A CATASTROPHE-THEORY APPROACH TO FRACTURE-MECHANICS

A cohesive crack model is applied to analyze the crack stability in elastic-softening materials. The shape of the global load-displacement response changes substantially by varying size-scale and keeping the geometrical shape of the structure unchanged. The softening branch becomes steeper and when the size-scale increases. A critical size-scale does exist for which the softening slope is infinite. In such a case, the load carrying capacity drastically decreases for relatively small displacement increments. Then, for larger size-scales, the softening slope becomes positive and a cusp catastrophe appears. It is proved that such a bifurcation point can be revealed by the simple LEFM condition. © 1990 Kluwer Academic Publishers.