Gradient Elastodamage Model for Quasi-Brittle Materials with an Evolving Internal Length

The article presents a new approach based on a strain gradient damage constitutive law for modeling quasi-brittle materials such as concrete. The authors use a weak type nonlocal formulation of the problem, relying on Mindlin's Form II strain gradient elasticity theory. Gibbs free energy is used and the influence of the positive and negative principal strains to damage evolution is separated. Additional energy dissipation due to the gradient of the positive principal strains is introduced. The model requires an internal length, which is treated as an internal variable dependent on the level of damage. The study shows that the internal length increases with damage, corroborating available experimental results. Calibration of the gradient internal length evolution with damage is established through experimental data from two independent tests: a uniaxial tension or compression test to establish the evolution of damage, and a four-point bending (loading-unloading) test to relate the variation of the internal length with the accumulated level of damage. Anumerical analysis of the response of a concrete beamspecimen under four-point bending is presented to describe the calibration procedure. (C) 2014 American Society of Civil Engineers.