On nonlocal coupling of damage and plasticity adopting integral theory

The effective stress concept was introduce by Kachanov to provide a phenomenological damage model for the isotropic case. Further in the early seventies a model of generalized standard elastoplastic material has been proposed by Halphen and Nguyen. In that model the flow rule is assigned by a normality rule to a generalized elastic domain defined in the product space of stresses and thermodynamic forces. The necessity for introducing the nonlocal or gradient theory stems from the well-known fact that the classical rate-independent plasticity or damage theories do not possess an intrinsic length scale (Voyiadjis et al., 2004). The aim of the paper is to formulate an nonlocal elastoplastic model coupled with strain damage in which the elastoplastic formulation as well as the stress decomposition of the nonlocal strain damage behaviour consistently follows from the thermodynamic analysis in a nonlocal integral context. The second objective of the paper is to derive a general thermodynamic framework which provides the tools to derive a consistent variational formulation for the nonlocal constitutive problem of elastoplasticity coupled with damage in the strain space. Accordingly the nonlocal counterpart of the Clausius–Duhem inequality is obtained and the maximum dissipation principle for the nonlocal coupled problem is obtained as a consequence of the model. From a computational point of view, an advantage of models with strain-based loading functions and explicit damage evolution laws is that the stress corresponding to a given strain can be evaluated directly without any need for solving a nonlinear system of equations (see e.g. Marotti de Sciarra, 2009).