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Gurtin, M. E.

Variational principles in the linear theory of viscoelasticity. (English) Zbl 0123.40803

Arch. Ration. Mech. Anal. 13, 179-191 (1963).
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mechanics of solids
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\textit{M. E. Gurtin}, Arch. Ration. Mech. Anal. 13, 179--191 (1963; Zbl 0123.40803)
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References:

[1] Sokolnikoff, I. S.: Mathemat ical Theory of Elasticity, Second Ed. New York: McGraw-Hill 1956. · Zbl 0070.41104
[2] Southwell, R. V.: Castigliano’s principle of minimum strain-energy. Proc. R. Soc. London, Ser. A154, 4 (1936). · JFM 62.0937.02
[3] Langhaar, H. L.: The principle of complementary energy in nonlinear elasticity theory. J. Franklin Inst.256, 16, 255 (1953).
[4] Dorn, W. S., & A.Schild: A converse of the virtual work theorem for deformable solids. Quart. Appl. Math.14, 2, 209 (1956). · Zbl 0074.19201
[5] Hellinger, E.: Die Allgemeinen Ansätze der Mechanik der Kontinua, in: Encyklopädie der Mathematischen Wissenschaften, 4, Part 4 (1914), 5, 654. · JFM 45.1012.01
[6] Reissner, E.: On a variational theorem in elasticity. J. Math. Phys.29, 2, 90 (1950). · Zbl 0039.40502
[7] Reissner, E.: On variational principles in elasticity, Proceedings of Symposia in Applied Mathematics, Vol. 8, Calculus of Variations and its Applications. New York: McGraw-Hill 1958. · Zbl 0168.22405
[8] Hai-chang, Hu: On some variational principles in the theory of elasticity and the theory of plasticity. Sc. Sinica4, 1, 33 (1955). · Zbl 0066.17903
[9] Washizu, K.: On the variational principles of elasticity and plasticity. Rept. 25-18, Cont. N 5ori-07833, Massachusetts Institute of Technology, March 1955. · Zbl 0064.37703
[10] Biot, M. A.: Variational and Lagrangian methods in visco-elasticity, in: Deformation and Flow of Solids. Berlin-Göttingen-Heidelberg: Springer 1955. · Zbl 0067.23603
[11] Freudenthal, A. M., & H.Geiringer: The mathematical theories of the inelastic continuum, in: Encyclopedia of Physics, Vol. 6. Berlin-Göttingen-Heidelberg: Springer 1958.
[12] Onat, E. T.: On a variational principle in linear viscoelasticity. J. Mec.1 2, 135 (1962). · Zbl 0113.17801
[13] Gurtin, M. E., & E.Sternberg: On the linear theory of viscoelasticity. Arch. Rational Mech. Anal.11, 291-356 (1962). · Zbl 0107.41007
[14] Kellogg, O. D.: Foundations of Potential Theory. Berlin: Springer 1929. · JFM 55.0282.01
[15] Rogers, T. G., & A. C.Pipkin: Asymmetric relaxation and compliance matrices in linear viscoelasticity. Rept. No. 83, Contract Nonr 562(10), Brown University, July 1962. To appear in Z. angew. Math. Mech. · Zbl 0125.13601
[16] Taylor, A. E.: Introduction to Functional Analysis. New York: John Wiley 1961. · Zbl 0104.42803
[17] Gurtin, M. E.: A generalization of the Beltrami stress functions in continuum mechanics. Rept. No. 20, Cont. Nonr 562(25), Brown University, April 1963. To appear in the Arch. Rational Mech. Anal. · Zbl 0203.26802
[18] Nielsen, J.: Elementare Mechanik. Berlin: Springer 1935. · JFM 61.1465.01
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