Abstract
In this article a semi-smooth Newton method for frictional two-body contact problems and a solution algorithm for the resulting sequence of linear systems are presented. It is based on a mixed variational formulation of the problem and a discretization by finite elements of higher-order. General friction laws depending on the normal stresses and elasto-plastic material behavior with linear isotropic hardening are considered. Numerical results show the efficiency of the presented algorithm.
Highlights
Frictional, elasto-plastic multi-body contact problems play an important role in mechanical engineering [1,2,3].The nonlinearities caused by geometric contact and frictional constraints combined with the nonlinearity in the material law result in challenging numerical problems in forms of variational inequalities and efficient solving methods are needed
The nonlinear contact and frictional constraints as well as the elasto-plastic material behavior can be reformulated in terms of equations defined by semi-smooth functions and handled in one monolithic semi-smooth Newton method
A higher-order discretization is given in Section 3 whereas in Section 4 semi-smooth Newton methods for contact and general frictional constraints are developed for the described mixed finite elements
Summary
Frictional, elasto-plastic multi-body contact problems play an important role in mechanical engineering [1,2,3]. We transfer the approach of active-set strategies that have been developed for Mortar methods [9,10] to mixed finite elements introduced by Haslinger [28] and higher-order discretizations presented in [29,30]. In [30,31] a solution scheme for linear-elastic, frictional multi-body contact problems and higherorder discretizations is suggested It is based on the dual formulation of the discrete mixed variational formulation and leads to an optimization problem in the Lagrange multipliers. A higher-order discretization is given in Section 3 whereas in Section 4 semi-smooth Newton methods for contact and general frictional constraints are developed for the described mixed finite elements.
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