THE STRESS DRIVEN INSTABILITY IN ELASTIC CRYSTALS - MATHEMATICAL-MODELS AND PHYSICAL MANIFESTATIONS

被引:171
作者
GRINFELD, MA
机构
[1] Department of Mathematics, Rutgers University, New Brunswick, 08903, NJ
关键词
STRESS DRIVEN INSTABILITY; ELASTICITY; PHASE TRANSFORMATIONS; VARIATIONAL PROBLEMS; NONLINEAR PDE WITH FREE BOUNDARIES; MATERIALS SCIENCE; FRACTURE; EPITAXY; CRYSTAL GROWTH; METALLURGY; LOW TEMPERATURE PHYSICS;
D O I
10.1007/BF02429859
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Equilibrium equations and stability conditions for the simple deformable elastic body are derived by means of considering a minimum of the static energy principle. The energy is supposed to be sum of the volume (elastic) and the surface terms. The ability to change relative positions of different material particles is taken into account, and appropriate natural definitions of the first and second variations of the energy are introduced and calculated explicitly. 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. Surface tension suppresses the mentioned instability with respect to sufficiently short disturbances of the boundary surface and thus can probably provide local smoothness of the equilibrium shape of the crystal. We derive explicit formulas for critical wavelength for the simplest models of the internal and surface energies and for the simplest equilibrium configurations. 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, materials science, fracture, physical chemistry, and low-temperature physics.
引用
收藏
页码:35 / 83
页数:49
相关论文
共 62 条
  • [11] Dacorogna, 1989, APPL MATH SCI, V78
  • [12] DAVINI C, 1986, ARCH RATION MECH AN, V96, P295
  • [13] ENIKOLOPIAN NS, 1988, DOKL AKAD NAUK SSSR+, V302, P630
  • [14] ENIKOLOPIAN NS, 1987, DOKL AKAD NAUK SSSR+, V292, P1165
  • [15] ENIKOLOPIAN NS, 1987, DOKL AKAD NAUK SSSR+, V293, P389
  • [16] FINNEY R, 1986, EQUILIBRIUM CAPILLAR
  • [17] FONSECA I, 1988, ARCH RATION MECH AN, V101, P63
  • [18] STRESS-CONCENTRATION AT SLIGHTLY UNDULATING SURFACES
    GAO, HJ
    [J]. JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 1991, 39 (04) : 443 - 458
  • [19] GIBBS JW, 1978, COLLECTED PAPERS JW
  • [20] GILMER GH, 1987, J METALS JUN