A truly variationally consistent and symmetric mortar-based contact formulation for finite deformation solid mechanics

• Published in: Computer methods in applied mechanics and engineering Vol. 342; pp. 532 - 560
• Main Authors: Hiermeier, Michael, Wall, Wolfgang A., Popp, Alexander
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.12.2018; Elsevier BV
• Subjects: Angular momentum; Augmented Lagrangian; Contact; Contact problems; Deformation; Finite element analysis; Formulations; Lagrange multiplier; Linearization; Mortar; Mortars (material); Segment-to-segment; Solid mechanics; Solids; Variationally consistent; Segment-to-segment; Lagrange multiplier; Mortar; Variationally consistent; Augmented Lagrangian; Contact
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2018.07.020

In this work two mortar-based segment-to-segment contact formulations will be developed for the frictionless finite deformation case: While the first one is derived by consistent variation of all active contributions of a scalar-valued potential subject to inequality constraints, thus resulting in a truly variationally consistent and symmetric formulation, the second approach is designed in such a way that it is less computationally expensive, but still conserves important quantities such as linear and angular momentum. Since both formulations are derived side by side, the introduced simplifications and errors can be specifically analyzed and quantified. Based on a Lagrange multiplier approach the corresponding inequality constraint terms are introduced in two popular ways: Firstly, in form of a standard Lagrangian formulation and, secondly, via an augmented Lagrangian formulation. Both variational forms as well as both solution procedures will be consistently linearized and discussed. Finally, the obtained results will be compared to each other as well as to a well-established, yet slightly inconsistent, mortar-based contact formulation.