Effect of long-term exposure to water on the viscoelastic properties of an epoxy-based composition

For modeling the effect of volume change on the viscoelastic properties of a polymer, an equation underlying the concept of free volume is used. The parameters of the moisture–time reduction function, characterizing changes in the viscoelastic properties of an epoxy-based composition, are determined from tests results. To verify the approach suggested, results of long-term (up to one year) tests on stress relaxation under compression in an epoxy composition (COMFLOOR), both in the initial state and after a long-term (up to one year) exposure to water, are used. A satisfactory agreement between the reduction functions based on predictions and determined experimentally is found to exist. Translated from Mekhanika Kompozitnykh Materialov, Vol. 45, No. 2, pp. 201–210, March–April, 2009.     

Thermomechanical analysis of a toughened thermosetting system

The experimental results of viscoelastic mechanical tests, at five different levels of conversion, are reported for a thermoset composite matrix system toughened with an appropriate percentage of a thermoplastic polymer. The results from static tests are used to construct the master curves at a specific degree of cure, while the shift factors are compared with the corresponding values from dynamic experiments in order to assess the validity of the time-temperature superposition for each conversion. Neat resin plates were cured accurately, according to the full kinetics model for a dynamic and isothermal temperature regime; the conversion gradient in the plane and across the thickness of the plates was assessed by a thermal analysis of samples taken from different locations before extracting the samples from them. The viscoelastic behaviour of the resin matrix showed a sensible difference in the relaxation time spectrum upon conversion according to the provisional trend of mobility theory; a higher conversion induced a horizontal shift of the principal relaxation time for each level of conversion, which could be related very well to the glass transition at the same conversion. Good results were also obtained for the ultimate modulus of the resin at a temperature just before the onset of the co-curing phase for partially cured samples. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 2, pp. 265–278, March–April, 2008.     

A model of weak viscoelastic nematodynamics

The paper develops a continuum theory of weak viscoelastic nematodynamics of Maxwell type. It can describe the molecular elasticity effects in mono-domain flows of liquid crystalline polymers as well as the viscoelastic effects in suspensions of uniaxially symmetric particles in polymer fluids. Along with viscoelastic and nematic kinematics, the theory employs a general form of weakly elastic thermodynamic potential and the Leslie–Ericksen–Parodi type constitutive equations for viscous nematic liquids, while ignoring inertia effects and the Frank (orientation) elasticity in liquid crystal polymers. In general case, even the simplest Maxwell model has many basic parameters. Nevertheless, recently discovered algebraic properties of nematic operations reveal a general structure of the theory and present it in a simple form. It is shown that the evolution equation for director is also viscoelastic. An example of magnetization exemplifies the action of non-symmetric stresses. When the magnetic field is absent, the theory is reduced to the symmetric, fluid mechanical case with relaxation properties for both the stress and director. Our recent analyses of elastic and viscous soft deformation modes are also extended to the viscoelastic case. The occurrence of possible soft modes minimizes both the free energy and dissipation, and also significantly decreases the number of material parameters. In symmetric linear case, the theory is explicitly presented in terms of anisotropic linear memory functionals. Several analytical results demonstrate a rich behavior predicted by the developed model for steady and unsteady flows in simple shearing and simple elongation.     

A model of weak viscoelastic nematodynamics

The paper develops a continuum theory of weak viscoelastic nematodynamics of Maxwell type. It can describe the molecular elasticity effects in mono-domain flows of liquid crystalline polymers as well as the viscoelastic effects in suspensions of uniaxially symmetric particles in polymer fluids. Along with viscoelastic and nematic kinematics, the theory employs a general form of weakly elastic thermodynamic potential and the Leslie–Ericksen–Parodi type constitutive equations for viscous nematic liquids, while ignoring inertia effects and the Frank (orientation) elasticity in liquid crystal polymers. In general case, even the simplest Maxwell model has many basic parameters. Nevertheless, recently discovered algebraic properties of nematic operations reveal a general structure of the theory and present it in a simple form. It is shown that the evolution equation for director is also viscoelastic. An example of magnetization exemplifies the action of non-symmetric stresses. When the magnetic field is absent, the theory is reduced to the symmetric, fluid mechanical case with relaxation properties for both the stress and director. Our recent analyses of elastic and viscous soft deformation modes are also extended to the viscoelastic case. The occurrence of possible soft modes minimizes both the free energy and dissipation, and also significantly decreases the number of material parameters. In symmetric linear case, the theory is explicitly presented in terms of anisotropic linear memory functionals. Several analytical results demonstrate a rich behavior predicted by the developed model for steady and unsteady flows in simple shearing and simple elongation.     

