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Existence and uniqueness of solutions for a dynamic one-dimensional damage model. (English) Zbl 0920.73328
Summary: We consider a one-dimensional dynamic model that describes the evolution of damage caused by tension in a viscoelastic material. The process is modeled by a coupled set of two differential inclusions for the elastic displacement and damage fields. We establish the existence of local weak solutions. The existence result is derived from a priori estimates obtained for a sequence of regularized, truncated, and time-retarded approximations. We also establish the existence of unique weak solution in a simplified version of the model. \(\copyright\) Academic Press.

74R99 Fracture and damage
74Hxx Dynamical problems in solid mechanics
35Q72 Other PDE from mechanics (MSC2000)
Full Text: DOI
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