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Sawyers, Kenneth N.; Rivlin, Ronald S.

Some stability conditions for a compressible elastic material. (English) Zbl 0519.73035

Z. Angew. Math. Phys. 32, 255-266 (1981).
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MSC:

74H55 Stability of dynamical problems in solid mechanics
74B20 Nonlinear elasticity
74S30 Other numerical methods in solid mechanics (MSC2010)

Keywords:

two sets of restrictions on strain-energy function; compressible isotropic elastic material; necessary conditions for stability; rectangular block; finite pure homogeneous deformation; infinitesimal pure homogeneous deformation; arbitrary principal directions; incremental modulus; initial deformation; one pair of faces of block is force-free; superposed infinitesimal deformation; one of principal directions normal to these faces; principal extension ratio is unity
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References:

[1] R. S. Rivlin, J. Elasticity (in the press).
[2] M. Baker and J. L. Ericksen, J. Washington Acad. Sci.44, 25 (1951).
[3] J. L. Ericksen, J. Rat’l Mech. Anal.2, 141 (1953).
[4] K. N. Sawyers and R. S. Rivlin, Int. J. Solids Struct.9, 607 (1973). · Zbl 0264.73056 · doi:10.1016/0020-7683(73)90073-5
[5] K. N. Sawyers and R. S. Rivlin, Developments in mechanics (Proc. 13th Midwestern Mechanics Conference)7, 321 (1973).
[6] K. N. Sawyers and R. S. Rivlin, Z. Ang. Math. Phys.28, 1045 (1977). · Zbl 0371.73012 · doi:10.1007/BF01601672
[7] K. N. Sawyers and R. S. Rivlin, Meccanica13, 225 (1978). · Zbl 0417.73030 · doi:10.1007/BF02128388
[8] K. N. Sawyers and R. S. Rivlin, Z. Ang. Math. Phys.29, 245 (1978). · Zbl 0399.73035 · doi:10.1007/BF01601519
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