A gradient-damage theory for fracture of quasi-brittle materials

We present a gradient-damage theory for fracture of "quasi-brittle" materials under tensile dominated stress states. We develop our theory using the method of virtual-power. The macro- and microforce balances, obtained from the virtual power approach, together with a standard free-energy imbalance equation under isothermal conditions, when supplemented with a set of thermodynamically-consistent constitutive equations provide the governing equations for our theory. We have specialized our general theory to formulate a model for fracture of concrete - a quasi-brittle material of vast importance. We have numerically implemented our theory in a finite element program, and we present results from representative numerical calculations which show the ability of our simulation capability to reproduce the macroscopic load-deflection characteristics as well as crack-paths during failure of concrete in several technically relevant geometries reported in the literature. (C) 2019 Elsevier Ltd. All rights reserved.