A constrained‐optimization methodology for the detection phase in contact mechanics simulations

Aragón, Alejandro M.; Yastrebov, Vladislav; Molinari, Jean‐François

doi:10.1002/nme.4561

Cited by 6 publications

(5 citation statements)

References 47 publications

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“…Nevertheless, even if the closest local minimum lies outside the feasible region, the current segment is then rejected and a new projection is sought in the next adjacent element segment. It should be noted that another approach formulating an optimization problem with inequality constraints can be found in Reference .…”

Section: Tested Methodsmentioning

confidence: 99%

Assessment of methods for computing the closest point projection, penetration, and gap functions in contact searching problems

Kopačka

Gabriel

Plešek

et al. 2015

Int. J. Numer. Meth. Engng

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Summary In computational contact mechanics problems, local searching requires calculation of the closest point projection of a contactor point onto a given target segment. It is generally supposed that the contact boundary is locally described by a convex region. However, because this assumption is not valid for a general curved segment of a three‐dimensional quadratic serendipity element, an iterative numerical procedure may not converge to the nearest local minimum. To this end, several unconstrained optimization methods are tested: the Newton–Raphson method, the least square projection, the sphere and torus approximation method, the steepest descent method, the Broyden method, the Broyden–Fletcher–Goldfarb–Shanno method, and the simplex method. The effectiveness and robustness of these methods are tested by means of a proposed benchmark problem. It is concluded that the Newton–Raphson method in conjunction with the simplex method significantly increases the robustness of the local contact search procedure of pure penalty contact methods, whereas the torus approximation method can be recommended for contact searching algorithms, which employ the Lagrange method or the augmented Lagrangian method. Copyright © 2015 John Wiley & Sons, Ltd.

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Section: Tested Methodsmentioning

confidence: 99%

Assessment of methods for computing the closest point projection, penetration, and gap functions in contact searching problems

Kopačka

Gabriel

Plešek

et al. 2015

Int. J. Numer. Meth. Engng

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“…As shown in Fig. 1, the location of mismatching mesh nodes can be directly determined along the interface g in mesh coupling problems, whereas for contact problems the closest node projection [1,92] to an element edge is used to determine the location of enriched nodes at either side of contact surfaces.…”

Section: The Finite-dimensional Interface-enriched Generalized Finite...mentioning

confidence: 99%

Section: Contactmentioning

confidence: 99%

An interface-enriched generalized finite element formulation for locking-free coupling of non-conforming discretizations and contact

et al. 2022

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We propose an enriched finite element formulation to address the computational modeling of contact problems and the coupling of non-conforming discretizations in the small deformation setting. The displacement field is augmented by enriched terms that are associated with generalized degrees of freedom collocated along non-conforming interfaces or contact surfaces. The enrichment strategy effectively produces an enriched node-to-node discretization that can be used with any constraint enforcement criterion; this is demonstrated with both multi-point constraints and Lagrange multipliers, the latter in a generalized Newton implementation where both primal and Lagrange multiplier fields are updated simultaneously. We show that the node-to-node enrichment ensures continuity of the displacement field—without locking—in mesh coupling problems, and that tractions are transferred accurately at contact interfaces without the need for stabilization. We also show the formulation is stable with respect to the condition number of the stiffness matrix by using a simple Jacobi-like diagonal preconditioner.

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“…In our implementation, a computational geometric engine creates enriched nodes along the non-conforming interfaces or along contact surfaces, so that each enriched node corresponds to a standard mesh node on the surface of the opposite domain. As shown in Figure 1, the location of mismatching mesh nodes can be directly determined along the interface Γ g in mesh coupling problems, whereas for contact problems the closest node projection [1,92] to an element edge is used to determine the location of enriched nodes at either side of contact surfaces.…”

Section: The Finite-dimensional Interface-enriched Generalized Finite...mentioning

confidence: 99%

“…We use a generalized Newton method to solve the nonlinear contact load increment following the procedure outlined in Algorithm 1 which is now described. At each load increment we create enriched nodes using the closest projection method [1,92] to determined their location (refer to Figure 3). Integration elements are created afterwards, similarly to the procedure just discussed for the coupling of non-conforming meshes.…”

Section: Contactmentioning

confidence: 99%

An interface-enriched generalized finite element formulation for locking-free coupling of non-conforming discretizations and contact

Liu¹,

Boom²,

Simone³

et al. 2021

Preprint

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We propose an enriched finite element formulation to address the computational modeling of contact problems and the coupling of non-conforming discretizations in the small deformation setting. The displacement field is augmented by enriched terms that are associated with generalized degrees of freedom collocated along non-conforming interfaces or contact surfaces. The enrichment strategy effectively produces an enriched node-to-node discretization that can be used with any constraint enforcement criterion; this is demonstrated with both multiple-point constraints and Lagrange multipliers, the latter in a generalized Newton implementation where both primal and Lagrange multiplier fields are updated simultaneously. The method's ability to ensure continuity of the displacement field-without locking-in mesh coupling problems, and to transfer fairly accurate tractions at contact interfaces-without the need for contact stabilization-is demonstrated by means of several examples. In addition, we show that the formulation is stable with respect to the condition number of the stiffness matrix by using a simple Jacobi-like diagonal preconditioner.

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A constrained‐optimization methodology for the detection phase in contact mechanics simulations

Cited by 6 publications

References 47 publications

Assessment of methods for computing the closest point projection, penetration, and gap functions in contact searching problems

Assessment of methods for computing the closest point projection, penetration, and gap functions in contact searching problems

An interface-enriched generalized finite element formulation for locking-free coupling of non-conforming discretizations and contact

An interface-enriched generalized finite element formulation for locking-free coupling of non-conforming discretizations and contact

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