Semi-smooth Newton methods for mixed FEM discretizations of higher-order for frictional, elasto-plastic two-body contact problems

Blum, H.; Frohne, H.; Frohne, Jörg; Rademacher, Andreas

doi:10.1016/j.cma.2016.06.004

Cited by 7 publications

(4 citation statements)

References 37 publications

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“…We want to emphasize that for standard thermo-mechanical mortar methods, e.g. [11], a similar simplification is made implicitly by using a node-wise decoupled active set strategy, although strictly speaking the variational inequality does not not allow for such a decoupled treatment in that case [54,55].…”

Section: Mortar Finite Element Discretization Of Thermo-mechanical Comentioning

confidence: 99%

A computational approach for thermo-elasto-plastic frictional contact based on a monolithic formulation using non-smooth nonlinear complementarity functions

Seitz

Wall

Popp

2018

Adv. Model. and Simul. in Eng. Sci.

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A new monolithic solution scheme for thermo-elasto-plasticity and thermo-elasto-plastic frictional contact with finite deformations and finite strains is presented. A key feature is the reformulation of all involved inequality constraints, namely those of Hill's orthotropic yield criterion as well as the normal and tangential contact constraints, in terms of non-smooth nonlinear complementarity functions. Using a consistent linearization, this system of equations can be solved with a non-smooth variant of Newton's method. A quadrature point-wise decoupled plastic constraint enforcement and the use of so-called dual basis functions in the mortar contact formulation allow for a condensation of all additionally introduced variables, thus resulting in an efficient formulation that contains discrete displacement and temperature degrees of freedom only, while, at the same time, an exact constraint enforcement is assured. Numerical examples from thermo-plasticity, thermo-elastic frictional contact and thermo-elasto-plastic frictional contact demonstrate the wide range of applications covered by the presented method.

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Section: Mortar Finite Element Discretization Of Thermo-mechanical Comentioning

confidence: 99%

A computational approach for thermo-elasto-plastic frictional contact based on a monolithic formulation using non-smooth nonlinear complementarity functions

Seitz

Wall

Popp

2018

Adv. Model. and Simul. in Eng. Sci.

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“…In analogy to mass lumping techniques, it can be interpreted as a form of lumping of the contact constraints [28]. For an exemplary formulation considering fully coupled constraints, see [33]. The assessment of the impact of the Petrov-Galerkin approach on the mathematical structure of the method would fall beyond the scope of the present work and, therefore, this topic is addressed from a practical perspective in the numerical investigations presented in Section 8.…”

Section: Tablementioning

confidence: 99%

An Efficient Contact Algorithm for Rigid/Deformable Interaction based on the Dual Mortar Method

Carvalho,

Carneiro,

Pires

et al. 2022

Preprint

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In a wide range of practical problems, such as forming operations and impact tests, assuming that one of the contacting bodies is rigid is an excellent approximation to the physical phenomenon. In this work, the well-established dual mortar method is adopted to enforce interface constraints in the finite deformation frictionless contact of rigid and deformable bodies. The efficiency of the nonlinear contact algorithm proposed here is based on two main contributions. Firstly, a variational formulation of the method using the so-called Petrov-Galerkin scheme is investigated, as it unlocks a significant simplification by removing the need to explicitly evaluate the dual basis functions. The corresponding first-order dual mortar interpolation is presented in detail. Particular focus is, then, placed on the extension for second-order interpolation by employing a piecewise linear interpolation scheme, which critically retains the geometrical information of the finite element mesh. Secondly, a new definition for the nodal orthonormal moving frame attached to each contact node is suggested. It reduces the geometrical coupling between the nodes and consequently decreases the stiffness matrix bandwidth. The proposed contributions decrease the computational complexity of dual mortar methods for rigid/deformable interaction, especially in the three-dimensional setting, while preserving accuracy and robustness.

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“…) is dependent solely on transformed displacements u. Multipliers λ i appear only implicitly as −ϑ in the description of Q. This is a big difference with respect to other approaches, where the semismooth Newton method for equations is applied to mixed primal-dual systems or purely dual systems using some NCP-functions, see, e.g., [32], [5], [27].…”

Section: Algebraic Form Of the Discrete Contact Problem With Coulomb ...mentioning

confidence: 99%

On the SCD semismooth* Newton method for generalized equations with application to a class of static contact problems with Coulomb friction

Gfrerer¹,

Mandlmayr²,

Outrata³

et al. 2022

Preprint

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In the paper, a variant of the semismooth * Newton method is developed for the numerical solution of generalized equations, in which the multi-valued part is a so-called SCD (subspace containing derivative) mapping. Under a rather mild regularity requirement, the method exhibits (locally) superlinear convergence behavior. From the main conceptual algorithm, two implementable variants are derived whose efficiency is tested via a generalized equation modeling a discretized static contact problem with Coulomb friction.

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Semi-smooth Newton methods for mixed FEM discretizations of higher-order for frictional, elasto-plastic two-body contact problems

Cited by 7 publications

References 37 publications

A computational approach for thermo-elasto-plastic frictional contact based on a monolithic formulation using non-smooth nonlinear complementarity functions

A computational approach for thermo-elasto-plastic frictional contact based on a monolithic formulation using non-smooth nonlinear complementarity functions

An Efficient Contact Algorithm for Rigid/Deformable Interaction based on the Dual Mortar Method

On the SCD semismooth* Newton method for generalized equations with application to a class of static contact problems with Coulomb friction

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