Tensorial continuum damage model for concrete

A tensorial continuum damage model for concrete which can correctly predict the failure stress states and failure modes in general multiaxial stress states is presented.The model is thermodynamically consistent and is based on proper expressions for the specific Gibbs free energy and the complementary form of the dissipation potential.Damaging of the material is described by a symmetric positive definite second order damage tensor.Invariant theory is used in construction of the potential functions which guarantees that the proper symmetry behaviour is satisfied and no artificial symmetrization operations need not to be done.The failure surface is formulated in a way that it mimics the behaviour of the well-known Ottosen's four parameter failure surface.The predictions of the proposed model are compared to the Concrete Damaged Plasticity (CDP) model available in the commercial finite element software Abaqus in uniaxial and equibiaxial cases.The CDP model is calibrated against the uniaxial test results.However, for the CDP model the strain in the loading direction in the biaxial case starts to deviate from the experimental results already before the peak stress, while the present model yields accurate prediction.The constitutive model is implemented as an UMAT subroutine to be used in Abaqus.