有限变形下橡胶材料非线性高弹-粘弹性本构模型

基于唯象学原理提出一种适用于橡胶材料在有限应变条件下的非线性高弹-粘弹性本构模型。该模型将应力拆分为两部分:基于Yeoh模型计算得到的高弹性应力和由Boltzmann叠加原理计算得到的带有率依赖性的粘弹性应力。该本构模型中具有应变依赖性的高弹性应力通过修正Zener模型中的非线性弹簧表示,具有时间及应变依赖性的粘弹性应力通过修正Zener模型中的非线性Maxwell模型表示。利用此本构模型模拟不同应变下的拉伸、回复、应力松弛及多步松弛的复杂加载过程,与试验结果的吻合性良好,说明该本构模型合理、可靠。     

橡胶材料非线性高弹-粘弹性本构模型

本文提出的修正Zener模型,即以非线性弹簧与粘壶代替原来的线性弹簧与粘壶,得到一种适合橡胶材料在单轴作用下的非线性高弹-粘弹性本构模型。该模型可同时描述加载、卸载及应力松弛行为。模型将应力分解为弹性应力与粘性应力。弹性应力由Yeoh高弹性模型得到;粘性应力由加载及卸载过程的瞬时应力通过积分变换得到。此外考虑到应力松弛的作用,因此将粘性应力分解成两部分：一是在加载、卸载过程所用时间内由应变的改变所导致的粘性力;二是在该时间内由应力松弛所产生的反作用力。最后,将实验结果与该模型的计算结果进行对比,结果表明计算结果与实验结果具有良好的一致性,说明该本构模型可靠、合理。     

橡胶材料非线性高弹-粘弹性本构模型的研究

建立橡胶材料的非线性高弹-粘弹性本构模型。高弹-粘弹性本构模型的总应力可分解为弹性应力与粘性应力之和,考虑到应力松弛的影响,将粘性应力分解为在加载与卸载过程中应变变化产生的粘性应力与应力松弛产生的反作用力之和。对比测试与模拟数据以验证本构模型的可靠性。结果表明:本构模型能同时模拟加载、卸载与应力松弛过程,应力松弛与多步应力松弛试验也验证了本构模型的非线性与对时间的依赖性,进一步说明本构模型的可靠性与合理性。     

橡胶材料的混合高弹性本构模型研究

基于分子统计理论提出了一种适用于橡胶材料的混合高弹本构模型。采用修正Gaussian模型和修正8-链网络模型的非线性组合分别描述Gaussian变形和非Gaussian变形部分;对于微观层面上的分子链密度和宏观层面上的拉伸比,均将其分解为Gaussian变形和非Gaussian变形部分。不同拉伸模式下的应力-应变试验数据与Treloar数据的拟合对比证明了混合本构模型的适用性,且与Gaussian模型、3-链网络模型和8-链网络模型对比,其精确性有明显提高。     

AC-13级配钢渣沥青混合料粘弹塑本构模型研究

为了研究钢渣沥青混合料非线性粘弹塑性变形特性,提出Schapery模型与改进Swchartz模型组合的积分型粘弹塑本构模型。采用钢渣替换AC-13级配中粒径2.36 mm以上的石灰石粗骨料,制作得到钢渣沥青混合料试件。设计并开展一系列的单轴压缩蠕变实验,通过应力递增蠕变回复实验,获得不同应力条件下材料的弹性、粘弹性应变和粘塑性应变,进而拟合确定本构模型参数。利用0.4 MPa、1.0 MPa下的蠕变回复实验验证模型有效性。结果表明,模型不仅能准确刻画钢渣沥青混合料蠕变过程中的弹性、粘弹性与粘塑性变形,还可用于预测不同应力水平下钢渣沥青混合料蠕变变形规律。     

隔振橡胶材料基于简单应变模式的 蠕变特性研究

对隔振橡胶材料的单轴拉伸应力松弛试验数据进行归一化处理,应用Prony级数模型对其应力松弛试验数据进行拟合,获得对应的粘弹本构参数。将表征粘弹特性的Prony级数因子引入Ogden超弹本构方程,获得隔振橡胶材料基于时间效应的本构方程,进而分析单轴拉伸、双轴拉伸和平面拉伸模式的蠕变特性,最后采用沙漏弹簧进行蠕变仿真与试验验证。该蠕变仿真预测方法为隔振橡胶材料的粘弹试验、蠕变计算和工程应用提供一种新思路。     

基于超弹-黏弹本构模型的橡胶材料有限元分析

要确定橡胶制品在外部因素作用下的力学响应,就需要建立起能够精确描述橡胶材料力学性能的本构模型。通过对橡胶材料进行单轴压缩以及应力松弛实验,并与ABAQUS数值模拟相结合,建立并拟合了橡胶材料超弹-黏弹本构模型以及相关参数,同时建立了与实验条件一致的仿真模型。结果表明,实验数据与仿真数据的误差较小,验证了建立的超弹-黏弹本构模型的准确性。     

