Birefringence in viscoelastic materials

Zusammenfassung In der vorliegenden Arbeit werden isotrope Stoffe betrachtet, die sich verformen und für welche die elektromagnetischen Stoffgleichungen aus einer linearen Beziehung zwischen dem elektrischen Verschiebungsfeld und dem elektrischen Feld sowie einer linearen Relation zwischen der magnetischen Feldstärke und den magnetischen Induktionsfeldern bestehen. Bei der Dielektrizitätskonstante und dem spezifischen Widerstand wird angenommen, dass sie von der Geschichte und vom Verformungsgradienten abhängen. Für die Stoffbeziehungen wird die kanonische Form hergeleitet; ferner ergeben sich Formeln für die geringe Geschwindigkeit der Ausbreitung ebener Wellen. Diese werden insbesondere im Fall von zeitunabhängigen, rein homogenen Deformationen und Schubverformungen diskutiert.     

Near-surface failure of layered viscoelastic materials

Within the framework of a piecewise homogeneous body model, with the use of exact equations of the geometrically nonlinear theory of viscoelastic bodies, the distribution of near-surface self-balanced normal stresses in a body consisting of a viscoelastic half-plane, an elastic locally curved bond layer, and a viscoelastic covering layer is investigated. A method for solving the problem considered by employing the Laplace and Fourier transformations is developed. Numerical results for the self-balanced normal stresses caused by a local curving (imperfection) of an elastic bond layer upon tension and compression of the body mentioned along the free face plane are presented and analyzed. The viscoelasticity of the materials is described by the Rabotnov fractional-exponential operators. A macroscopic failure criterion is proposed, and the validity of this criterion is examined.     

Local near-surface buckling of a system consisting of an elastic (viscoelastic) substrate,a viscoelastic (elastic) bond layer,and an elastic (viscoelastic) covering layer

Within the framework of a piecewise homogenous body model and with the use of a three-dimensional linearized theory of stability (TLTS), the local near-surface buckling of a material system consisting of a viscoelastic (elastic) half-plane, an elastic (viscoelastic) bond layer, and a viscoelastic (elastic) covering layer is investigated. A plane-strain state is considered, and it is assumed that the near-surface buckling instability is caused by the evolution of a local initial curving (imperfection) of the elastic layer with time or with an external compressive force at fixed instants of time. The equations of TLTS are obtained from the three-dimensional geometrically nonlinear equations of the theory of viscoelasticity by using the boundary-form perturbation technique. A method for solving the problems considered by employing the Laplace and Fourier transformations is developed. It is supposed that the aforementioned elastic layer has an insignificant initial local imperfection, and the stability is lost if this imperfection starts to grow infinitely. Numerical results on the critical compressive force and the critical time are presented. The influence of rheological parameters of the viscoelastic materials on the critical time is investigated. The viscoelasticity of the materials is described by the Rabotnov fractional-exponential operator. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 6, pp. 771–788, November–December, 2007.     

Generalized criterion of the long-term strength of viscoelastic materials

A long-term strength condition of the same type as the Il'yushin [2] or Moskvitin [1] nonlinear criterion is proposed. A method is suggested for determining the stress and time functions forming part of the proposed criterion from the long-term strength diagrams and from the data of pulsed or stepped loading tests. It is shown, on the basis of the experimental data, that the proposed criterion, which in a particular case is identical with the Moskovitin criterion, describes the experimental results better than the Bailey criterion.     

Features of viscoelastic behavior of materials based on heat-resistant polymers

Conclusions In the example of polybenzoxazole, the relationships of viscoelastic behavior have been investigated for monolithic heat-resistant polymers over a wide range of temperatures (from 22° to 230°C) and initial deformations (from 0.5 to 2.5%). The experimental data on stress relaxation, covering the regions of linear and nonlinear viscoelasticity, are approximated by the basic equation of the primary cubic theory of Il'yushin, using the singular kernel of Rzhanitsyn. For the first time, the region of stable mechanical capability of monolithic heat-resistant polymers has been defined with due regard for relaxation characteristics.Paper presented at Fourth All-Union Conference on Polymer Mechanics and Composite Materials (Riga, October 1980).Translated from Mekhanika Kompozitnykh Materialov, No. 6, pp. 978–983, November–December, 1980.     

Nonlinear constitutive equations for directed viscoelastic materials with memory

Zusammenfassung Es werden die nichtlinearen Konstitutionsgleichungenfür ein richtungsorientiertes viskoelastisches Material mit Gedächtnis entwickelt. Die Beziehungen zwischen dieser Theorie und derjenigen der klassischen Elastizität und Viskoelastizität und einige andere Arbeiten auf dem Gebiete der Theorie der richtungsorientierten Medien werden besprochen.

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Acknowledgment. This work was sponsored by the National Science Foundation under Research Grants NSF GK 1608 and GK 1769.     

Three-dimensional travelling waves for nonlinear viscoelastic materials with memory

In this paper, we show the existence of nontrivial travelling wave solutions, which propagating speeds are between ones determined by the equilibrium and instantaneous elastic tensor, respectively, to the nonlinear three-dimensional viscoelastic system with fading memory.     

Decay property for second order hyperbolic systems of viscoelastic materials

We study a class of second order hyperbolic systems with dissipation which describes viscoelastic materials. The considered dissipation is given by the sum of the memory term and the damping term. When the dissipation is effective over the whole system, we show that the solution decays in L² at the rate t−n/4 as t→∞, provided that the corresponding initial data are in L²∩L¹, where n is the space dimension. The proof is based on the energy method in the Fourier space. Also, we discuss similar systems with weaker dissipation by introducing the operator (1−Δ)^−θ/2 with θ>0 in front of the dissipation terms and observe that the decay structure of these systems is of the regularity-loss type.