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mechanics of solids
In the paper the llinear isothermal quasi-static theory of homogeneous and isotropic viscoelastic bodies with couple-stresses is established. The general representations of the linear hereditary laws both in an integral and differential form are given. Uniqueness of the mixed boundary-value problems is proved. The generalization of Betti's reciprocal theorem and that of Galerkin and Papkovich stress functions are obtained.
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[2] Mindlin R. D., Tiersten H. F.: Effects of couple-stresses in linear elasticity. Arch. Rat. Mech. Anal., 11, 5, 1962. DOI 10.1007/BF00253946 | MR 0144513
[3] Misicu M.: Theory of viscoelasticity with couple-stresses and some reductions to two-dimensional problem. Revue de Mécanique Appl. Acad. Rep. P. Roumaine, 8, 6, 1963. MR 0168199
[4] Koiter W. T.: Couple-stresses in the theory of elasticity. Proceedings Koninklijke Nederlandse Akad. van Wet, Ser. B, 67, 1, 1964. Zbl 0124.17405
[5] Doyle I. M.: On completness of stress functions in elasticity with couple-stresses. J. of Appl. Mech. (Trans. ASME), Ser. E, 4, 1964.
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