Graded damage in quasi‐brittle solids
Nunziante Valoroso, Claude Stolz
Abstract
Abstract 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 so‐called nonlocal 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, that is, 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.