Nonlocal models for damage and fracture: Comparison of approaches

The paper analyzes nonlocal constitutive models used in simulations of damage and fracture processes of quasibrittle materials. A number of nonlocal formulations found in the literature are classified according to the type of variable subjected to nonlocal averaging. Analytical and numerical solutions of a simple one-dimensional localization problem are presented. It is shown that some of the formulations inevitably lead to residual stresses even at very late stages of the deformation process and, consequently, they are not capable of modeling complete separation in a widely open macroscopic crack. The mechanisms leading to this specific type of stress locking are explained based on a theoretical analysis of the nonlocal constitutive equations. It is also pointed out that the nonlocal approach distorts the shape of the stress-strain diagram, which has to be taken into account when designing an appropriate local softening law. Q 1998 Elsevier Science Ltd. All rights reserved.