A constitutive model based on the evolution and coalescence of elliptical micro-cracks for quasi-brittle materials

Damage and failure of quasi-brittle materials are caused by the evolution and coalescence of micro-cracks. To solve the problem of elliptical micro-crack growth at the elastic deformation stage, a method of complex potential functions is proposed and the effect of the initial orientation on micro-crack growth and deflection is discussed. The critical stress condition for the initial damage is derived according to the criterion of micro-crack growth. Based on energy conservation during wing-crack propagation, a damage constitutive model is developed with the strain criterion created in the condition of micro-crack coalescence. The stress-strain curves of quasi-brittle materials in uniaxial compression obtained based on this model are examined with the experimental results.