Material characterization and interfacial boundary identification by solving an inverse elasto statics boundary elements problem

An inverse geometry problem of identifying simultaneously two irregular interfacial boundaries along with the mechanical properties of the interface domain located between the components of multiple (three) connected regions is investigated. A discrete number of displacement measurements obtained from a uniaxial tension test are used as extra information to solve this inverse problem. A unique combination of global and local optimization method is used, that is, the imperialist competitive algorithm (ICA) to find the best initial guesses of the unknown parameters to be used by the local optimization methods, that is, the conjugate gradient method (CGM) and the simplex method (SM). The CGM and SM are used in series. The performance of these local optimization methods is dependents on the initial guesses of the unknown boundaries and the mechanical properties, that is, Poisson’s ratio and Young’s modulus, so ICA provides the best initial guesses. The boundary elements method is employed to solve the direct two-dimensional (2D) elastostatics problem. A fitness function, which is the summation of squared differences between measured and computed displacements at identical locations on the exterior boundary, is minimized. Several example problems are solved and the accuracy of the obtained results is discussed. The influence of the value of the material properties of the subregions and the effect of measurement errors on the estimation process are also addressed.