Numerical solution of some inverse problems in solid mechanics

This thesis develops numerical methods for solving two inverse problems in solid mechanics. The first problem determines unknown boundary tractions using measurements of internal displacement and is applicable to the analysis of metal forming processes. The second determines unknown elastic material properties and material interfaces using known boundary conditions and measurements of displacement; this is relevant to nondestructive testing. In both problems, static or quasi-static conditions are assumed. The solutions incorporate least squares matching of the measured displacements to those calculated with a mathematical model, along with techniques for stabilizing the solution.; Finite element methods are presented for solving the first inverse problem in two dimensions assuming elastic or elasto-viscoplastic material behavior. The calculated traction distribution is smoothed spatially using the regularization method or a polynomial approximation technique known as the keynode method. For elasto-viscoplastic behavior, the solution is also smoothed in time utilizing a variation of Beck's future time method.; The solution of the second inverse problem assumes that the domain is composed of several homogeneous, isotropic, elastic materials. Semi-analytical and spline approximation methods are derived for solving this problem in one dimension. In two dimensions, the special case of a domain containing a single, circular inclusion is considered. The objective is to determine the location and size of the inclusion as well as the Young's moduli of the inclusion and matrix materials. The solution procedure combines optimization, finite element analysis and automatic finite element mesh generation.