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Summary:
An abstract ordinary differential equation with retarded argument is deduced as a model of incremental, rate independent strain theory. The concept of experience of materials as well as some quantities chracterizing the hardering of the material are introduced. The traction problem is considered, but neither the existence nor the uniqueness of the solution is proved. This remains an open problem.
References:
[1] K. Washizu: Variational methods in elasticity and plasticity. Pergamon Press, 1968. MR 0391679 | Zbl 0164.26001
[2] J. Kratochvíl O. W. Dillon: Thermodynamics of Elastic-Plastic Materials as a Theory with Internal State Variables. J. Applied Physics, Vol. 40, n. 8, 3207-3218, 1969.
[3] J. Nečas: Les méthodes directes en théorie des équations elliptiques. Academia, Prague 1967. MR 0227584
[4] I. Hlaváček J. Nečas: On Inequalities of Korn's Type. Archive for Rat. Mech. Anal. Vol. 36, No. 4, 1970, 305-311, 312-334. DOI 10.1007/BF00249518
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