Some issues related to the development of methods for forecasting creep processes are considered. For this purpose, the temporal equivalence principle, the temperature-time analogy, the stress-time analogy, other analogies, and the modern relations between stresses and strains of the heriditary type in the form that allows describing irreversible plastic deformations are used. The expressions for multiple reduction coefficients are obtained using the time equivalence principle. A brief description is given to implementation of the method of analogies. An example of application of the concept of reduced time directly to the creep diagram is provided.

On the Prediction of High-Temperature Creep Processes in Metals

Some features of the behavior of viscoelastic materials whose existence leads to the choice of nonlinear constitutive relations are discussed. A classification of such constitutive relations is given and a number of requirements imposed by practice on their adequacy are formulated. A nonlinear theory of viscoelasticity is proposed; this theory offers the advantages over the theory in which stresses are expressed in terms of strains by integral operators of increasing multiplicity. By a one-dimensional example, it is shown that the constitutive operator relations are reciprocal.

Adequacy of a nonlinear theory of viscoelasticity

A generalization of Pobedrya’s viscoelasticity constitutive relations is considered for an isotropic material with an elastic behavior of the material volume. Two model problems are discussed for a specimen under uniform compression and uniaxial tension. The resulting expressions for strains are used to formulate some necessary conditions for a nonrelaxing behavior of the material volume. The case of an arbitrary low loading of the specimen is examined. It is proved that the obtained nonrelaxing conditions are not only necessary but are also sufficient.

New constitutive relations in the nonlinear theory of viscoelasticity

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B. E. Pobedrya

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Adequacy of a nonlinear theory of viscoelasticity

New constitutive relations in the nonlinear theory of viscoelasticity