Finite-amplitude Waves in Deformed Elastic Materials: Analytical Results and Energy Properties

The context of this book is the non linear elasticity theory. This theory accounts for the behaviour of elastic materials which can suffer large deformations, such as rubberlike materials, biological soft tissues,... This book deals with wave propagation in prestrained isotropic elastic materials. There is a vast literature about the incremental theory where the amplitude of the wave is assumed to be small, so that the theory is linearized about the prestrained state. There are much less results concerning waves of arbitrary amplitude, called finite-amplitude waves. Here, we present a set of analytical results about such finite-amplitude waves, with a detailed analysis of the properties of the associated energy fluxes. First, the basic equations of non linear elasticity are recalled. Then, waves in unbounded media are considered. Finally, a problem with boundaries is presented: a non linear Love surface wave is exhibited. This book should be useful for graduate students in applied mathematics, physics and mechanical engineering, and for Ph. D. students and researchers with interest in the non linear elasticity theory and its applications.