For strain-softening material models such as the ductile damage model of Chap. 18, the boundary value problem may become ill-posed and bifurcation might occur. As a consequence, finite element (FE) simulations involving such models are faced with problems of loss of uniqueness and strain localization. If localization occurs, the size of the region where the strains concentrate is determined by the mesh size and no convergence can be obtained with mesh refinement. In order to circumvent those difficulties, nonlocal or internal-length models have been proposed in the literature. In this chapter, we study the above-mentioned issues and give analytical and numerical examples, limiting ourselves to the small-strain case for simplicity.
KeywordsStrain Localization Uniaxial Tension Representative Volume Element Mesh Refinement Damage Variable
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