ARBITRARY LAGRANGIAN-EULERIAN FINITE-ELEMENT ANALYSIS OF STRAIN LOCALIZATION IN TRANSIENT PROBLEMS

Non-local models guaranty that finite element computations on strain s oftening materials remain sound up to failure from a theoretical and c omputational viewpoint. The non-locality prevents strain localization with zero global dissipation of energy,:and consequently finite elemen t calculations converge upon mesh refinements to non-zero width locali zation zones. One of the major drawbacks of these models is that the e lement size needed in order to capture the localization zone must be s maller than the internal length. Hence, the total number of degrees of freedom becomes rapidly prohibitive for most engineering applications and there is an obvious need for mesh adaptivity. This paper deals wi th the application of the arbitrary Lagrangian-Eulerian (ALE) formulat ion, well known in hydrodynamics and fluid-structure interaction probl ems, to transient strain localization in a non-local damageable materi al. It is shown that the ALE formulation which is employed in large bo undary motion problems can also be well suited for non-linear transien t analysis of softening materials where localization bands appear. The remeshing strategy is based on the equidistribution of an indicator t hat quantifies the interelement jump of a selected state variable. Two well known one-dimensional examples illustrate the capabilities of th is technique: the first one deals with localization due to a propagati ng wave in a bar, and the second one studies the wave propagation in a hollow sphere.