A thermodynamically motivated implicit gradient damage framework and its application to brick masonry cracking Original Research Article

A new gradient damage model is derived starting from thermodynamic statements. Nonstandard terms are added to the free energy potential for this purpose. In contrast with existing approaches, these terms are related to the kinematics of the problem and therefore come into play already in the elastic regime. Following the argument that the second law of thermodynamics need only be satisfied globally for a nonlocal continuum, an energy balance equation is derived which must be solved together with the usual equilibrium equations. Numerical solutions of this coupled set of equations have been generated for a one-dimensional problem in order to study the localisation behaviour of the new model. In the limit where the elastic modulus related to the energy balance goes to 0, an earlier gradient damage model is retrieved. This simplified model is used to study cracking of brick masonry under the influence of mechanical loading.