based algorithm

Including friction in the mathematics of classical plasticity

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