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Online ISSN 1552-4485; Print ISSN 0033-569X
The linear theory of second-grade elastic materials
Author:
R. W. Lardner
Journal:
Quart. Appl. Math. 27 (1969), 323-334
DOI:
https://doi.org/10.1090/qam/99821
MathSciNet review:
QAM99821
Full-text PDF Free Access
Abstract | References | Additional Information
Abstract: Second-grade elastic materials have an energy density which depends on both first and second deformation gradients. The behaviour of these materials is investigated for deformations sufficiently small that the equations of motion can be linearized. The elastic materials with couple stress studied by Mindlin and Tiersten [1] are a special case of the materials studied here, and our results reduce to theirs with an appropriate choice for our elastic constants.
- R. D. Mindlin and H. F. Tiersten, Effects of couple-stresses in linear elasticity, Arch. Rational Mech. Anal. 11 (1962), 415–448. MR 144513, DOI https://doi.org/10.1007/BF00253946
- R. A. Toupin, Elastic materials with couple-stresses, Arch. Rational Mech. Anal. 11 (1962), 385–414. MR 144512, DOI https://doi.org/10.1007/BF00253945
- W. T. Koiter, On the dynamic boundary conditions in the theory of thin shells, Nederl. Akad. Wetensch. Proc. Ser. B 67 (1964), 117–126. MR 0165767
- Rokur\B{o} Muki and Eli Sternberg, The influence of couple-stresses on singular stress concentrations in elastic solids, Z. Angew. Math. Phys. 16 (1965), 611–648 (English, with German summary). MR 198747, DOI https://doi.org/10.1007/BF01590966
- R. A. Toupin, Theories of elasticity with couple-stress, Arch. Rational Mech. Anal. 17 (1964), 85–112. MR 169425, DOI https://doi.org/10.1007/BF00253050
Additional Information
Article copyright:
© Copyright 1969
American Mathematical Society