Skip to main content
Log in

Variational and minimum theorems for the linear theory of viscoelasticity

  • Original Papers
  • Published:
Zeitschrift für angewandte Mathematik und Physik ZAMP Aims and scope Submit manuscript

Zusammenfassung

Es werden zwei Variationsprinzipien und zwei zugeordnete Minimalprinzipien für die lineare Theorie der Viscoelastizität aufgestellt. Dabei werden Bedingungen formuliert, welche hinreichend sind für eine Lösung mit Variablen-Trennung.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. M. A. Biot,Linear Thermodynamics and the Mechanics of Solids, Proc. 3rd U. S. Natl. Cong. Appl. Mech. 1–18 (1958).

  2. R. A. Schapery,On the Time Dependence of Viscoelastic Variational Solutions, Quart. Appl. Math.22, 207–215 (1964).

    Google Scholar 

  3. E. T. Onat,On a Variational Principle in Linear Viscoelasticity, J. Méch.1, 135–140 (1962).

    Google Scholar 

  4. M. E. Gurtin,Variational Principles in the Linear Theory of Viscoelasticity, Arch. Ratl. Mech. Anal.13, 179–191 (1963).

    Google Scholar 

  5. M. J. Leitman,Variational Principles in the Linear Dynamic Theory of Viscoelasticity, Quart. Appl. Math.24, 37–46 (1966).

    Google Scholar 

  6. P. M. Naghdi,On a Variational Theorem in Elasticity and Its Applications to Shell Theory, J. Appl. Mech.31, 647–653 (1964).

    Google Scholar 

  7. Z. Hashin,The Elastic Moduli of Heterogeneous Materials, J. Appl. Mech.29, 143–150 (1962).

    Google Scholar 

  8. M. E. Gurtin andI. Hereera,On Dissipation Inequalities and Linear Viscoelasticity, Quart. Appl. Math.23, 235–245 (1965).

    Google Scholar 

  9. R. M. Christensen andP. M. Naghdi,Linear Non-Isothermal Viscoelastic Solids, Acta Mech.3, 1–12 (1967).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Christensen, R.M. Variational and minimum theorems for the linear theory of viscoelasticity. Journal of Applied Mathematics and Physics (ZAMP) 19, 233–243 (1968). https://doi.org/10.1007/BF01601468

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01601468

Keywords

Navigation