Frictionless 2D Contact formulations for finite deformations based on the mortar method

By K. Fischer, Peter Wriggers. 2005

231 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/a5ef70b04b50bc03134d305e7ff32af519d2dada

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In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Isogeometric contact: a review (2014, background): “Very similar characteristics are exhibited by more recently developed formulations based on the enforcement of the contact constraints at an arbitrary number of contact quadrature points located along the contact surface (Fischer and Wriggers 2005, 2006).”
A mortar method for energy‐momentum conserving schemes in frictionless dynamic contact problems (2009, background): “We refer to the books by Laursen [4] and Wriggers [5] for more background on the subject.”
Three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS (2012, methodology): “an exact evaluation of the surface integrals contributing to the weak formulation, combined with a discrete satisfaction of the continuous contact constraints through projected quantities [54,22,49,25,13,50,48,21,26,59].”
Segment-based vs. element-based integration for mortar methods in computational contact mechanics (2015, methodology): “The second method was firstly introduced in [10,11] and has been used in many different contact specific contributions since then, e.”
A large deformation frictional contact formulation using NURBS‐based isogeometric analysis (2011, methodology): “This section summarizes the theoretical and algorithmic background of the contact between two deformable bodies undergoing finite deformations, for more details see Laursen [16] and Wriggers [17].”
Isogeometric collocation: Neumann boundary conditions and contact (2015, unknown): “Among the most widely used contact formulations within the Galerkin framework, the node-to-surface (NTS) algorithm is known to fail the contact patch test, as the local enforcement of the nonpenetration condition at the slave nodes leads to local violation of the equilibrium of moments at the contac”
A mortar formulation for 3D large deformation contact using NURBS-based isogeometric analysis and the augmented Lagrangian method (2012, methodology): “For general discretizations this procedure will introduce an error, which can however be reduced by increasing the number of integration points on the contact surface, see also Fischer and Wriggers [13].”
On the contact domain method: A comparison of penalty and Lagrange multiplier implementations (2012, methodology): “However applications of Lagrange multiplier based formulations are widespread till date and they can be found in [5,10,20], to name a few.”
A formulation based on localized Lagrange multipliers for BEM–FEM coupling in contact problems (2008, methodology): “[9] solving frictionless large deformation contact problems using non-matching meshes and mortar methods, and the dual mortar method proposed by Wohlmuth [33] applied to 2D contact problems in elasticity by Flemish et al.”