Microstructured Materials: Inverse Problems

The book presents a detailed treatment of the mathematical modelling and inverse problems of non-destructive evaluation (NDE) of spatially inhomogeneous microstructured materials using ultrasound measurements. The unique value of the book is a clear description of linear and nonlinear mathematical models derived for the modelling of propagation of ultrasonic deformation waves and then the solution of corresponding inverse problems to determine the physical parameters of models. The informative effects are related to nonlinearities on both macro- and micro-level and to dispersion. The goal is to build algorithms which would permit to determine parameters characterizing microstructure. For that not only the conventional harmonic waves are used but a novel concept based on using solitary waves in NDE is proposed. Uniqueness and stability of solutions is studied and numerical examples presented.