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One-dimensional models of damage. (English) Zbl 0915.73041
Summary: We consider two one-dimensional models for the evolution of the damage of an elastic material caused by compression or tension. Each model consists of a coupled set of differential inclusions for the elastic displacement and the damage fields. Both models decouple, and once the damage is found, the elastic deformations are obtained by quadrature. In the first problem damage is caused by tension only; in the second one by compression and by tension. We establish the existence and uniqueness of local weak solutions to both models. Moreover, we obtain lower and upper estimates on the solution existence time for the first problem. The existence of an upper bound indicates that such solutions may cease to exist in finite time, i.e., quench; physically the system snaps.

74R99 Fracture and damage
74B99 Elastic materials