ALE analyses of localization in wave propagation problems

Abstract

The computational modelling of localization of deformation in cohesive-frictional materials must be carried out in a proper, accurate and efficient manner. A proper solution can be obtained by using an enriched material description such as a non-local damage model or Perzyna's viscoplasticity model. However, still a large number of finite elements is needed for an accurate description of the localization zone. To improve efficiency, mesh adaption is applied here by means of the Arbitrary Lagrangian–Eulerian (ALE) technique. The ALE technique must typically be applied in combination with an enriched material model. Otherwise, the use of a standard model gives a zero-width solution of the localization zone and therefore remeshing results in a continuing decrease of finite element size. Implementation of this method requires the addition of convective forces in the equations of motion, transport of the state variables and the formulation of a remeshing strategy. The remeshing strategy heavily determines the success of the ALE method. Three examples of wave propagation have been treated and it is shown that a suitable remeshing strategy in combination with an enriched material model leads to proper, accurate and efficient analyses of the localization process. © 1998 John Wiley & Sons. Ltd.