DOI: 10.1007/bf00253942. On the linear theory of viscoelasticity

10.1007/bf00253942

Crossref journal-article

Springer Science and Business Media LLC

Archive for Rational Mechanics and Analysis (297)

Bibliography

Gurtin, M. E., & Sternberg, E. (1962). On the linear theory of viscoelasticity. Archive for Rational Mechanics and Analysis, 11(1), 291â356.

Authors 2

M. E. Gurtin (first)
Eli Sternberg (additional)

References 43 Referenced 431

Boltzmann, L.: Zur Theorie der elastischen Nachwirkung. Sitzungsberichte der Mathematisch-Naturwissenschaftlichen Classe der Kaiserlichen Akademie der Wissenschaften 70, 2, 275 (1874). / Sitzungsberichte der Mathematisch-Naturwissenschaftlichen Classe der Kaiserlichen Akademie der Wissenschaften by L. Boltzmann (1874)
Volterra, V.: Sulle equazioni integro-differenziali della teoria dell'elasticità. Atti della Reale Accademia dei Lincei 18, 2, 295 (1909). / Atti della Reale Accademia dei Lincei by V. Volterra (1909)
Gross, B.: Mathematical Structure of the Theories of Viscoelasticity. Paris: Hermann & Co. 1953. / Mathematical Structure of the Theories of Viscoelasticity by B. Gross (1953)
Staverman, A. J., & F. Schwarzl: Linear Deformation Behavior of High Polymers, Chapter 1 in: Die Physik der Hochpolymeren, edited by H. A. Stuart, Vol. 4. Berlin-Göttingen-Heidelberg: Springer 1956. / Die Physik der Hochpolymeren by A. J. Staverman (1956)
Freudenthal, A. M., & Hilda Geiringer: The Mathematical Theories of the Inelastic Continuum, in: Encyclopedia of Physics, edited by S. Flügge, Vol. 6. Berlin-Göttingen-Heidelberg: Springer 1958. / Encyclopedia of Physics by A. M. Freudenthal (1958)
Bland, D. R.: The Theory of Linear Viscoelasticity. New York: Pergamon Press 1960. / The Theory of Linear Viscoelasticity by D. R. Bland (1960)
Love, E. R.: Linear superposition in visco-elasticity and theories of delayed effects. Australian J. of Physics 9, 1, 1 (1956). (10.1071/PH560001) / Australian J. of Physics by E. R. Love (1956)
König, H., & J. Meixner: Lineare Systeme und lineare Transformationen. Mathematische Nachrichten 19, 256 (1958). (10.1002/mana.19580190122) / Mathematische Nachrichten by H. König (1958)
Biot, M. A.: Linear Thermodynamics and the Mechanics of Solids. Proceedings, Third U.S. National Congress of Applied Mechanics, The American Society of Mechanical Engineers, New York, 1958. / Proceedings, Third U.S. National Congress of Applied Mechanics by M. A. Biot (1958)
Coleman, B. D., & W. Noll: Foundations of linear viscoelasticity. Reviews of Modern Physics 33, 2, 239 (1961). (10.1103/RevModPhys.33.239) / Reviews of Modern Physics by B. D. Coleman (1961)
Alfrey, T.: Non-homogeneous stresses in visco-elastic media. Quarterly of Applied Mathematics 2, 2, 113 (1944). (10.1090/qam/10499) / Quarterly of Applied Mathematics by T. Alfrey (1944)
Read, W. T.: Stress analysis for compressible viscoelastic materials. J. of Applied Physics 21, 7, 671 (1950). / J. of Applied Physics by W. T. Read (1950)
Lee, E. H.: Stress analysis in viscoelastic bodies. Quarterly of Applied Mathematics 13, 2, 183 (1955). / Quarterly of Applied Mathematics by E. H. Lee (1955)
Lee, E. H.: Viscoelastic Stress Analysis. Proceedings, First Symposium on Naval Structural Mechanics. New York; Pergamon Press 1960. / Proceedings, First Symposium on Naval Structural Mechanics by E. H. Lee (1960)
Hu Hai-Chang: On reciprocal theorems in the dynamics of elastic bodies and some applications. Scientia Sinica 7, 2, 137 (1958). / Scientia Sinica by Hu Hai-Chang (1958)
Volterra, V.: Sulle equazioni integro-differenziali. Atti della Reale Accademia dei Lincei 18, 1, 167 (1909). / Atti della Reale Accademia dei Lincei by V. Volterra (1909)
Kellogg, O. D.: Foundations of Potential Theory. Berlin: Springer 1929. (10.1007/978-3-642-90850-7) / Foundations of Potential Theory by O. D. Kellogg (1929)
Mikusinski, J.: Operational Calculus. New York: Pergamon Press 1959. / Operational Calculus by J. Mikusinski (1959)
Apostol, T.: Mathematical Analysis. London: Addison-Wesley Publishing Company 1960. / Mathematical Analysis by T. Apostol (1960)
Smithies, F.: Integral Equations. London: Cambridge University Press 1958. / Integral Equations by F. Smithies (1958)
Riesz, F., & B. Sz.-Nagy: Functional Analysis, translated by Leo F. Boron. New York: Frederick Ungar Publishing Company 1955. / Functional Analysis by F. Riesz (1955)
Natanson, I. P.: Theory of Functions of a Real Variable, translated by Leo F. Boron. New York: Frederick Ungar Publishing Company 1955. / Theory of Functions of a Real Variable by I. P. Natanson (1955)
Temple, G.: Cartesian Tensors. New York: John Wiley & Sons 1960. / Cartesian Tensors by G. Temple (1960)
