Continuum Models for Phase Transitions and Twinning in Crystals: 1st Edition (Hardback) book cover

Continuum Models for Phase Transitions and Twinning in Crystals

1st Edition

By Mario Pitteri, G. Zanzotto

Chapman and Hall/CRC

392 pages | 45 B/W Illus.

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Hardback: 9780849303272
pub: 2002-06-27
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Description

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.

Reviews

"This text presents a comprehensive introduction into the thematic of solid-solid phase transformations. … includes a comprehensive index and an extensive list of references … that are ideal starting points for further reading."

- Mathematical Reviews, Issue 2004m

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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

About the Series

Applied Mathematics

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MAT003000
MATHEMATICS / Applied
SCI041000
SCIENCE / Mechanics / General
TEC021000
TECHNOLOGY & ENGINEERING / Material Science