A modified fractional-order thermo-viscoelastic model and its application to a polymer micro-rod heated by a moving heat source

Classical thermo-viscoelastic models may be challenged to predict the precise thermo-mechanical behavior of viscoelastic materials without considering the memorydependent effect.Meanwhile,with the miniaturization of devices,the size-dependent effect on elastic deformation is becoming more and more important.To capture the memory-dependent effect and the size-dependent effect,the present study aims at developing a modified fractional-order thermo-viscoelastic coupling model at the microscale to account for two fundamentally distinct fractional-order models which govern the memory-dependent features of thermal conduction and stress-strain relation,respectively.Then,the modified theory is used to study the dynamic response of a polymer micro-rod heated by a moving heat source.The governing equations are obtained and solved by the Laplace transform method.In calculation,the effects of the fractional-order parameter,the fractional-order strain parameter,the mechanical relaxation parameter,and the nonlocal parameter on the variations of the considered variables are analyzed and discussed in detail.

A thermo-viscoelastic model for particle-reinforced composites based on micromechanical modeling

Micromechanics-based constitutive models offer superior ability to estimate the effective mechanical properties for the composites,which greatly promote the computational efficiency in the multiscale analysis for composite structures.In this work,a thermo-viscoelastic model for particle-reinforced composites is proposed to estimate their thermal-mechanical coupling behaviors in terms of a micromechanics-based homogenization method in the time domain.The matrix and particles of the composites are modeled as“thermo-rheologically complex”viscoelastic materials.The temperature-dependent effective elastic strain energy ratios of particle to composite are proposed to evaluate the contributions of the matrix and particles.The thermo-viscoelastic model for the composites is then formulated by superposing the matrix and particle’s contributions.Finite element simulations based on the representative volume element models are employed to validate the constitutive model under various thermal-mechanical coupling loads.The effects of the loading rate,viscous parameter and particle content on the effective thermal-mechanical responses of the composites are also comprehensively discussed.The experimental data from literature are also employed to verify the constitutive model.The findings show that the proposed thermo-viscoelastic model can accurately predict the thermal-mechanical coupling behaviors for the particle-reinforced composites.

A new interpretation of internal-variable theory in finite thermo-viscoelasticity

Based on the non-equilibrium thermodynamics,an internal-variable theory in thermo-viscoelasticity at finite deformation was proposed by Huang in 1999.In this theory,a modified stretch of the molecular chain was introduced,and hence the molecular network model in rubber elasticity was extended to take into account the viscous and thermal effects of the material.The viscous dissipation of the material can then be described by means of these internal variables,which appear in the expression of the modified stretch.In order to give a clearer explanation on the physical implication of the internal variables,a connection between the internal-variable theory and theoretical formulation based on the multiplicative decomposition of the deformation gradient in existing literature is presented in this paper,which allows the above internal-variable theory to be more systematic.

An internal-variable theory of thermo-viscoelastic constitutive relations at finite strain

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 consti-tutive theory in thermo-viscoelasticity at finite strain is formulated. An explicit expression of a thermo-viscoelastic 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 be-tween 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.

STRESS ANALYSIS OF INJECTION MOLDED PARTS IN POST-FILLING STAGE

The linear isothermo-viscoelastic constitutive equation is established according to the principle of viscoelastic mechanics. Given the boundary conditions of the temperature field, the linear thermo-viscoelastic constitutive equation is established acording to the analysis of the thermorheologically simple. The stress analysis model is constructed on the base of some reasonable hypotheses which consider the restraint conditions of mold and the characteristics of injection molding in the post-filling stage. The mathematical model is calculated by the finite difference method. The results can help to predict the warpage of plastic products.

Novel model of thermo-magneto-viscoelastic medium with variable thermal conductivity under effect of gravity

The basic equations for a homogeneous and isotropic thermo-magnetoviscoelastic medium are formulated based on three different theories, i.e., the GreenLindsay(G-L) theory, the coupled(CD) theory, and the Lord-Shulman(L-S) theory. The variable thermal conductivity is considered as a linear function of the temperature. Using suitable non-dimensional variables, these basic equations are solved via the eigenvalue approach. The medium is initially assumed to be stress-free and subject to a thermal shock.The numerical results reveal that the viscosity, the two-temperature parameter, the gravity term, and the magnetic field significantly influence the distribution of the physical quantities of the thermoelastic medium.

MECHANICAL BEHAVIOR OF AMORPHOUS POLYMERS IN SHEAR

Based on the non-equilibrium thermodynamic theory, a new thermo-viscoelastic constitutive model for an incompressible material is proposed. This model can be considered as a kind of generalization of the non-Gaussian network theory in rubber elasticity to include the viscous and the thermal effects. A set of second rank tensorial internal variables was introduced, and in order to adequately describe the evolution of these internal variables, a new expression of the Helmholtz free energy was suggested. The mechanical behavior of the thermo-viscoelastic material under simple shear deformation was studied, and the “viscous dissipation induced” anisotropy due to the change of orientation distribution of molecular chains was examined. Influences of strain rate and thermal softening produced by the viscous dissipation on the shear stress were also discussed. Finally, the model predictions were compared with the experimental results performed by G'Sell et al., thus the validity of the proposed model is verified.

Nonlinear Viscoelastic Response of Thermoplastic-Elastomer Melts

Observations are reported on thermoplastic elastomer(ethylene-octene copolymer)melt in small-amplitude shear oscillatory tests and start-up shear tests with various strain rates in the interval of temperatures between 120 and 210◦C.Based on the concept of heterogeneous non-affine polymer networks,constitutive equations are developed for the thermo-mechanical behavior of a melt at threedimensional deformations with finite strains.Adjustable parameters in the stress–strain relations are found by fitting the experimental data.The model is applied to the analysis of Poiseuille flow.The effects of temperature and pressure gradient on the steady velocity profile are studied numerically.