Foundations of the Theory of Elasticity, Plasticity, and Viscoelasticity

The aim of the study is to describe the two-component polymer composites as a viscoelastic heterogeneous medium. The proposed computational and experimental approach to the determination of effective viscoelastic parameters is based on a statistical method of moment functions and Prony model. The validity of the hypothesis of aliasing relaxation times of the matrix and the filler in the absence of the interfacial layer is established, as well as the use of standardized tests in uniaxial tensioncompression at constant temperature in order to determine the parameters of the thermoviscoelasticity equations. To illustrate the proposed approach we determine the viscoelastic parameters of polytetrafluoroethylene, filled with particles of polyethylene terephthalate. By approximating the deformation diagrams in uniaxial tension obtained at different temperatures, we also found the viscoelastic parameters of glass-nylon composite. Temperature independence of the relaxation core dimensionless parameter and the activation energy of the relaxation process is defined

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“…For these materials bond component of the stress and the deformation tensors can be described by the following physical equation [3] 0 0 2 ,…”

Section: Application Of the Methods Of Moment Functions To Determine Tmentioning

confidence: 99%

Computational and Experimental Determination of the Viscoelastic Parameters of the Dispersed-filled Polymeric Materials

Шилько

Черноус

Kropotin

et al. 2015

Procedia Engineering

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“…The functions Y r 0 ( ) l and K r 0 ( ) l have a logarithmic singularity at the origin of coordinates [11,13], i.e., at the center of the plate. Therefore, we have to assume that C C 5 6 0 = = in Eq.…”

Section: Free Vibrationsmentioning

confidence: 99%

“…The radial displacement and relative shear follow from the first two equations of system (2) and the condition ψ ( , ) ( , ) r t u r t The coefficients A n and B n in formulas (11) and (12) are determined by the initial conditions of motion (3).…”

Section: Free Vibrationsmentioning

confidence: 99%

Resonance Vibrations of a Circular Composite Plates on an Elastic Foundation

2015

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The axisymmetric resonance vibrations of a circular elastic composite plate on an elastic foundation under the action of periodic local surface loads of rectangular, sinusoidal, and parabolic form are investigated. To describe the kinematics of the package, asymmetric across its thickness, the hypotheses of broken normal are assumed. The response of the foundation is described based on the Winkler model. The filler is light. Analytical solutions of the corresponding initial-boundary-value problems are found, and their numerical-comparative analysis is carried out.

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“…where ( ) k xx s and ( ) k xx ε are the deviator parts of the stress and strain tensors, σ (k) and ε (k) are the spherical parts of the stress and strain tensors, α k is the linear temperature expansion coeffi cient, and G k and K k are the temperature-dependent moduli of shear and dilatation computed from the Bell formula [7,8].…”

Section: ( )mentioning

confidence: 99%

Deformation of a Step Composite Beam in a Temperature Field

Старовойтов

Pleskachevskii

Леоненко

et al. 2015

J Eng Phys Thermophy

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Consideration is given to thermal force deformation of an elastic three-layer beam with a stepwise thickness of one supporting layer. To describe the kinematics of a rod that is asymmetric across the bundle, the hypotheses of a broken normal are adopted. A system of equilibrium equations is derived and its general analytical solution in displacements is obtained. A numerical parametric analysis of the stressed-strained state of a metal-polymer threelayer beam is carried out.Introduction. Since composite structural elements are widely used in industry, the problem of their strength calculation for various external effects and internal confi gurations is topical. Static and dynamic deformations of three-layer (sandwich) composite structural elements with a smooth confi guration were studied in [1]. The theory of homogeneous thinwalled structures of stepwise varying thickness was developed in [2]. In [3,4], consideration was given to the deformation of a three-layer rod with an irregular boundary under isothermal loading. Studies [5,6] were devoted to the dynamic deformation of three-layer building structures.Problem Formulation. Consideration is given to an asymmetric-across-the thickness elastic three-layer beam with a stiff fi ller (Fig. 1), i.e., with regard for the work of shear stresses. The system of coordinates x, y, and z is tied to the fi ller midplane. The bundle kinematics is described using the hypothesis of a "broken" normal: for thin supporting layers 1 and 2, the Bernoulli hypothesis is valid, in the stiff fi ller 2, which is incompressible across the thickness, the normal remains rectilinear and does not change its length but turns by a certain angle ψ(x). Presumably, deformations are small, but the external layer 1 of the beam is acted upon by a distributed force load q(x) and p(x) and the temperature fi eld T k in the rod is known. In accordance with the adopted assumptions, the defl ections will be the same at all points of the rod cross section. There are stiff diaphragms on the rod faces, which hinder the relative shear of the layers. The layer thickness h k is defi ned as

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Foundations of the Theory of Elasticity, Plasticity, and Viscoelasticity

Cited by 25 publications

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Computational and Experimental Determination of the Viscoelastic Parameters of the Dispersed-filled Polymeric Materials

Computational and Experimental Determination of the Viscoelastic Parameters of the Dispersed-filled Polymeric Materials

Resonance Vibrations of a Circular Composite Plates on an Elastic Foundation

Deformation of a Step Composite Beam in a Temperature Field

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