Computational modelling of gradient‐enhanced damage in quasi‐brittle materials

Abstract

To avoid the well-known drawbacks of the classical continuum damage theory when localization occurs, an isotropic gradient-enchanced damage model is proposed in which the loading function not only depends on the damage value, but also on its Laplacian. The initial boundary value problem obtained adopting this model is considered both in statics and in dynamics. In the dynamic context the finite-step problem is formulated according to a Newmark scheme; the constitutive law is integrated by the backward difference rule. An iterative procedure for the finite-step solution is discussed. Finite elements space discretization is carried out in terms of generalized variables on the basis of two variational principles pertinent to the two phases of the iterative process. One- and two-dimensional numerical tests show the regularizing effect of the gradient term and the effectiveness of the proposed discretization technique. Copyright © 1999 John Wiley & Sons, Ltd.