Effects of temperature and moisture on the mechanical properties of polyester resin in tension

The effect of environment on the physical and mechanical properties of composite materials in some cases is determined by the environmental sensitivity of the binder. The results of experimental investigation of the deformability and strength of polyester resin, widely used as a binder in composites, upon the action of stationary and quasi-stationary loads, temperatures, and moisture are presented. The ranges of acceptable values of these services factors are determined. The elastic modulus and tensile strength of the material are obtained from quasi-static tests. The viscoelastic behavior of the resin is investigated in creep tests. From the results of a short-term experiment with stepwise loading up to failure, it is found that the creep of specimens with a moisture content of 0.14% can be described by a linear viscoelastic model for stresses up to 20 MPa (two thirds of the strength). The action of single loading impulses is summarized according to the Boltzmann superposition principle. The temperature and absorbed moisture are considered as factors accelerating the relaxation processes in the material. The creep activation under the action of these factors is described using the methods of time-temperature and time-moisture equivalence. The results of short-term creep tests allow us to determine the relaxation characteristics of the material in stationary conditions. The long-term creep under close-to-service conditions is predicted using these data and quite good agreement with the control test is obtained. The sensitivity of the material characteristics (strength, elastic modulus, and creep strain) to the action of temperature and moisture is estimated. The creep strain is most sensitive to the action of environmental factors. For a fully saturated material (moisture content 1.64 wt.%), after one hour creep, this strain four times exceeds that of a dry one. The same growth in deformability is caused by an 18°C increase in temperature. A quantitative comparison of the characteristics of polyester and epoxy resins allows us to choose the binder for composites and to estimate the expected environmental effect. Presented at the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 3, pp. 395–406, May–June, 2000.     

Creep of polymer concrete in the nonlinear region

Two polyester-based polymer concretes with various volume content of diabase as an extender and aggregate are tested in creep under compression at different stress levels. The phenomenological and structural approaches are both used to analyze the experimental data. Common features of changes in the instantaneous and creep compliances are clarified, and a phenomenological creep model which accounts for the changes in the instantaneous compliance and in the retardation spectrum depending on the stress level is developed. It is shown that the model can be used to describe the experimental results of stress relaxation and creep under repeated loading. Modeling of the composite structure and subsequent solution of the optimization problem confirm the possibility of the existence of an interphase layer more compliant than the binder. A direct correlation between the interphase volume content and the instantaneous compliance of the composite is revealed. It is found that the distinction in nonlinearity of the viscoelastic behavior of the two polymer concretes under investigation can be due to the difference in their porosity. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000.) Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 147–164, 2000.     

On the three-dimensional undulation instability of a rectangular viscoelastic composite plate in biaxial compression

Within the frame work of the second version of small precritical deformation in the three-dimensional linearized theory of stability of deformable bodies (TDLTSDB), the undulation instability problem for a simply supported rectangular plate made of a viscoelastic composite material is investigated in biaxial compression in the plate plane. The corresponding boundary-value problem is solved by employing the Laplace transformation and the principle of correspondence. For comparison and estimation of the accuracy of results given by the TDLTSDB, the same problem is also solved by using various approximate plate theories. The viscoelasticity properties of the plate material are described by the Rabotnov fractional-exponential operator. The numerical results and their discussion are presented for the case where the plate is made of a multilayered viscoelastic composite material. In particular, the variation range of problem parameters is established for which it is necessary to investigate the undulation instability of the viscoelastic composite plate by using the TDLTSDB. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 1, pp. 93–108, January–February, 2009.     

