Strain-softening materials and finite-element solutions

Closed form and finite-element solutions are examined for several problems with strain-softening materials. In the closed form solutions, strain-softening causes localization of the strain which is accompanied by an instantaneous vanishing of the stress. The finite-element solutions agree closely with analytic solutions in many cases and exhibit a rate of convergence only slightly below that for linear problems. The main difficulty which has been identified in strain-softening constitutive models for damage is the absence of energy dissipation in the strain-softening domain, and this can be corrected by a nonlocal formulation. Finite-element solutions for the converging spherical wave problem exhibit multiple points of localization which change dramatically with mesh refinement. With a nonlocal material formulation, this pathology is eliminated.