Algorithmic symmetrization of coulomb frictional problems using augmented lagrangians

A major drawback of most implicit algorithmic treatments of Coulomb frictional contact problems is the nonsymmetry of the algorithmic tangent operator, which emanates from the nonassociativity of the slip (flow) rule. Reliable algorithms leading to symmetric equation systems are highly desirable, especially in three-dimensional problems where the computational cost is dominated by equation solving. In this paper such an algorithm symmetrization is proposed. The method is derived from the augmented Lagrangian treatment of friction given by Simo and Laursen (Comput. & Structures 42 (1992) 97–116), and exploits the iterative nature of the classical method of multipliers. More specifically, symmetrization is achieved by a modified multiplier update scheme in which all nonassociativity is removed from the solution phase and placed in the multiplier update phase. The result is an algorithm involving only the solution of symmetric equations, which maintains the attributes of an augmented Lagrangian method.