On the surface instability of elastic half spaces. (English) Zbl 0659.73045
We present some work on the surface instability of elastic half spaces. An analysis of surface instability of an incompressible half space under biaxial loading is summarized, and the critical condition for the onset of surface buckling is given. As an example in the case of compressible materials, the axisymmetric problem of surface instability for a half space made of standard material is analyzed and the dependence of buckling parameters on the material is revealed.
MSC:
74G60 | Bifurcation and buckling |
74B99 | Elastic materials |
74C99 | Plastic materials, materials of stress-rate and internal-variable type |
74D99 | Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials) |
References:
[1] | Brunelle, E. J., Surface instability due to initial compressive stress,Bulletm of the Seismological Society of America,63, 6 (1973), 1885–1893. |
[2] | Biot, M. A.,Mechanics of Incremental Deformations, Wiley (1965). |
[3] | Novozhiov, V. V.,Nonlinear Theory of Elasticity, Graylock (1953). |
[4] | Dorris, J. F. and S. Nemat-Nasser, Instability of a layer on a half space.J. Appl. Mech.,47 (1980), 304–312. · doi:10.1115/1.3153660 |
[5] | Cao Guang-zhong, Surface instability of an incompressible elastic half space – axisymmetric analysis,Journal of East China Engineering Institute. 1 (1984), 1–13. (in Chinese) |
[6] | Wu, C. H. and G.-Z. Cao, Buckling of an axially compressed incompressible half space,J. Struct. Mech.,11, 1 (1983), 37–48. |
[7] | Cao Guang-zhong, Surface instability of an incompressible elastic half space subjected to biaxial loading,Acta Mechanica Solida Sinica (in press). (in Chinese) |
[8] | Wu, C. H. and G.-Z. Cao, Buckling problems in finite plane elasticity – harmonic materials,Quart. Appl. Math.,41, 4 (1984), 461–474. · Zbl 0567.73055 |
[9] | Sensenig, C. B., Instability thick elastic solids,Comm. Pure Appl. Math.,17 (1964), 451–491. · Zbl 0127.15001 · doi:10.1002/cpa.3160170406 |
[10] | Wu, C. H., Plane-strain buckling of a crack in a harmonic solid subjected to crack-parallel compression.J. Appl. Mech.,46 (1979), 597–604. · Zbl 0414.73078 · doi:10.1115/1.3424613 |
[11] | Wu, C. H., Plane-strain backling of cracks in incompressible elastic solids,J. Elast.,10, 2 (1980), 163–177. · Zbl 0424.73039 · doi:10.1007/BF00044501 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.