Existence and Convergence Questions in Computational Modelling of Crack Growth in Brittle and Quasi-Brittle Materials

Computational modelling of the crack growth in brittle and quasi-brittle materials used in mechanical, civil, etc. engineering applies the cohesive zone model with various traction separation laws; determination of micro-mechanical parameters comes then from static tests, microscopic observation and numerical calibration. Although most authors refer to ill-possedness and need of artificial regularization in inverse problems (identification of material parameters), some difficulties originate even in nonlinear formulations of direct and sensitivity problems. This paper demonstrates the possibility of proper analysis of the existence of a weak solution and of the convergence of a corresponding numerical algorithm for such model problem, avoiding non-physical assumptions.