Continuum Models for Phase Transitions and Twinning in Crystals / Edition 1

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Overview

Continuum Models for Phase Transitions and Twinning in Crystals presents the fundamentals of a remarkably successful approach to crystal thermomechanics. Developed over the last two decades, it is based on the mathematical theory of nonlinear thermoelasticity, in which a new viewpoint on material symmetry, motivated by molecular theories, plays a central role.

This is the first organized presentation of a nonlinear elastic approach to twinning and displacive phase transition in crystalline solids. The authors develop geometry, kinematics, and energy invariance in crystals in strong connection and with the purpose of investigating the actual mechanical aspects of the phenomena, particularly in an elastostatics framework based on the minimization of a thermodynamic potential. Interesting for both mechanics and mathematical analysis, the new theory offers the possibility of investigating the formation of microstructures in materials undergoing martensitic phase transitions, such as shape-memory alloys.

Although phenomena such as twinning and phase transitions were once thought to fall outside the range of elastic models, research efforts in these areas have proved quite fruitful. Relevant to a variety of disciplines, including mathematical physics, continuum mechanics, and materials science, Continuum Models for Phase Transitions and Twinning in Crystals is your opportunity to explore these current research methods and topics.

Continuum Models for Phase Transitions and Twinning in Crystals presents the fundamentals of a remarkably successful approach to crystal thermomechanics. Developed over the last two decades, it is based on the mathematical theory of nonlinear thermoelasticity, in which a new viewpoint on material symmetry, motivated by molecular theories, plays a central role. This is the first organized presentation of a nonlinear elastic approach to twinning and displacive phase transition in crystalline solids. The authors develop geometry, kinematics, and energy invariance in crystals in strong connection and with the purpose of investigating the actual mechanical aspects of the phenomena, particularly in an elastostatics framework based on the minimization of a thermodynamic potential. Interesting for both mechanics and mathematical analysis, the new theory offers the possibility of investigating the formation of microstructures in materials undergoing martensitic phase transitions, such as shape-memory alloys.Although phenomena such as twinning and phase transitions were once thought to fall outside the range of elastic models, research efforts in these areas have proved quite fruitful. Relevant to a variety of disciplines, including mathematical physics, continuum mechanics, and materials science, Continuum Models for Phase Transitions and Twinning in Crystals is your opportunity to explore these current research methods and topics.

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Editorial Reviews

From The Critics
This book presents a model for crystal thermomechanics, based on the mathematical theory of nonlinear thermoelasticity. It treats the geometry, kinematics, and energy invariance in crystals, particularly in connection with an elastostatic framework based on the minimization of a thermodynamic potential. The book is of interest to those in a variety of disciplines ranging from continuum mechanics to variational calculus and materials science. Chapters cover areas including simple lattices, weak transformation neighborhoods and variants, energetics, bifurcation patterns, and microstructures. Pitteri is a professor and Zanzotto is a researcher in mechanics affiliated with the Department of Mathematical Methods and Models for Applied Sciences at the University of Padova, Italy. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780849303272
  • Publisher: Taylor & Francis
  • Publication date: 6/28/2002
  • Series: Applied Mathematics Series , #19
  • Edition number: 1
  • Pages: 392
  • Product dimensions: 6.30 (w) x 9.50 (h) x 1.04 (d)

Table of Contents

Introduction
Preliminaries
Simple Lattices
Weak-Transition Neighborhoods
Subgroups, Cosets and variants
Nonlinear Elasticity of Crystals
Bifurcation Patterns
Mechanical Twinning
Transformation Twins
Microstructures

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