Structural failure prediction of quasi-brittle structures: Modeling and simulation

In order to avoid the loss of well-posedness in the post-localization range, some continuum damage theories introduce higher order gradients of the damage variable in the constitutive model. This paper discuss the possibility of structural failure prediction of quasi-brittle materials through a special kind of gradient-enhanced damage theory in which the material is considered to possess a substructure or microstructure. In these theories the microscopic movements are accounted for by the damage variable and a reformulation of the kinematics (to include the possible “micro-motions’’) and of some basic governing principles of the classical continuum mechanics is necessary. The theory allows an adequate description of the strain-softening and localization behavior due to the material degradation. Within this framework, a numerically predicted macro-crack is the set of points in the structure where the damage variable has reached its critical value. A simple numerical technique, based on the finite element method, is proposed to approximate the solution of the resulting nonlinear problem. The main features of such kind of approach are discussed through examples concerning macro-crack initiation and propagation in plates under different loading conditions.