STRAIN-SOFTENING MATERIALS AND FINITE ELEMENT SOLUTIONS.

Closed form and finite element solutions are reviewed 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, such as one which is reviewed here.