Efficient simulation of multi‐body contact problems on complex geometries: A flexible decomposition approach using constrained minimization

Dickopf, Thomas; Krause, Rolf

doi:10.1002/nme.2481

Cited by 46 publications

(35 citation statements)

References 41 publications

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“…Herein,

{bold-sans-serif I}_{3} \in R^{3 \times 3}

is the identity, and

χ_{h} : {normalγ}_{normalc, normalh}^{false(1 false)} \to {normalγ}_{normalc, normalh}^{false(2 false)}

represents a suitable discrete approximation of the mapping χ between the contact sides, see, eg, Dickopf and Krause and Puso for more details. Discretization of the nonpenetration constraint in yields the discrete gap function

{sans-serif g}_{⋆, j}

at each node j , ie,

g_{⋆, j} = {sans-serif g}_{normaln, normalh} = {bold-sans-serif n}_{j} ([], {\overset{x}{true}}^{false(2 false)} ((), x_{j}^{false(1 false)}) - {boldx}_{j}^{false(1 false)}) j = 1, ⋯, n_{⋆}^{false(1 false)} .

…”

Section: Contact Evaluationmentioning

confidence: 99%

A mortar finite element approach for point, line, and surface contact

Farah

Wall

Popp

2018

Numerical Meth Engineering

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Summary An approach for investigating finite deformation contact problems with frictional effects with a special emphasis on nonsmooth geometries such as sharp corners and edges is proposed in this contribution. The contact conditions are separately enforced for point contact, line contact, and surface contact by employing 3 different sets of Lagrange multipliers and, as far as possible, a variationally consistent discretization approach based on mortar finite element methods. The discrete unknowns due to the Lagrange multiplier approach are eliminated from the system of equations by employing so‐called dual or biorthogonal shape functions. For the combined algorithm, no transition parameters are required, and the decision between point contact, line contact, and surface contact is implicitly made by the variationally consistent framework. The algorithm is supported by a penalty regularization for the special scenario of nonparallel edge‐to‐edge contact. The robustness and applicability of the proposed algorithms are demonstrated with several numerical examples.

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“…Herein,

{bold-sans-serif I}_{3} \in R^{3 \times 3}

is the identity, and

χ_{h} : {normalγ}_{normalc, normalh}^{false(1 false)} \to {normalγ}_{normalc, normalh}^{false(2 false)}

{sans-serif g}_{⋆, j}

at each node j , ie,

g_{⋆, j} = {sans-serif g}_{normaln, normalh} = {bold-sans-serif n}_{j} ([], {\overset{x}{true}}^{false(2 false)} ((), x_{j}^{false(1 false)}) - {boldx}_{j}^{false(1 false)}) j = 1, ⋯, n_{⋆}^{false(1 false)} .

…”

Section: Contact Evaluationmentioning

confidence: 99%

A mortar finite element approach for point, line, and surface contact

Farah

Wall

Popp

2018

Numerical Meth Engineering

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“…Since our operator is based on a weak formulation of the transfer conditions with respect to the L 2 -scalar product, quadrature is necessary for assembling its algebraic representation. For a detailed description of the related data structures and methods we refer to [23], where a similar quadrature problem in the context of non-linear contact problems is treated.…”

Section: K Fackeldey and R Krausementioning

confidence: 99%

Multiscale coupling in function space—weak coupling between molecular dynamics and continuum mechanics

Fackeldey¹,

Krause²

2009

Numerical Meth Engineering

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SUMMARYWe present a function space-oriented coupling approach for the multiscale simulation of non-linear processes in mechanics using finite elements and molecular dynamics concurrently. The key idea is to construct a transfer operator between the different scales on the basis of weighted local averaging instead of using point wise taken values. The local weight functions are constructed by assigning a partition of unity to the molecular degrees of freedom (Shepard's approach). This allows for decomposing the micro scale displacements into a low-frequency and a high-frequency part by means of a weighted L 2 -projection. Numerical experiments illustrating the stabilizing effect of our coupling approach are given.

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“…The mortar approximation of contact conditions was used by many researchers including Puso [18], Puso and Laursen [19], Wriggers [25], Dickopf and Krause [3], and Chernov et al [2], and was enhanced into the e cient algorithms for contact problems as by Wohlmuth and Krause [24]. Wohlmuth [23] gave a comprehensive exposition of the variationally consistent mortar approximation of contact conditions and of the related solvers.…”

Section: Introductionmentioning

confidence: 98%

On Conditioning of Constraints Arising from Variationally Consistent Discretization of Contact Problems and Duality Based Solvers

Vlach

Dostál

Kozubek

2015

Computational Methods in Applied Mathematics

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Variationally consistent approximation of the non-penetration conditions and friction laws was introduced by Wohlmuth [23] as a powerful tool for the e ective discretization of contact problems. This approach is especially useful when the potential contact interface is large and curved or when non-matching grids are applied. The point of this note is to give bounds on the singular values of the constraint matrices arising from the variationally consistent approximation and to indicate their application in the analysis of the scalable duality based domain decomposition algorithms for the solution of multi-body contact problems [7]. The theoretical results are illustrated by numerical experiments.

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Efficient simulation of multi‐body contact problems on complex geometries: A flexible decomposition approach using constrained minimization

Cited by 46 publications

References 41 publications

A mortar finite element approach for point, line, and surface contact

A mortar finite element approach for point, line, and surface contact

Multiscale coupling in function space—weak coupling between molecular dynamics and continuum mechanics

On Conditioning of Constraints Arising from Variationally Consistent Discretization of Contact Problems and Duality Based Solvers

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