An anisotropic gradient damage model for quasi-brittle materials

An anisotropic continuum damage model based on the microplane concept is el aborated. Scalar damage laws are formulated on several individual microplan es representing the planes of potential failure. These uniaxial constitutiv e laws can be cast into a fourth-order damage formulation such that anisotr opy of the overall constitutive law is introduced in a natural fashion. Str ain gradients are incorporated in the constitutive equations in order to ac count for microstructural interaction. Consequently, the underlying boundar y value problem remains well-posed even in the softening regime. The gradie nt continuum enhancement results in a set of additional partial differentia l equations which are satisfied in a weak form. Additional nodal degrees of freedom are introduced which leads to a modified element formulation. The governing equations can be linearized consistently and solved within an inc remental-iterative Newton-Raphson solution procedure. The capability of the present model to properly simulate the localized failure of quasi-brittle materials will be demonstrated by means of several examples. (C) 2000 Elsev ier Science S.A. All rights reserved.