An algorithm for the matrix-free solution of quasistatic frictional contact problems

A contact enforcement algorithm has been developed for matrix-free quasista tic finite element techniques. Matrix-free (iterative) solution algorithms such as non-linear conjugate gradients (CG) and dynamic relaxation (DR) are desirable for large solid mechanics applications where direct linear equat ion solving is prohibitively expensive, but in contrast to more traditional Newton-Raphson and quasi-Newton iteration strategies, the number of iterat ions required for convergence is typically of the same order as the number of degrees of freedom of the model. It is therefore crucial that each of th ese iterations be inexpensive to perform, which is of course the essence of a matrix free method. In applying such methods to contact problems we emph asize here two requirements: first, that the treatment of the contact shoul d not make an average equilibrium iteration considerably more expensive; an d second, that the contact constraints should be imposed in such a way that they do not introduce spurious energy that acts against the iterative solv er. These practical concerns are utilized to develop an iterative technique for accurate constraint enforcement that is suitable for non-linear conjug ate gradient and dynamic relaxation iterative schemes. Copyright (C) 1999 J ohn Wiley & Sons, Ltd.