Combined sticking: a new approach for finite-amplitude Coulomb frictional contact

Abstract

Engineering-level accuracy of discretization methods for frictional contact originates from precise representation of discontinuous frictional and normal interaction laws and precise discrete contact techniques. In terms of discontinuous behavior in the quasi-static case, two themes are of concern: the normal interaction (i.e. impact) and the jumps in tangential directions arising from high frictional values. In terms of normal behavior, we use a smoothed complementarity relation. For the tangential behavior, we propose a simple and effective algorithm, which is based a stick predictor followed by corrections to the tangential velocity. This allows problems with impact and stick-slip behavior to be solved with an implicit code based on Newton-Raphson iterations. Three worked examples are shown with comparisons with published results. An extension to node-to-face form in 3D is also presented.

Improved Gauss Seidel based projection–contraction algorithm for the mixed complementarity problem in contact problem

“…The frictional contact problem has always been a difficult point, and there are many studies based on this problem. [11][12][13][14][15][16] For the numerical model in the geological field, a series of difficulties are caused by the contact problem. Shi 6 invented the DDA to solve the contact problem of the block system in engineering.…”

“…The methods generally used to deal with contact problems include penalty function method, 7 Lagrange multiplier method, 8,9 nonsmooth Newton method, 10 projection–contraction algorithm (PCA), and so on. The frictional contact problem has always been a difficult point, and there are many studies based on this problem 11–16 …”