Variational modelling of diffused and localized damage with applications to fiber-reinforced concretes

Abstract

A variational model for the evolution of damage in elastic materials is proposed, which is based on incremental energy minimization. Analytical solutions are determined in the one-dimensional case of a tensile bar, and the issue of their stability is addressed. Analytical results have given insights into the properties that elastic and damage energies must have in order that specific evolution processes are captured, such as diffuse damaging, progressive damage localization or brutal failure. Accordingly, expressions of elastic and damage energies are proposed aimed at reproducing the evolution of damage observed in high-performance fiber-reinforced concretes, which typically exhibit initial micro-cracking and subsequent macro-crack opening. Tensile tests on bone-shaped samples and three-points bending tests are reproduced, by implementing the model in a finite element code, and numerical results are compared with experimental evidences.