Nonlinear Viscoelasticity Raised at Low Temperatures by Intermolecular Cooperation of Bulk Amorphous Polymers

We performed dynamic Monte Carlo simulations of stress relaxation in parallel-aligned and uniaxially stretched bulk amorphous polymers at low temperatures.We observed an extra-slowing down in the early stage of stress relaxation,which causes nonlinear viscoelasticity as deviated from Debye relaxation and Arrhenius-fluid behaviors observed previously at high temperatures.Meanwhile,fluctuation analysis of stress relaxation revealed a substantial increase in the stretch fractions of polymers at the transient periods of high-temperature Debye relaxation.Structural analysis of free volume further revealed the scenario that,at low temperatures,the modulus of polymer entropy elasticity decreases with temperature and eventually loses its competition to the imposed modulus(Deborah number becomes larger than one),and hence upon stress relaxation under constant strains,monomers are firstly accumulated nearby two stretching ends of polymers,resulting in tentative global jamming like physical cross-linking there,and thus retarding the coming transient state of stress relaxation.We concluded that intermolecular cooperation raises physical crosslinking for nonlinear viscoelasticity of polymer stress relaxation as well as the rubbery states unique to bulk amorphous polymers.The new microscopic mechanism of the fluid-rubbery transition of polymers may bring insights into the intermolecular cooperation mechanism of glass transition of small molecules,if the fluid-rubbery transition is regarded as an extrapolation of glass transition from low to high molecular weights.

A MOLECULAR NETWORK MODEL TO DESCRIBE THE NONLINEAR VISCOELASTIC BEHAVIOR OF POLYMERS

A transient molecular network model is built to describe the non- linear viscoelasticity of polymers by considering the effect of entanglement loss and regeneration on the relaxation of molecular strands. It is an extension of previous network theories. The experimental data on three thermoplastic polymers (ABS, PVC and PA6) obtained under various loading conditions are used to test the model. Agreement between the theoretical and experimental curves shows that the suggested model can describe successfully the relaxation behavior of the thermoplastic polymers under different loading rates by using relatively few relaxation modes. Thus the mi- cromechanism responsible for strain-rate dependence of relaxation process and the origin of nonlinear viscoelasticity may be disclosed.

CRACK PROPAGATION IN THE POWER-LAW NONLINEARVISCOELASTIC MATERIAL

An analysis on crack creep propagation problem of power-law nonlinear viscoelastic materials is presented. The Creep incompressilility assumption is used Tosimulate fracture behavior of craze region. it is assumed that in the .fracture processzone near the crack tip, the cohesive stress fo acts upon the crack surfaces and resistscrack opening. Through a perturbation method i. e., by superposing the Mode-Iapplied force onto a referential uniform stress state, which has a trivial solution and gives no effect on the solution of the original problem, the nonlinear viscoelasticproblem is reduced to linear problem. For weak nonlinear materials, for which thepower-law index n=1, the expressions of stress and crack surface displacement arederived. Then, the fracture process zone local energy criterion is proposed and basedon which the formulas of crucking incubation time t. and crack slow propagationvelocity a are derired.

Fugue Effect on Bending of Nonlinear Viscoelastic Beams

Based on the Leaderman constitutive relations in nonlinear viscoelasticity and the linear geometrical assumption, a mathematical model for the bending of nonlinear viscoelastic beams was established in this paper. The Laplace transformation method and the Titchmarsh theorem were used to prove that some relations exist between solutions to bending problems of visco- and elastic beams, which reveals the fugue effect of viscoelastic materials. The high-order Galerkin approximate solution to the quasi-static response of nonlinear viscoelastic beams under a step load was obtained by using the new method suggested in this paper as well as the Mathematica software and the Newton iteration technique.

POWER LAW NONLINEAR VISCOELASTIC CRACK-TIP FIELDS

The aim of this paper is to derive the power law type nonlinear viscoelastic crack-tip fields.For the requirement of later derivation,the HRR singular fields and the high-order asymp- totic fields are first examined.That they are essentially the isotropic,incompressible,power law type nonlinear elastic crack-tip fields is illustrated.After a concise review of the elasticity recov- ery correspondence principle for solving the nonlinear viscoelastic problems,the correspondence principle for solving the crack problems of power law type nonlinear viscoelastic materials under the first type boundary condition is proposed.The solution of the crack-tip stress,strain fields for the power law type nonlinear viscoelastic materials,especially for the modified polypropylene, is obtained.

