Graded damage in quasi‐brittle solids
Résumé
A novel approach to damage modeling for quasi-brittle solids is presented relying upon a differential inclusion that is closely related to the one of implicit gradient models. The proposed formulation naturally fits in the socalled non-local standard approach, whereby the framework of Generalized
Standard Materials is extended to include gradients of internal variables to account for the physics of the fracture phenomenon in a regularized sense, i.e. via extended constitutive equations in which a length scale parameter brings to the macro level information about material microstructure. This concept is fully embodied into the present approach to quasi-brittle fracture, whereby progressive damage occurs in layers of finite thickness where the gradient of damage is bounded and a fully damaged region is understood as a fracture with no ambiguity. Key to the effective implementation of the model are the choice of two constitutive functions and the implicit tracking of regions in a state of progressive damage via Lagrange multipliers acting on internal constraints. The ideas are developed for a general Cauchy continuum and representative numerical simulations are included that demonstrate the model capabilities.
Domaines
Mécanique [physics.med-ph]
Origine : Fichiers produits par l'(les) auteur(s)