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The stress driven instability in elastic crystals: Mathematical models and physical manifestations. (English) Zbl 0843.73040
Equilibrium equations and stability conditions for the simple deformable elastic body are derived by means of considering a minimum of the static energy principle. Considering the case of negligible magnitude of the surface tension, we establish that an equilibrium state of a nonhydrostatically stressed simple elastic body (of any physically reasonable elastic energy potential and of any symmetry) possessing any small smooth part of free surface is always unstable with respect to relative transfer of the material particles along the surface. We also formulate the simplest problem of mathematical physics, revealing peculiarities and difficulties of the problem of equilibrium shape of elastic crystals, and discuss possible manifestations of the above-mentioned instability in the problems of crystal growth, material science, fracture, physical chemistry, and low-temperature physics.

##### MSC:
 74G99 Equilibrium (steady-state) problems in solid mechanics 74H99 Dynamical problems in solid mechanics 74B99 Elastic materials 82D25 Statistical mechanical studies of crystals 35R35 Free boundary problems for PDEs
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