Finite-Amplitude Waves in Deformed Elastic Materials
Analytical results and energy properties
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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 a...
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.
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.
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