Finite linear theory of viscoelastic generalized thermorheologically simple ferromagnets

A finite linear theory of viscoelastic generalized thermorheologically simple ferromagnets is constructed with allowance for nonuniform exchange, when the derivative with respect to intrinsic time is an arbitrary functional of the independent field variables and their derivatives. Free energy is treated as an arbitrary functional of the past history of these variables. Specific constitutive equations are presented for such a model. Variants of the history of the variables are also examined for the case when a small nonsteady perturbation is superimposed on the steady state. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 9, pp. 13–18, September, 1999.     

A theory of thermo-visco-elastic-plastic materials: thermomechanical coupling in simple shear

The constitutive relations of a theory of thermo-visco-elastic-plastic continuum have been formulated in Lagrangian form. The Lagrangian strains, strain rates, temperature, temperature rate and temperature gradients are considered as the independent constitutive variables. Three internal state variables (plastic strain tensor, back strain tensor and a scalar hardening parameter) are also incorporated. The axioms of objectivity and equipresence are followed. The Clausius–Duhem inequality is taken as the second law of thermodynamics. Several special theories are deduced based on material symmetries and/or conventionally adopted assumptions. The applications to the formation of shear bands and dynamic crack propagation are discussed.     

One method of solution of problems in the linear theory of viscoelasticity for aging anisotropic materials

A method of solution of problems in the linear theory of viscoclasticity for aging anisotropic materials is discussed. The method is based on evaluation of irrational functions of nondiffcrence viscoelasticity operators using the theory of continued fractions. It is shown that operator-valued continuedS-fractions converge for a wide class of integral Voltcrra operators. Application of the method is illustrated by the evaluation of an irrational function of a linear combination of nondiffcrence-type resolvent operators obtained in the solution of a concrete problem of failure of an aging anisotropic viscoclastic body. Translated from Prikladnaya Mekhanika, Vol. 34, No. 11, pp. 60–65, November, 1998.     

A version of modeling of nonlinear-hereditary viscoelasticity of polymer materials

We propose a version of the mathematical model of nonlinear-hereditary viscoelasticity of polymer materials, which is used to predict strain processes of various complexity, from simple relaxation and simple creep processes to complicated strain recovery processes and reverse relaxation processes with alternating loading and unloading.     

One method of solving boundary-value problems of the linear theory of viscoelasticity

A form of integral resolvent viscoelastic operators with arbitrary analytic difference-type kernel is found using an improved method of calculating irrational functions. The approach is illustrated by determining the viscoelastic characteristics of the plane stressed state of an orthotropic plate. Translated from Prikladnaya Mekhanika, Vol. 34, No. 12, pp. 77–85, December, 1998.     

An improved simple version of a nonlinear theory of elasto-viscous polymer media

Summary Some rheological equations describing the elastoviscous behavior of concentrated polymer solutions and melts were suggested using a two-parameter elastic potential. These equations, containing a small number of parameters, are based upon a representation involving a set of nonlinear noninteracting relaxators (the Maxwellian models). As examples, shear and extension deformations are considered. The reasons for the choice of rheological constants are given. A comparison between the theory and some experiments for a simplest four-parameter model (two noninteracting nonlinear relaxators) has shown that it describes the tests much better than the simplest three parameter model developed previously.

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Zusammenfassung Ausgehend von einem zweiparametrigen elastischen Potential werden rheologische Stoffgleichungen abgeleitet, die das viskoelastische Verhalten von konzentrierten Polymerlösungen und Schmelzen beschreiben sollen. Diese Gleichungen, die nur wenige Parameter enthalten, basieren auf der Superposition einer Anzahl nichtlinearer, nicht miteinander in Wechselwirkung stehender Maxwell-Modelle (Relaxatoren). Als Beispiele werden Scher- und Dehnvorgänge betrachtet, wobei die Wahl der rheologischen Konstanten begründet wird. Ein Vergleich der Theorie für das einfachste Vier-Parameter-Modell (d. h. Parallelschaltung zweier nichtlinearer Relaxatoren) mit einigen Experimenten zeigt, daß diese hiermit wesentlich besser zu beschreiben sind als mit einem früher entwickelten einfachen Drei-Parameter-Modell.

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With 6 figures     

Determination of material functions for the linear moment theory of viscoelasticity

An analytic method is proposed to find material functions for the linear moment theory of viscoelasticity with consideration of the structure of the composite material under study.