A MICROMECHANICAL ANALYSIS OF THE NONLINEAR ELASTIC AND VISCOELASTIC CONSTITUTIVE RELATION OF A POLYMER FILLED WITH RIGID PARTICLES

Micromechanical theory is applied to study the nonlinear elastic and viscoelastic constitutive relations of polymeric matrix filled with high rigidity solid particles. It is shown that Eshelby's method can be extended to the case of nonlinear matrix and Eshelby's tensor still exists provided that Poisson's ratio of the nonlinear matrix assumes constant value in deforming process and the rigidity of elastic filling particles is much higher than that of the matrix. A new method for averaging process is proposed to overcome the difficulty that occured in applying the ordinary equivalent inclusion method or the seff-consistant method to nonlinear matrices. A rather simple constitutive equation is obtained finally and the strengthening effect of solid particles to composites is investigated.

Modeling the Tensile Properties of Soybean Protein Yarns

The tensile properties of a series of soybean protein yarns are tested in USTER THINKPAID Ⅲ. A nonlinear viscoelastic model has been proposed to describe the tensile behavior of soybean protein yarns. The model is composed of a Maxwell element, a linear spring and a nonlinear spring. The tensile properties of soybean protein yam are analyzed. The stress-strain curves of the yams are fitted. The average breaking tenacity and specific work of rupture are calculated using the average breaking strain. Comparisons indicate that theoretical predictions conform the experimental results very well.

HIGH ACCURACY ANALYSIS OF THE FINITE ELEMENT METHOD FOR NONLINEAR VISCOELASTIC WAVE EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS

The standard finite elements of degree p over the rectangular meshes are applied to solve a kind of nonlinear viscoelastic wave equations with nonlinear boundary conditions, and the superclose property of the continuous Galerkin approximation is derived without using the nonclassical elliptic projection of the exact solution of the model problem. The global superconvergence of one order higher than the traditional error estimate is also obtained through the postprocessing technique.

Global Existence and Exponential Decay for a Nonlinear Viscoelastic Equation with Nonlinear Damping

In this paper we investigate a nonlinear viscoelastic equation with nonlinear damping. Global existence of weak solutions and uniform decay of the energy have been established. The Faedo-Galerkin method and the perturbed energy method are employed to obtain the results.

Nonlinear vibration analysis of fractional viscoelastic Euler–Bernoulli nanobeams based on the surface stress theory

The nonlinear vibrations of viscoelastic Euler-Bernoulli nanobeams are studied using the fractional calculus and the Gurtin-Murdoch theory. Employing Hamilton＇s principle, the governing equation considering surface effects is derived. The fractional integro-partial differential governing equation is first converted into a fractional-ordinary differential equation in the time domain using the Galerkin scheme. Thereafter, the set of nonlinear fractional time-dependent equations expressed in a state-space form is solved using the predictorcorrector method. Finally, the effects of initial displacement, fractional derivative order, viscoelasticity coefficient, surface parameters and thickness-to-length ratio on the nonlinear time response of simply-supported and clamped-free silicon viscoelastic nanobeams are investigated.

Traveling Wave Solutions to the Three-Dimensional Nonlinear Viscoelastic System

In this paper, we establish the existence of traveling wave solutions to the nonlinear three-dimensional viscoelastic system exhibiting long range memory. Under certain hypotheses, if the speed of propagation is between the speeds determined by the equilibrium and instantaneous elastic tensors, then the system has nontrivial trav- eling wave solutions. Moreover, the system has only trivial traveling wave solution in some cases.

GENERAL DECAY RATE ESTIMATES FOR VISCOELASTIC WAVE EQUATION WITH VARIABLE COEFFICIENTS

The authors study decay properties of solutions for a viscoelastic wave equation with variable coefficients and a nonlinear boundary damping by the differential geometric approach.