Mesh objective tensile cracking via a local continuum damage model and a crack tracking technique

This paper describes a procedure for the solution of problems involving tensile cracking using the so-called smeared crack approach, that is, standard finite elements with continuous displacement fields and a standard local constitutive model with strain-softening. An isotropic Rankine damage model is considered. The softening modulus is adjusted according to the material fracture energy and the element size. The resulting continuum and discrete mechanical problems are analyzed and the question of predicting correctly the direction of crack propagation is deemed as the main difficulty to be overcome in the discrete problem. It is proposed to use a crack tracking technique to attain the desired stability and convergence properties of the corresponding formulation. Numerical examples show that the resulting procedure is well-posed, stable and remarkably robust; the results obtained do not seem to suffer from spurious mesh-size or mesh-bias dependence.