Boley, B. A., & J. H. Weiner: Theory of thermal stresses. New York: John Wiley & Sons 1960. / Theory of thermal stresses by B. A. Boley (1960)
Corneliussen, A. R., & E. H. Lee: Stress distribution analysis for linear viscoelastic materials, Report No. 2, Contract No. DA-19-020-ORD-4750, Brown University, December 1958. To appear in Proceedings, Symposium on Creep in Structures, International Union of Theoretical and Applied Mechanics. Berlin-Göttingen-Heidelberg: Springer 1962. (10.1007/978-3-642-86014-0_1)
Sokolinikoff, I. S.: Mathematical Theory of Elasticity, Second Edition. New York: McGraw-Hill Book Company 1956. / Mathematical Theory of Elasticity by I. S. Sokolinikoff (1956)
Duffin, R. J.: Analytic continuation in elasticity. J. of Rational Mechanics and Analysis 5, 6, 939 (1956). / J. of Rational Mechanics and Analysis by R. J. Duffin (1956)
Friedrichs, K. O.: On the first boundary value problem of the theory of elasticity and Korn's inequality. Annals of Mathematics 48, 2, 441 (1947). (10.2307/1969180) / Annals of Mathematics by K. O. Friedrichs (1947)
Frank, Ph., & R. v. Mises: Die Differential-und Integralgleichungen der Mechanik und Physik, Vol. 1 New York: Mary S. Rosenberg 1943. / Die Differential-und Integralgleichungen der Mechanik und Physik, Vol. 1 by Ph. Frank (1943)
Gurtin, M. E., & E Sternberg: Theorems in linear elastostatics for exterior domains. Arch. Rational Mech. Anal. 8, 2, 99 (1961). (10.1007/BF00277433) / Arch. Rational Mech. Anal. by M. E. Gurtin (1961)
Breuer, S., & E. T. Onat: On uniqueness in linear viscoelasticity. Quarterly of Applied Mathematics 19, 4, 355 (1962). (10.1090/qam/136170) / Quarterly of Applied Mathematics by S. Breuer (1962)
Gurtin, M. E., & E. Sternberg: On the first boundary-value problem of linear elastostatics. Arch. Rational Mech. Anal. 6, 3, 177 (1960). (10.1007/BF00276161) / Arch. Rational Mech. Anal. by M. E. Gurtin (1960)
Widder, D. V.: The Laplace Transform. Princeton: Princeton University Press 1941. / The Laplace Transform by D. V. Widder (1941)
Goldberg, R. R.: Fourier Transforms. London: Cambridge University Press 1961. / Fourier Transforms by R. R. Goldberg (1961)
Loève, M.: Probability Theory, Second Edition. New York: D. van Nostrand Company 1960. / Probability Theory by M. Loève (1960)
Boa-Teh Chu: Stability criteria for isotropic linear viscoelastic materials. Technical Report No. 26, Contract Nonr-562(20), Brown University, November 1961.
Galerkin, B.: Contribution à la solution général du problème de la théorie de l'élasticité dans le cas de trois dimensions. Comptes Rendus, Académie des Sciences, Paris 190, 17, 1047 (1930). / Comptes Rendus, Académie des Sciences, Paris by B. Galerkin (1930)
Papkovich, P. F.: The representation of the general integral of the fundamental equations of elasticity theory in terms of harmonic functions (in Russian).
Izvestiya Akademii Nauk SSSR, Physics-Mathematics Series 10, 1425 (1932). / Physics-Mathematics Series by Izvestiya Akademii Nauk SSSR (1932)
Neuber, H.: Ein neuer Ansatz zur Lösung räumlicher Probleme der Elastizitätstheorie. Z. für angewandte Mathematik und Mechanik 14, 203 (1934). (10.1002/zamm.19340140404) / Z. für angewandte Mathematik und Mechanik by H. Neuber (1934)
Courant, R.: Partial Differential Equations, Vol. 2 of Methods of Mathematical Physics by R. Courant & D. Hilbert. New York: Interscience Publishers 1962. / Partial Differential Equations, Vol. 2 of Methods of Mathematical Physics by R. Courant (1962)
Sternberg, E., & M. E. Gurtin: On the completeness of certain stress functions in the linear theory of elasticity. Technical Report No. 12, Contract Nonr-562(25), Brown University, July 1961. To appear in the Proceedings of the Fourth U. S. National Congress of Applied Mechanics.
Elder, A. S.: Stress function theory for linearly viscoelastic solids. Memorandum Report No. 1282, Ballistic Research Laboratories, Aberdeen Proving Ground, Maryland, June 1960. / Stress function theory for linearly viscoelastic solids / Memorandum Report by A. S. Elder (June 1960)

Dates

Type	When
Created	20 years, 11 months ago (Sept. 30, 2004, 3:24 a.m.)
Deposited	5 years, 5 months ago (April 3, 2020, 3:21 a.m.)
Indexed	16 minutes ago (Sept. 4, 2025, 1:25 a.m.)
Issued	63 years, 8 months ago (Jan. 1, 1962)
Published	63 years, 8 months ago (Jan. 1, 1962)
Published Print	63 years, 8 months ago (Jan. 1, 1962)

Funders 0

None

BibTeX

@article{Gurtin_1962, title={On the linear theory of viscoelasticity}, volume={11}, ISSN={1432-0673}, url={http://dx.doi.org/10.1007/bf00253942}, DOI={10.1007/bf00253942}, number={1}, journal={Archive for Rational Mechanics and Analysis}, publisher={Springer Science and Business Media LLC}, author={Gurtin, M. E. and Sternberg, Eli}, year={1962}, pages={291–356} }

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