Approximation and numerical realization of 3D quasistatic contact problems with Coulomb friction

Haslinger, Jaroslav; Kučera, Radek; Vlach, Oldřich; Baniotopoulos, Charalampos

doi:10.1016/j.matcom.2011.01.004

Cited by 6 publications

(5 citation statements)

References 8 publications

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“…This proceeding extends the results of Haslinger et al [7] and [8] from unilateral 2D and 3D problems to multibody contact case. One can read more about the formulation for unilateral contact in [8,9].…”

Section: Introductionsupporting

confidence: 86%

“…One can read more about the formulation for unilateral contact in [8,9]. Our notation of the multibody case is similar to the prepared article [3] on transient problems.…”

Section: Introductionmentioning

confidence: 99%

“…Only the small change will appear in the nonsmooth friction term formulation which is in each timestep corrected from the previous timestep solution. For details see Haslinger et al [8]. The variational formulation of Coulomb friction is the implicit variational inequality due to the occurrence of the term λ N in the nonsmooth part of it.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Numerically and parallel scalable TFETI based algorithms for quasistatic contact problems of mechanics

Vlach¹,

́al²,

Kozubek³

et al. 2012

WIT Transactions on the Built Environment

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This paper deals with the solution of the discretized quasistatic 3D Signorini problems with local Coulomb friction. After a time discretization we obtain a system of static contact problems with Coulomb friction. Each of these problems is decomposed by the TFETI domain decomposition method used in auxiliary contact problems with Tresca friction. The algebraic formulation of these problems in 3D leads to the quadratic programing with equality constraints together with box and separable quadratic constraints. For the solution we used the scalable algorithm SMALSE developed at our department. The efficiency of the method is demonstrated by results of numerical experiments with parallel solution of 3D contact problems of elasticity.

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Section: Introductionsupporting

confidence: 86%

“…One can read more about the formulation for unilateral contact in [8,9]. Our notation of the multibody case is similar to the prepared article [3] on transient problems.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Numerically and parallel scalable TFETI based algorithms for quasistatic contact problems of mechanics

Vlach¹,

́al²,

Kozubek³

et al. 2012

WIT Transactions on the Built Environment

Self Cite

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“…In the latter case, the problem is still a box constrained QP since it contains only polyhedral constraints. In (Haslinger et al, 2012) the authors propose a successive approximation technique in 3D with the special solver of (Kučera, 2007(Kučera, , 2008 which is itself an extension to disk constraints of the Polyak method (conjugate gradient with active set on the bounds constraint) and its improvements (Dostál, 1997;Dostál and Schöberl, 2005). Other improvements of the method may be found in (Dostál and Kučera, 2010) with a last improvement of the method in (Dostál and Kozubek, 2012).…”

Section: Successive Approximation Methodsmentioning

confidence: 99%

On Solving Contact Problems with Coulomb Friction: Formulations and Numerical Comparisons

Acary¹,

Brémond²,

Huber³

2018

Advanced Topics in Nonsmooth Dynamics

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In this chapter, we review several formulations of the discrete frictional contact problem that arises in space and time discretized mechanical systems with unilateral contact and three-dimensional Coulomb's friction. Most of these formulations are well-known concepts in the optimization community, or more generally, in the mathematical programming community. To cite a few, the discrete frictional contact problem can be formulated as variational inequalities, generalized or semismooth equations, second-order cone complementarity problems, or as optimization problems such as quadratic programming problems over second-order cones. Thanks to these multiple formulations, various numerical methods emerge naturally for solving the problem. We review the main numerical techniques that are wellknown in the literature and we also propose new applications of methods such as the fixed point and extra-gradient methods with self-adaptive step rules for variational inequalities or the proximal point algorithm for generalized equations. All these numerical techniques are compared over a large set of test examples using performance profiles. One of the main conclusion is that there is no universal solver. Nevertheless, we are able to give some hints to choose a solver with respect to the main characteristics of the set of tests.

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“…to avoid working with the space H 1 / 2 ( Γ 2 ) defined by (see e.g. [30], [31], [32])…”

Section: Variational Formulationmentioning

confidence: 99%

A quasistatic frictional contact problem with normal compliance and unilateral constraint

Cǎpǎţînǎ

2016

Mathematics and Mechanics of Solids

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A mathematical model describing the quasistatic process of frictional contact between a nonlinearly elastic body and an elastic-rigid foundation is considered. The contact is modeled by normal compliance with unilateral constraint, and the friction by a slip-dependent version of Coulomb’s law. A weak formulation of the problem is derived and, under a smallness assumption on contact and friction functions, an existence result is proved by using incremental techniques, Kakutani’s fixed point theorem, and compactness, monotonicity, and lower semicontinuity arguments.

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Approximation and numerical realization of 3D quasistatic contact problems with Coulomb friction

Cited by 6 publications

References 8 publications

Numerically and parallel scalable TFETI based algorithms for quasistatic contact problems of mechanics

Numerically and parallel scalable TFETI based algorithms for quasistatic contact problems of mechanics

On Solving Contact Problems with Coulomb Friction: Formulations and Numerical Comparisons

A quasistatic frictional contact problem with normal compliance and unilateral constraint

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