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1.
Experimental analysis of ferroelectric composites with a viscoelastic and dielectric relaxation matrix is carried out, and
the electromechanical coupling behavior of the ferroelectric composites is calculated by means of the constitutive model proposed
in this paper. Comparisons between the experimental results and the calculations show that the constitutive model can reflect
the electromechanical coupling behavior of the ferroelectric composites. The analysis indicates that the effect of viscoelasticity
and dielectric relaxation of the matrix on the electromechanical coupling behavior of ferroelectric composites cannot be neglected. 相似文献
2.
Debanjana Mitra Mythily Ramaswamy Michael Renardy 《Journal of Differential Equations》2018,264(2):575-603
We prove results on approximate controllability for linear viscoelastic flows, with a localized distributed control in the momentum balance equation. The constitutive law is a multimode Maxwell or Jeffreys model with an infinite number of relaxation modes. 相似文献
3.
《Mathematical and Computer Modelling》2000,31(8-9):79-95
Constitutive equations are derived for linear viscoelastic response and enthalpy relaxation in amorphous polymers in the vicinity of the glass transition temperature. According to the concept of cooperative relaxation, a glassy polymer is treated as an ensemble of weakly-connected relaxing regions. Mechanical relaxation in a region occurs when the thermally activated flow unit reaches some liquid-like state. Structural recovery is modeled as a sequence of hops in which rearranging regions change their traps. A constitutive model for the linear viscoelastic behavior and enthalpy relaxation in a glassy polymer is validated using experimental data in mechanical and calorimetric tests on polycarbonate and poly (methyl methacrylate). Fair agreement is demonstrated between observations and results of numerical simulation. 相似文献
4.
Multiscale methods are frequently used in the design process of textile reinforced composites. In addition to the models for the local material structure it is necessary to formulate appropriate material models for the constituents. While experiments have shown that the reinforcing fibers can be assumed as linear elastic, the material behavior of the polymer matrix shows certain nonlinearities. These effects are mainly due to strain rate dependent material behavior. Fractional order models have been found to be appropriate to model this behavior. Based on experimental observations of Polypropylene a one-dimensional nonlinear fractional viscoelastic material model has been formulated. Its parameters can be determined from uniaxial, monotonic tensile tests at different strain rates, relaxation experiments and deformation controlled processes with intermediate holding times at different load levels. The presence of a process dependent function for the viscosity leads to constitutive equations which form nonlinear fractional differential equations. Since no analytical solution can be derived for these equations, a numerical handling has been developed. After all, the stress-strain curves obtained from a numerical analysis are compared to experimental results. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
5.
Constitutive Modelling of Resins in the Stiffness Domain 总被引:1,自引:1,他引:0
An analytic method for inverting the constitutive compliance equations of viscoelasticity for resins is developed. These equations describe the HWKK/H rheological model, which makes it possible to simulate, with a good accuracy, short-, medium- and long-term viscoelastic processes in epoxy and polyester resins. These processes are of first-rank reversible isothermal type. The time histories of deviatoric stresses are simulated with three independent strain history functions of fractional and normal exponential types. The stiffness equations are described by two elastic and six viscoelastic constants having a clear physic meaning (three long-term relaxation coefficients and three relaxation times). The time histories of axiatoric stresses are simulated as perfectly elastic.The inversion method utilizes approximate constitutive stiffness equations of viscoelasticity for the HWKK/H model. The constitutive compliance equations for the model are a basis for determining the exact complex shear stiffness, whereas the approximate constitutive stiffness equations are used for determining the approximate complex shear stiffness. The viscoelastic constants in the stiffness domain are derived by equating the exact and approximate complex shear stiffnesses. The viscoelastic constants are obtained for Epidian 53 epoxy and Polimal 109 polyester resins. The accuracy of the approximate constitutive stiffness equations are assessed by comparing the approximate and exact complex shear stiffnesses. The constitutive stiffness equations for the HWKK/H model are presented in uncoupled (shear/bulk) and coupled forms. Formulae for converting the constants of shear viscoelasticity into the constants of coupled viscoelasticity are given as well. 相似文献
6.
Structural analysis of viscoelastic solid polymers is one of the most important subjects in engineering structures. Several
attempts have been so far made for the integral equation approach to viscoelastic problems. From the basic assumptions of
viscoelastic constitutive equations and weighted residual techniques, a simple but effective boundary element formulation
(BEF) is implemented for the standard linear solid (SLS) viscoelastic models. The SLS model provides an approximate representation
of the observed behavior of a real polymer in its viscoelastic range. This formulation needs only Kelvin’s fundamental solution
of isotropic elastostatics with material constants prescribed as explicit functions of time. This approach avoids the use
of relaxation functions and mathematical transformations, and it is able to solve the quasistatic viscoelastic problems with
any load time-dependence and boundary conditions. As an application, a numerical example is provided to validate the proposed
formulation. The problem of the pressurization of thick-walled cylindrical viscoelastic tanks made of PMMA polymer is completely
analyzed by this approach. 相似文献
7.
