Three‐dimensional finite element computations for frictional contact problems with non‐associated sliding rule

Abstract

International audienceThis paper presents an algorithm for solving anisotropic frictional contact problems where the sliding rule is non-associated. The algorithm is based on a variational formulation of the complex interface model that combine the classical unilateral contact law and an anisotropic friction model with a non-associated slip rule. Both the friction condition and the sliding potential are elliptical and have the same principal axes but with different semi-axes ratio. The frictional contact law and its inverse are derived from a single non-differentiable scalar-valued function, called a bi-potential. The convexity properties of the bi-potential permit to associate stationary principles with initial/boundary value problems. With the present formulation, the time-integration of the frictional contact law takes the form of a projection onto a convex set and only one predictor-corrector step addresses all cases (sticking, sliding, no-contact). A solution algorithm is presented and tested on a simple example that shows the strong influence of the slip rule on the frictional behaviour

Bi-First: A simple and efficient algorithm to identify dissipated energy in impact problems

“…We have felt that this approach could easily be extended to three-dimensional dynamic contact problems including nonlinear material constitutive laws and more complex frictional models [31]. This work is being undertaken.…”

Three-dimensional quasi-static frictional contact by using second-order cone linear complementarity problem

“…The present SOCLCP formulation has in common with the bi-potential formulation of de Saxcé and Feng [28] (see, also, Reference [29]) in the fact that the static variables and the modified kinematic variables belong, in both formulations, to mutually dual cones. The specificity of the SOCLCP formulation is that those cones are rewritten so that they are selfdual.…”

“…The specificity of the SOCLCP formulation is that those cones are rewritten so that they are selfdual. In what concerns the algorithms used to solve the problems obtained with these different formulations, Hjiaj et al [29] proposed the Uzawa algorithm (a single predictor-corrector step involving a projection onto the friction cone) to solve the bi-potential formulation, while, to solve the SOCLCP formulation, we use the method proposed by Hayashi et al [16] in which the complementarity condition and the inclusions in the second-order cones are rewritten as equations and a Newton method with the smoothing and regularization techniques is used.…”

“…Consider r t , r n , u t , n and t as variables. It should be emphasized that (i) the inequality constraints of (28) are convex; (ii) in the complementarity condition (29), 1 is linear with respect to r t , r n , n and t ; (iii) the stationary condition (30) is linear. From the view point of the Lagrangian, the 'nice' properties (i)-(iii) are achieved since L 1 defined by (26) is linear function with respect to (r t , r n , u t , ) at any point (r t , ) ∈ dom L 1 .…”

Modelling of Contact Between Stiff Bodies in Automotive Transmission Systems

“…Instantaneous contact formulations are often related to nonsmooth dynamic methods [1,13]. The discontinuities in the velocity field require the use of special integration methods [12,16,5]. For instance, event-driven approaches require the interruption of the time integration at each impact whereas time-stepping methods discretize in time the complete multibody system dynamics including the unilateral constraints and the impact forces.…”