Generalized thermoelastic infinite medium with spherical cavity subjected to moving heat source

This paper deals with a problem of thermoelastic interactions in an isotropic unbounded medium with spherical cavity due to the presence of moving heat sources in the context of the linear theory of generalized thermoelasticity with one relaxation time. The governing equations are expressed in the Laplace transform domain and solved in that domain. The inversion of the Laplace transform is done numerically using the Riemann-sum approximation method. The numerical estimates of the displacement, temperature, stress, and strain are obtained for a hypothetical material. The results obtained are presented graphically to show the effect of the heat source velocity and the relaxation time parameters on displacement, temperature, stress, and strain.     

General decay of solutions of a nonlinear system of viscoelastic wave equations

This work is concerned with a system of two viscoelastic wave equations with nonlinear damping and source terms acting in both equations. Under some restrictions on the nonlinearity of the damping and the source terms, we prove that, for certain class of relaxation functions and for some restrictions on the initial data, the rate of decay of the total energy depends on those of the relaxation functions. This result improves many results in the literature, such as the ones in Messaoudi and Tatar (Appl. Anal. 87(3):247–263, 2008) and Liu (Nonlinear Anal. 71:2257–2267, 2009) in which only the exponential and polynomial decay rates are considered.     

Designing of layered rod structures from viscoelastic materials at a given service life

The problem on the rational design of a layered rod structure subjected to force and temperature actions under the conditions of creep is considered. The linear hereditary theory is used for the viscoelastic materials of layers. The rods are packages of several homogeneous layers with a rectangular cross section. The variable geometrical parameters of the rods are determined from the energy equal-strength condition at a given in stant of time. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 5, pp. 581–594, September–October, 2007.     

Approximate Description of the Dynamics of Thin Isotropic Elastic Coatings and Interlayers by Using Asymptotics of High Order of Accuracy

Asymptotically accurate low-frequency models for isotropic elastic coatings and interlayers are developed. The main constraint is the requirement on contact conditions for the layer and the base that at least one of the boundary conditions must include the displacement component in an explicit form. The displacement and stress fields in the three-dimensional elastic system are sought in the form of asymptotic expansion into power series of a small parameter — the ratio between the half-thickness of the layer and the minimum length of the wave in the longitudinal direction. The action of the layer is approximated by impedance boundary conditions, which are transferred to the contact surface with the basic, more thick body. These conditions are obtained with an asymptotic error up to and including the sixth order of magnitude. A numerical testing, which is carried out with the example of partial waves, shows a satisfactory accuracy, comparable with that of high-order theories of plates. The results obtained can be utilized in fast algorithms for calculating spectra of natural waves in half-spaces, thick laminated plates, and shallow shells with coatings and interlayers. The physical limit of applicability of the theory developed is the frequency of the first quasi-resonance in the corresponding deformable system. The number of alternating interlayers is unlimited. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 6, pp. 783–794, November–December, 2005.     

具有立方对称性及两个弛豫时间的微极热弹性介质中调和时间源引起的变形

研究了具有立方对称性及两个弛豫时间的微极热弹性介质在调和时间源中的响应．采用了Fourier变换以及数值逆变换技术．在物理域中,得到了位移、应力、微转动和温度分布的数值结果．将微极立方晶体法向位移、法向力应力、切向耦合应力和温度分布的计算结果,与微极各向同性固体的结果进行比较．绘制了指定材料的数值结果图形．还推断了某些特殊情况的结果．     

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.     

Strong relaxation limit of multi-dimensional isentropic Euler equations

This paper is devoted to study the strong relaxation limit of multi-dimensional isentropic Euler equations with relaxation. Motivated by the Maxwell iteration, we generalize the analysis of Yong (SIAM J Appl Math 64:1737–1748, 2004) and show that, as the relaxation time tends to zero, the density of a certain scaled isentropic Euler equations with relaxation strongly converges towards the smooth solution to the porous medium equation in the framework of Besov spaces with relatively lower regularity. The main analysis tool used is the Littlewood–Paley decomposition.     

