A yield‐limited Lagrange multiplier formulation for frictional contact

An analogy with rigid-plasticity is used to develop a constitutive framework for quasi-static frictional contact between finitely deforming solids. Within this setting, a Lagrange multiplier method is used to impose a sharp distinction between stick and slip. The scope of the multipliers is limited by a constitutivelydefined “yield” function and a finite element-based predictor-corrector scheme is employed to efficiently determine the regions of stick and slip and the associated tractions. Selected simulations of planar quasi-static problems are presented to validate the method and illustrate its capabilities.

[1]  Raymond D. Mindlin,et al.  Compliance of elastic bodies in contact , 1949 .

[2]  F. P. Bowden,et al.  Anisotropy of Friction in Crystals , 1964, Nature.

[3]  E. Rabinowicz,et al.  Friction and Wear of Materials , 1966 .

[4]  P. Panagiotopoulos,et al.  A nonlinear programming approach to the unilateral contact-, and friction-boundary value problem in the theory of elasticity , 1975 .

[5]  B. Fredriksson.  Finite element solution of surface nonlinearities in structural mechanics with special emphasis to contact and fracture mechanics problems , 1976 .

[6]  A. Curnier,et al.  A finite element method for a class of contact-impact problems , 1976 .

[7]  Z. Mroz,et al.  Associated and non-associated sliding rules in contact friction problems. , 1978 .

[8]  D. Play,et al.  An Attempt to Provide a Unified Treatment of Tribology Through Load Carrying Capacity, Transport, and Continuum Mechanics , 1980 .

[9]  N. Suh,et al.  The genesis of friction , 1981 .

[10]  A. Ruina.  Slip instability and state variable friction laws , 1983 .

[11]  A. Curnier.  A Theory of Friction , 1984 .

[12]  J. Casey.  On finitely deforming rigid-plastic materials , 1986 .

[13]  Witold Kosiński.  Field singularities and wave analysis in continuum mechanics , 1986 .

[14]  P. Alart,et al.  A generalized Newton method for contact problems with friction , 1988 .

[15]  Moon Hyuk Im.  Finite element analysis of frictional contact problems , 1989 .

[16]  P. Wriggers,et al.  FINITE ELEMENT FORMULATION OF LARGE DEFORMATION IMPACT-CONTACT PROBLEMS WITH FRICTION , 1990 .

[17]  R. Taylor,et al.  A mixed formulation for the finite element solution of contact problems , 1992 .

[18]  A. Klarbring,et al.  Solution of large displacement contact problems with friction using Newton's method for generalized equations , 1992 .

[19]  A. Curnier,et al.  Anisotropic dry friction between two orthotropic surfaces undergoing large displacements , 1993 .

[20]  J. C. Simo,et al.  A continuum-based finite element formulation for the implicit solution of multibody, large deformation-frictional contact problems , 1993 .

[21]  J. Casey.  A Treatment of Internally Constrained Materials , 1995 .

[22]  Tod A. Laursen,et al.  Energy consistent algorithms for frictional contact problems , 1998 .

[23]  Panayiotis Papadopoulos,et al.  A Lagrange multiplier method for the finite element solution of frictionless contact problems , 1998 .