In this paper, a microstructurally motivated approach to take into account the anisotropic viscoelastic behaviour of soft biological tissues is proposed. The constitutive model is based on the assumption that this behaviour results from an interaction between collagen fibres and surrounding matrix constituents. Accordingly, a non–linear viscoelastic one–dimensional model for fibres and the nearby ground substance is developed. This model is then generalised to the anisotropic three–dimensional case. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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9.
On the growth behavior of one-dimensional acceleration waves in the linear theory of viscoelasticity
Frederick Bloom 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1975,26(3):361-367
The growth behavior of one-dimensional accelaration waves which propagate in linear viscoelastic materials with time-dependent relaxation functions is examined. Such a time dependence arises either by linearizing the constitutive equation of a simple material about an arbitrary deformation history or by linearizing about a natural state when there is an aging process taking place in the body. Explicit results are obtained for simple types of time dependence and the results are then compared with those which follow in the usual theory of isothermal linear viscoelasticity. 相似文献
10.
The theoretical background of nonlinear constitutive magneto-ferroelectric behavior as well as the Finite Element implementation are presented. On this basis the polarization in the ferroelectric matrix (BaTiO3) with embedded dielectric-magnetostrictive particels (CoFe2O4) is simulated and the resulting effects are analyzed. Numerical simulations focus on the prediction of local crystal orientations and residual stress going along with the poling process, in the future supplying information on favorable electric-magnetic loading sequences. Further, multifield homogenization procedures enable the prediction of the electromagnetomechanical properties of smart multiferroic composites and supply useful means for their optimization. The resulting final state of a poling simulation can be implemented as a starting condition for approximate linear simulations. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Arkady I. Leonov 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2008,59(2):333-359
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. 相似文献
14.
Arkady I. Leonov 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2008,44(4):333-359
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. 相似文献
15.
In this paper we present the theoretical background and application of Finite Element algorithms for linear and nonlinear problems of multiple field coupling. They enable the prediction of the electromagnetomechanical behavior of materials and structures and supply useful tools for the optimization of multifunctional composites. First, linear three-field coupling is presented within the context of a Finite Element implementation. Then, a homogenization procedure is discussed. Finally, a micromechanical model for nonlinear ferroelectric constitutive behavior and its numerical realization are outlined. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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The theoretical background of nonlinear constitutive multifield behavior is presented. Nonlinear material models describing the ferroelectric or ferromagnetic behaviors are presented. Both physically and phenomenologically motivated constitutive models have been developed for the numerical calculation of the nonlinear magnetostrictive and ferroelectric behaviors. On this basis, the polarization in the ferroelectric and magnetization in the ferromagnetic respectively magnetostrictive phases are simulated and the resulting effects analyzed. The developed tools enable the prediction of the electromagnetomechanical properties of smart multiferroic composites and supply useful means for their optimization. Goals are to improve the efficiency of ME coupling and to reduce damage associated with the poling process. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
18.
In this study Kelvin and Boltzmann viscoelastic models are implemented in a two-dimensional boundary element atmosphere. This general methodology is based on differential constitutive relations for viscoelasticity, avoiding the use of relaxation functions. In this part of the study, important algebraic operations are introduced into the formulation allowing analysing viscoelastic problems without using internal cells. This improvement is very important to model infinite and semi-infinite regions. The formulation is verified comparing the numerical results with analytical solutions. An extension of the formulation to consider soil–structure interaction is presented in order to demonstrate the vast applicability of the technique. 相似文献
19.
Based on the nonequilibrium thermodynamic theory, a new thermo-viscoelastic relation at finite strain is proposed. Under the
assumption that the specific heat at a fixed strain and fixed internal variables can be regarded as a constant, a new expression
for the free energy which decouples the mechanical and the thermal effects is derived. Through an analysis of the mesoscopic
deformation mechanism of solid polymers, a set of internal variables is introduced, and an internal-variable constitutive
theory in thermo-viscoelasticity at finite strain is formulated. An explicit expression of a thermoviscoelastic constitutive
relation is obtained for solid polymers in the case where their molecular network has a randomly oriented distribution function
at reference configuration. Moreover, the relationship between the relaxation time and the temperature is also discussed.
The viscoelastic constitutive theory proposed in reference is only a linear approximation of the present theory. 相似文献
20.
Jiří Vala 《Applications of Mathematics》1998,43(5):351-380
In [Sv1] a new micromechanical approach to the prediction of creep flow in composites with perfect matrix/particle interfaces, based on the nonlinear Maxwell viscoelastic model, taking into account a finite number of discrete slip systems in the matrix, has been suggested; high-temperature creep in such composites is conditioned by the dynamic recovery of the dislocation structure due to slip/climb motion of dislocations along the matrix/particle interfaces. In this article the proper formulation of the system of PDE's generated by this model is presented, some existence results are obtained and the convergence of Rothe sequences, applied in the specialized software CDS, is studied. 相似文献