Nonlinear programming approaches for an inverse problem in quasibrittle fracture

Characterization of the parameters describing the cohesive crack model is an important and difficult problem. Based on the availability of load-deflection data, obtained from such standard tests as the three-point bending and wedge splitting experiments, we formulate the required parameter identification as a special type of inverse problem. The formulation is in the form of a constrained optimization problem known as a mathematical program with equilibrium constraints characterized, in the present instance, by complementarity conditions involving the orthogonality of two sign-constrained vectors. Due to the difficulty of solving such a mathematical program directly, we investigate a number of numerical algorithms that are all based on solving a series of standard nonlinear programming problems. Computational results, using actual experimental data, are presented to compare the various schemes proposed.