INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS Int. J. Numer. Anal. Meth. Geomech. 2004; 00:1–20Prepared using nagauth.cls [Version: 2002/09/18 v1.02] A new damage model based on nonlocal displacements Antonio Rodr´ ıguez-Ferran ∗ , Irene Morata and Antonio Huerta Laboratori de C`alcul Num` eric(LaC`aN) Edifici C2, Campus Nord, Universitat Polit` ecnica de Catalunya E-08034 Barcelona, Spain. e-mail:{antonio.rodriguez-ferran,irene.morata,antonio.huerta}@upc.es web page: www-lacan.upc.es key words: nonlocal damage models; nonlocal displacements; gradient models; consistent tangent matrix; quadratic convergence SUMMARY A new nonlocal damage model is presented. Nonlocality (of integral or gradient type) is incorporated into the model by means of nonlocal displacements. This contrasts with existing damage models, where a nonlocal strain or strain-related state variable is used. The new model is very attractive from a computational viewpoint, especially regarding the computation of the consistent tangent matrix needed to achieve quadratic convergence in Newton iterations. At the same time, its physical response is very similar to that of the standard models, including its regularization capabilities. All these aspects are discussed in detail and illustrated by means of numerical examples. Copyright c  2004 John Wiley & Sons, Ltd. 1. INTRODUCTION Nonlocal damage models are used to model failure of quasi-brittle materials [1]. Nonlocality –needed to correct the pathological mesh-dependence exhibited by local models– can be incorporated into the model in two different ways. In integral-type models [2, 3, 4], a nonlocal state variable is computed as the weighted average of the local state variable in a neighbourhood of the point under consideration. In gradient-type models [5], on the other hand, higher-order derivatives (typically second-order) are added to the partial differential equation that describes the evolution of the nonlocal variable. Both approaches yield similar results and are in some cases equivalent [6]. Apart from the state variable, other variables can be selected to incorporate nonlocality. Either scalar or tensorial quantities may be transformed into the corresponding nonlocal * Correspondence to: Antonio Rodr´ ıguez-Ferran, Departament de Matem`atica Aplicada III, E.T.S. d’Enginyers de Camins. Edifici C2, Campus Nord, Universitat Polit` ecnica de Catalunya. E-08034 Barcelona, Spain. Contract/grant sponsor: Ministerio de Educaci´on y Ciencia; contract/grant number: DPI2004-03000 Copyright c  2004 John Wiley & Sons, Ltd.