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.
Finite-Amplitude Waves in Deformed Elastic Materials
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Description
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.
Written by physicist F. John, this book presents mathematical models for understanding the way materials deform under stress. It focuses in particular on isotropic materials, which exhibit the same...
The main goal of the book is a coherent treatment of the theory of propagation in materials of nonlinearly elastic waves of displacements, which corresponds to one modern line of development of the...
This meticulous and precise account of the theory of finite elasticity fills a significant gap in the literature. The book is concerned with the mathematical theory of non-linear elasticity, the...
Recent progress in the study of nonlinear wave propagation has been influenced by developments in mechanics, acoustics, hydro dynamics, plasma physics and many other fields of physics. This vast...
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