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Stability of an elastic material. (English) Zbl 0789.73035

Ricci, Paolo Emilio (ed.), Actual problems in analysis and mathematical physics. Proceedings of the international symposium dedicated to Gaetano Fichera on the occasion of his 70th birthday, Taormina, Italy, 15-17 October, 1992. Roma: Dipartimento di Matematica, Università di Roma ”La Sapienza”, 201-226 (1993).
Summary: This paper, for the most part, reviews and modifies previous work on material stability by K. N. Sawyers and the author [Z. Angew. Math. Phys. 32, 255-266 (1981; Zbl 0519.73035)], L. Zee and E. Sternberg [Arch. Ration. Mech. Anal. 83, 53-90 (1983; Zbl 0553.73011)] and H. C. Simpson and S. J. Spector [Arch. Ration. Mech. Anal. 84, 55-68 (1983; Zbl 0526.73026)]. Some aspects of the concept of material stability are discussed. A basic criterion for material stability is proposed. The restrictions imposed on the strain-energy function for an isotropic elastic material, by the requirement that the incremental shear moduli in the homogeneously deformed material are to be positive, are derived, as well as the conditions for the velocities of propagation in it of plane waves of infinitesimal amplitude to be real.
For the entire collection see [Zbl 0786.00028].

MSC:

74G99 Equilibrium (steady-state) problems in solid mechanics
74H99 Dynamical problems in solid mechanics
74B99 Elastic materials
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