The paper deals with a viscous damage model including two damage variables, a local and a non-local one, which are coupled through a penalty term in the free energy functional. Under certain regularity conditions for linear elasticity equations, existence and uniqueness of the solution is proven, provided that the penalization parameter is chosen suciently large. Moreover, the regularity of the unique solution is investigated, in particular the dierentiability w.r.t. time.
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Christian Meyer, Livia Mihaela Susu, Analysis of a Viscous Two-Field Gradient Damage Model I: Existence and Uniqueness. Z. Anal. Anwend. 38 (2019), no. 3, pp. 249–286DOI 10.4171/ZAA/1637