CDM based modelling of damage and fracture mechanisms in concrete under tension and compression

Anisotropic damage evolution and crack propagation in the elastic–brittle materials is analysed by the concepts of continuum damage mechanics (CDM) and finite element method (FEM). The modified Murakami–Kamiya (MMK) model of elastic-damage material is used to describe damage anisotropy in concrete. The Helmholtz free energy representation is discussed. The unilateral crack opening/closure effect is incorporated in such a way that the continuity requirement during unloading holds. The incremental form of the stress–strain equations is developed. The general failure criterion is proposed by checking the positive definiteness of the Hessian matrix of the free energy function. The local approach to fracture (LAF) by FEM is applied to the pre-critical damage evolution that precedes the crack initiation, and the post-critical damage/fracture interaction. Crack is modelled as the assembly of failed finite elements in the mesh, the stiffness of which is reduced to zero when the critical points at stress–strain curves are reached. A concrete specimen with the pre-load, inclined crack is analysed in order to simulate different fracture mechanisms in tension or compression. The constitutive model is capable of predicting the kinked-type crack under tension and the wing-type crack under compression.