A model for predicting the multiscale crack growth due to an impact in heterogeneous viscoelastic solids

A two-scale model for predicting the multiple crack growth in viscoelastic solids due to an impact is presented. The cracks are considered only at the local scale through the use of a micromechanical viscoelastic cohesive zone model. The multiscale model has been implemented in a finite-element code. In order to minimize the computation time, the local finite-element meshes are solved in parallel by multiple processors. An example problem is given in order to demonstrate the capabilities of the model. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 2, pp. 211–222, March–April, 2009.     

Thermo-viscoelastic analysis of biological tissue during hyperthermia treatment

Although viscoelastic properties of biological tissue has been reported in many articles, no effort has been made to investigate the coupled thermal and mechanical behavior of biological tissue based on the viscoelastic theory. This provides us a motivation to study the transient thermoelastic coupling response in the context of generalized thermo-viscoelastic model. The dual phase lag thermo-viscoelastic model is established to capture the micro-scale responses of biological tissue. The governing equations are solved by Laplace transformation. The effects of relaxation times and viscoelastic property on the responses of the tumor and normal tissues are discussed and illustrated graphically. According to the numerical results, we can obtain (1) the viscoelastic parameter has a significant effect on the distributions of displacement and stress; (2) the lagging thermo-viscoelastic responses depend not only on the ratio of τ_t/τ_q, but also on the absolute values of τ_t and τ_q.     

General Decay of Solutions of a Nonlinear System of Viscoelastic Equations

In this paper we consider a system of two coupled viscoelastic equations with Dirichlet boundary condition which describes the interaction between two different fields arising in viscoelasticity. For certain class of relaxation functions and certain initial data, we prove that the decay rate of the solution energy is similar to that of relaxation functions which is not necessarily of exponential or polynomial type. This result improves earlier one of Messaoudi and Tatar (Appl. Anal. 87(3):247–263, 2008) and extends some existing results concerning the general decay for a single equation to the case of a system.     

The thermally stressed state of a thickwalled hollow composite cylinder

We propose an approach to the determination of the temperature, stress, and displacement, fields in laminated hollow composite cylinders. The cylinders are studied in three-dimensional formulation; the material of each lamina has the properties of thermal and elastic orthotropy. We study the influence of the heat flow passing through the end surfaces and nonuniform heating of the cylinder to its thermally stressed state. We exhibit peculiarities in the stress and displacement distributions caused both by anisotropy of the mechanical and thermophysical properties and by the nature of the thermal actions applied. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 23, 1992, pp. 14–18     

Damping properties of composites based on interpenetrating polymer networks formed in the presence of compatibilizing additives

From the results of an analysis of the viscoelastic characteristics of semi-interpenetrating polymer networks (semi-IPNs) that are based on a crosslinked polyurethane and a linear polystyrene and are formed in the presence of compatibilizing additives (oligourethane dimethacrylate and ethylene glycol monomethacrylate), their damping ability is est mated. Such parameters as the tangent of mechanical loss (tan δ) at the glass-transition temperature, the temperature interval of effective damping (where tan δ > 0.3), and the loss area under the loss modulus vs. temperature plots are used as the criteria of damping ability. It is shown that the introduction of the compatibilizing additives to the semi-IPNs extends the interval of their effective damping temperature. By varying the composition of the material and the amount of the compatibilizing additives, it is possible to realize a purposeful selection of vibration-damping materials for solving specific technological problems. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 4, pp. 545–558, July–August, 2006.     

Exponential growth of positive initial-energy solutions of a system of nonlinear viscoelastic wave equations with damping and source terms

This work is concerned with a system of nonlinear viscoelastic wave equations with nonlinear damping and source terms acting in both equations. We will prove that the energy associated to the system is unbounded. In fact, it will be proved that the energy will grow up as an exponential function as time goes to infinity, provided that the initial data are large enough. The key ingredient in the proof is a method used in Vitillaro (Arch Ration Mech Anal 149:155–182, 1999) and developed in Said-Houari (Diff Integr Equ 23(1–2):79–92, 2010) for a system of wave equations, with necessary modification imposed by the nature of our problem.