Chapter 3: Defects
Overview
The first paper in this series, "Volterra dislocations in nonlinearly elastic bodies," deals with the definition and some elementary features of a generalization to finite deformations of Volterra dislocations. The second, "Twinning of crystals," is an exposition of twinning theory, as I then understood it. One thing discussed in "Thermoelastic considerations for continuously dislocated crystals" is what could be regarded as an antecedent of the X-ray theory or one interpretation of theory sometimes used by physicists. I found fault with it and discussed reasons for believing that Gibbs would have disliked it. Also, I discussed thermoelasticity theory, including the difficulty of defining entropy when changes in distributions of dislocations occur, and some thoughts about calculating forces on dislocations. Further, I discuss defining thermodynamic potentials when continuous distributions occur, but are not really changed by deformation. In different ways the subsequent two papers, "Some surface defects in unstressed thermoelastic solids" and "Stable equilibrium configurations of elastic crystals", cover elementary theory of twinning based on nonlinear elasticity theory and illustrative examples.
I then present in "On nonlinear elasticity theory for crystal defects" my thoughts on using nonlinear elasticity theory to treat dislocations in crystals. One thing discussed here is the possibility of having dislocations not of the Volterra or Somigliana kinds. Another is the desirability of better combining twinning theory with dislocation theory. Also, some common misconceptions are mentioned. One of the theories mentioned in the title of "On correlating two theories of twinning" is the X-ray theory that does not...