Principles of stability analysis of ideal crystals

It is current practice to determine the "strength" profile of an ideal crystal by calculating the domain of homogeneous deformation in which the crystal is classically stable. This approach is here implemented in a less restricted manner than previously: first, by admitting any generalized coordinates to specify the strain; second, by assessing the stability in an arbitrary load environment. From this standpoint the intrinsic subjectivity of the usual concept of strength appears clearly. In illustration divergent estimates of uniaxial strength in the literature are compared within a common framework. With a view to rationalizing the whole approach, the present analysis gives prominence to the objective notion of coordinate invariance. Special "failure" modes, associated with path branchings at a domain perimeter, are also examined in this light. Finally, the stability of purely volumetric deformation is examined in detail.