Thermoinelasticity pp 17-32 | Cite as

# Equations of the Theory of Thermal Stresses in Double-Modulus Materials

## Summary

The study deals with the development of the theory of thermo-inelasticity for the “elastic” material whose elastic moduli are different in tension (*E* ^{+}) and in compression (*E* ^{−}).

The proposed theory is based upon the mathematical theory of elasticity of double-modulus materials and upon the familiar Neuman’s hypothesis.

Proceeding from accepted principles, the general theory of thermo-inelasticity for the double-modulus material is developed and the solutions of some problems are presented.

A vital characteristic of the nonlinear equations and formulae derived is the fact that all the nonlinear terms representations depend upon the parameter (*E* ^{+} − *E* ^{−})/(*E* ^{+} + *E* ^{−}), which is assumed small.

It is shown that neglect of heteroresistance may introduce significant errors.

Proceeding from the general principles of the heteromodulus theory of elasticity [1, 2] and from the fundamental hypotheses of the mathematical theory of thermo-elasticity [3, 4], a general stress-strain theory of heteromodulus materials, in a field of thermal effects, has been developed.

## Keywords

Thermal Stress Principal Stress Plane Strain Classical Theory Plane Problem## Preview

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## References

- [1]Ambartsumian, S. A., and A. A. Khachaturian: Basic Equations of the Theory of Elasticity for Materials Which Resist Tension and Compression in a Different Manner. Mechanics of Solids (Mekhanika Tverdogo Tela), No.
**2**(1966).Google Scholar - [2]Ambabtsumian, S. A.: Equations of the Plane Problem of the Elastic Theory of Materials Which Resist Differently Tension and Compression or of Different Modulus in Tension and Compression. News of the Academy of Sciences of the Armenian Socialist Republic, Mechanics,
**19**, No. 2 (1966).Google Scholar - [3]Nowacki, W.: Thermoelasticity. London: Pergamon Press. 1962.Google Scholar
- [4]Boley, B. A., and J. H. Weener: Theory of Thermal Stresses. New York: J. Wiley and Sons. 1960, and MIR. 1964.Google Scholar
- [5]Libenson, L. S.: Course in the Theory of Elasticity. Gostekhizdat. 1947.Google Scholar
- [6]Novozhilov, V. V.: Theory of Elasticity. Sudpromgiz. 1958.Google Scholar
- [7]Timoshenko, S. P.: Theory of Elasticity. New York: Mc Graw-Hill. 1934.MATHGoogle Scholar
- [8]Melan, E., and H. Parkus: Wärmespannungen infolge stationärer Temperaturfelder. Wien: Springer. 1953.Google Scholar