Parameter identification of quasibrittle materials as a mathematical program with equilibrium constraints Original Research Article

The identification of the cohesive fracture parameters of quasibrittle materials forms the focus of the present work. This important and challenging task is formulated as an inverse problem, requiring the solution of a special type of constrained optimization problem known as a Mathematical Program with Equilibrium Constraints (MPEC), a key feature of which is the presence of complementarity conditions involving the orthogonality of two nonnegative vectors. We propose a simple scheme, based on transforming the MPEC into a standard nonlinear programming problem through appropriate smoothing of the complementarity constraints, for solving the parameter identification problem. Some computational results, using actual experimentally obtained data, are presented to assess the effectiveness of the approach.