Asymptotic numerical methods for unilateral contact

New algorithms based upon the asymptotic numerical method (ANM) are proposed to solve unilateral contact problems. ANM leads to a representation of a solution path in terms of series or Padé approximants. To get a smooth solution path, a hyperbolic relation between contact forces and clearance is introduced. Three key points are discussed: the influence of the regularization of the contact law, the discretization of the contact force by Lagrange multipliers and prediction–correction algorithms. Simple benchmarks are considered to evaluate the relevance of the proposed algorithms. Copyright 2006 John Wiley & Sons, Ltd