On a damage-plasticity approach to model concrete failure
  A damage-plasticity constitutive model for the description of fracture in plain concrete is presented. Two approaches, the local model comprising the adjustment of the softening modulus and the nonlocal model based on spatial averaging of history variables, are applied to the analysis of a concrete bar subjected to uniaxial tension and to a three-point bending test. The influence of mesh size and the decomposition into damage and plasticity components are discussed. It is shown that for the two examples studied, both approaches result in mesh-independent results. However, the nonlocal model, which relies on spatial averaging of history variables, exhibits sensitivity with respect to boundary conditions, which requires further studies. 
Peter Grassl