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Preface
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- By G.A. Maugin
- Gerard A. Maugin, Université de Paris VI (Pierre et Marie Curie)
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- Book:
- The Thermomechanics of Plasticity and Fracture
- Published online:
- 05 June 2012
- Print publication:
- 21 May 1992, pp xi-xiv
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Summary
The present book is an outgrowth of my lecture notes for a graduate course on ‘Plasticity and fracture’ delivered for the past five years to students in Theoretical Mechanics and Applied Mathematics at the Pierre-et-Marie Curie University in Paris. It also corresponds to notes prepared for an intensive course in modern plasticity to be included in a European graduate curriculum in Mechanics. It bears the imprint of a theoretician, but it should be of equal interest to practitioners willing to make an effort on the mathematical side. The prerequisites are standard and include classical (undergraduate) courses in applied analysis and Cartesian tensors, a basic course in continuum mechanics (elasticity and fluid mechanics), and some knowledge of the strength of materials (for exercises with a practical touch), of numerical methods, and of elementary thermodynamics. More sophisticated thermodynamics and elements of convex analysis, needed for a good understanding of the contents of the book, are recalled in Appendices.
The book deals specifically with what has become known as the mathematical theory of plasticity and fracture as (unduly) opposed to the physical theory of these fields. The first expression is reserved for qualifying the macroscopic, phenomenological approach which proposes equations abstracted from generally accepted experimental facts, studies the adequacy of the consequences drawn from these equations to those facts, cares for the mathematical soundness of these equations (do they have nice properties?), and then, with some confidence, provides useful tools to designers and engineers.
Solitons in Elastic Solids Exhibiting Phase Transitions
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- By G.A. Maugin
- Edited by R. J. Knops, A. A. Lacey
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- Book:
- Non-Classical Continuum Mechanics
- Published online:
- 11 May 2010
- Print publication:
- 24 September 1987, pp 272-283
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Summary
Abstract. Among elastic crystals which are subjected to phase transitions are those which represent so-called ferroic states. These are elastic ferroelectrics, elastic ferromagnets and ferroelastic crystals such as twinned shape-memory materials. In these three wide classes studied by the author and co-workers, the solitary waves which can be shown to exist and represent either moving domain walls or nuclei of transformations, are not true solitons since the interaction of two such waves always is accompanied by some linear radiation. This is a consequence of the very form of the governing systems of equations which may be of different types (e.g., sine-Gordon equation coupled to wave equations, modified Boussinesq equation) and are usually obtained either from a discrete lattice model or a rotationally invariant continuum model. For the sake of illustration the case of shape-memory materials is presented in greater detail through the first approach.
INTRODUCTION
Nearby, but below, the order-disorder phase-transition temperature, the dynamical equations that govern elastic crystals with a microstructure exhibit all the necessary, if not sufficient, properties (essentially, nonlinearity and dispersion with a possible compensation between the two effects) to allow for the propagation of so-called solitary waves. Whether these are true solitons or not is a question that can be answered only in each case through analysis and/or numerical simulations. These waves, however, are supposed to represent domain walls in motion. The latter are layers of relatively small thickness which carry a strong nonuniformity in a relevant parameter between two adjacent phases or degenerate ground states (see, e.g., Maugin and Pouget, 1986).