Identification of cohesive crack fracture parameters using mathematical programming - Que, Norbert S.
This thesis is concerned with the characterization of the parameters governing the tension-softening relations of the cohesive crack model. Parameters identification is an important area in fracture mechanics as it enables the use of a fracture model for the simulation of fracture processes in structure. Research, however, has shown that such a task is not trivial and continues to pose challenging problems to experimentalists and analysts alike. This dissertation presents general and efficient indirect methods for the characterization of mode I fracture parameters defining the cohesive crack model.
The identification problem is formulated as special type of inverse problem. The formulation is in the form of a constrained optimisation problem known as a mathematical program with equilibrium constraints characterised, in the present instance, by complementary conditions involving the orthogonality of two-sign constrained vectors. The solution of such a mathematical program is computationally challenging as it is disjunctive and nonconvex by nature. A number of nonlinear programming based approaches are proposed, after appropriate reformulation of the mathematical program as an equivalent nonlinear programming problem.
Actual experimental data are used to validate and determine the most suitable algorithm for parameter identification. It was found that the smoothing-based method is by far superior than other schemes. As the problem is nonconvex and the nonlinear program can only guarantee a local or stationary point, global optimisation procedures are introduced in order to verify the accuracy of the solutions obtained by the algorithm.
Two evolutionary search methods capable of finding the global optimum are implemented for parameter identification. The results generated by the evolutionary search techniques confirm the reliability of the solutions identified by the best nonlinear programming algorithm. All computations carried out in the thesis suggest the suitability and robustness of the selected algorithm for parameter identification.
Thesis (Ph.D. Civil and Environmental Engineering)--The University of New South Wales, Sydney, Australia.