© 2011

Nonlinear Mechanics of Crystals

  • Appendices and tables present key information such as material coefficients for crystal classes

  • Extensive up-to-date bibliography (1901-2010)

  • Self-contained background on kinematics and thermomechanics


Part of the Solid Mechanics and Its Applications book series (SMIA, volume 177)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. John D. Clayton
    Pages 1-9
  3. John D. Clayton
    Pages 11-64
  4. John D. Clayton
    Pages 65-166
  5. John D. Clayton
    Pages 167-195
  6. John D. Clayton
    Pages 197-272
  7. John D. Clayton
    Pages 273-336
  8. John D. Clayton
    Pages 337-378
  9. John D. Clayton
    Pages 379-421
  10. John D. Clayton
    Pages 423-480
  11. John D. Clayton
    Pages 481-542
  12. Back Matter
    Pages 543-700

About this book


This book describes behavior of crystalline solids primarily via methods of modern continuum mechanics. Emphasis is given to geometrically nonlinear descriptions, i.e., finite deformations.

Primary topics include anisotropic crystal elasticity, plasticity, and methods for representing effects of defects in the solid on the material's mechanical response. Defects include crystal dislocations, point defects, twins, voids or pores, and micro-cracks. Thermoelastic, dielectric, and piezoelectric behaviors are addressed. Traditional and higher-order gradient theories of mechanical behavior of crystalline solids are discussed. Differential-geometric representations of kinematics of finite deformations and lattice defect distributions are presented. Multi-scale modeling concepts are described in the context of elastic and plastic material behavior. Representative substances towards which modeling techniques may be applied are single- and poly- crystalline metals and alloys, ceramics, and minerals.

This book is intended for use by scientists and engineers involved in advanced constitutive modeling of nonlinear mechanical behavior of solid crystalline materials. Knowledge of fundamentals of continuum mechanics and tensor calculus is a prerequisite for accessing much of the text. This book could be used as supplemental material for graduate courses on continuum mechanics, elasticity, plasticity, micromechanics, or dislocation mechanics, for students in various disciplines of engineering, materials science, applied mathematics, and condensed matter physics.


Crystals continuum mechanics lattice defects plasticity solid mechanics

Authors and affiliations

  1. 1., RDRL-WMP-BUS Army Research LaboratoryAberdeen Proving GroundUSA

Bibliographic information

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From the reviews:

“The book is a mathematical introduction to the thermodynamics of nonlinear mechanics of crystals and generally to continuum mechanics. … The book ends with references which are very large … . The book seems to be a very good work on the subject, and can be recommended to all those interested in the mechanics of crystals.” (N. D. Cristescu, Zentralblatt MATH, Vol. 1209, 2011)