Transient three-dimensional contact problems: mortar method. Mixed methods and conserving integration

Abstract

The present work deals with the development of an energy-momentum conserving method to unilateral contact constraints and is a direct continuation of a previous work (Hesch and Betsch in Comput Mech 2011, doi:10.1007/ s00466-011-0597-2) dealing with the NTS method. In this work, we introduce the mortar method and a newly developed segmentation process for the consistent integration of the contact interface. For the application of the energy-momentum approach to mortar constraints, we extend an approach based on a mixed formulation to the segment definition of the mortar constraints. The enhanced numerical stability of the newly proposed discretization method will be shown in several examples.

Hierarchical NURBS and a higher-order phase-field approach to fracture for finite-deformation contact problems

“…which have to be assembled into the global system, see Hesch and Betsch [34,35] and the references therein. Moreover, the Jacobian of each segment is required…”

A Higher Order Phase-Field Approach to Fracture for Finite-Deformation Contact Problems

“…Herein, we restrict our consideration to the IGA case for the Lagrange discretized case we refer to the Mortar method given in [15]. In order to simplify the approach without violation of the required C 1 continuity of the primal space we use linear approximation of the dual space as has been proposed in [17,7].…”

“…For a more detailed explanation of the Mortar method, especially the technically demanding segmentation and the assembly see [14,15,17,7].…”

“…like the node-to-surface method, the variational consistent Mortar method has been wellestablished (see e.g. [31,15,30,36]). In a recent publication (see [7]) we applied the Mortar method for thermo-mechanical frictional contact problems.…”

An augmentation technique for large deformation frictional contact problems

“…Similar to these works, the spatial discretization of the contact surface used in the present work is based on the node-to-surface (NTS) method. The extension to more sophisticated models using mortar-based formulations [17][18][19][20][21][22] will be dealt with in a subsequent work.…”