PE80燃气管道的应力松弛模型与实验验证

采用实验方法研究聚乙烯(PE)管道在机械载荷条件下的应力松弛行为,通过卷积分解析法和基于Maxwell模型的有限单元数值模拟法对其进行验证。结果表明,在小应变下采用Boltzmann叠加原理推导出的PE黏弹性本构模型可用于预测PE管道的应力松弛行为;基于实验参数,利用有限单元法能有效地对PE的黏弹性行为进行预测。     

航空轮胎的准静态粘弹性有限元模型

为了计算粘弹性应力,修正了弹性大位移壳体混合有限元。在单元应变节点采用了内应变变量,并用内应变变量来建立粘性材料模型。一阶常微分方程建立了内应变变量与在应力节点的相应弹性应变的关系式。采用为弹性模量几分之一的粘性模量根据内应变变量可计算出粘弹性应力。在混合变分函数中包含有由于粘性应力而产生的能耗散。这样,可以获得非线性准静态粘弹性平衡公式。为了将粘性项列入公式中,对此前展开的有关非线性弹性平衡公式的泰勒展开式进行了修正。采用预示校正时间步进求解算法进行求解代数微分方程。用粘性壳体元素计算模拟了航空轮胎在与非摩擦表面接触时的梯级负载加载和卸载。     

黏弹流体动态黏度数学模型与实验研究

针对经典Maxwell本构模型的局限性进行了相应的非线性修正,提出了一种新的黏弹本构模型,利用修正模型和基于黏性耗散机理建立的黏滞动力方程,得到了振动剪切流场黏弹流体的动态黏度函数.通过将动态黏度函数应用于简单振动剪切流,得到了与传统计算方法相一致的结果.最后,进行了同轴圆筒动态流变实验.实验数据与垂直叠加振动剪切流场中LDPE熔体黏度的理论值进行了对比,发现动态黏度函数在小振幅范围内具有较好的预测能力.     

Constitutive modeling of visco-hyperelastic behavior of double-network hydrogels using long-term memory theory

Double-network hydrogels with viscoelastic behavior are appropriate materials for biomechanical applications. In this article, the standard linear solid (SLS) rheological model for the linear viscoelastic materials is generalized to the viscoelastic materials with large nonlinear deformations. Based on this viewpoint, the constitutive equation is proposed as sum of two parts including the strain-dependent elastic stress, and the viscous stress, which depends on the strain and strain rate. The elastic part of the stress is modeled via considering a hyperelastic strain energy function, while the main core of the viscous stress part requires a time-dependent weight function to satisfy the long-term memory fading principle. In addition, the weight function is proposed such that it can capture the mechanical behavior trend corresponding to the strain and strain rate for a double-network hydrogel in the relaxation test. Finally, to evaluate the performance of the proposed constitutive equation for the mechanical behavior modeling of double-network hydrogels, the tests on these materials have been used, and the material parameters are determined from fitting the experimental results to the theory. The agreement of test and theory results showed that the proposed model is capable to model the mechanical behavior of double-network hydrogels.     

Modeling of visco‐hyperelastic behavior of transversely isotropic functionally graded rubbers

In this article, visco‐hyperelastic constitutive model is developed to describe the rate‐dependent behavior of transversely isotropic functionally graded rubber‐like materials at finite deformations. Zener model that consists of Maxwell element parallel to a hyperelastic equilibrium spring is used in this article. Steady state response is described by equilibrium hyperelastic spring and rate‐dependence behavior is modeled by Maxwell element that consists of a hyperelastic intermediate spring and a nonlinear viscous damper. Modified and reinforced neo‐Hookean strain energy function is proposed for the two hyperelastic springs. The mechanical properties and material constants of strain energy function are graded along the axial direction based on exponential function. A history‐integral method has been used to develop a constitutive equation for modeling the behavior of the model. The applied history integral method is based on the Kaye‐BKZ theory. The material constant parameters appeared in the formulation have been determined with the aid of available uniaxial tensile experimental tests for a specific material and the results are compared to experimental results. It is then concluded that, the proposed constitutive equation is quite proficient in forecasting the behavior of rubber‐like materials in different deformation and wide ranges of strain rate. POLYM. ENG. SCI., 56:342–347, 2016. © 2016 Society of Plastics Engineers     

A rate‐type nonlinear viscoelastic–viscoplastic cyclic constitutive model for polymers: Theory and application

A thermodynamically consistent rate‐type viscoelastic–viscoplastic constitutive model is developed in the framework of isothermal and small deformation to describe the nonlinear and time‐dependent deformation behaviors of polymers, e.g., ratchetting, creep, and stress relaxation. The model is proposed on the base of a one‐dimensional rheological model with several springs and dashpot elements. The strain is divided into viscoelastic and viscoplastic parts, and the stress is also decomposed into two components. Each stress component is further divided into elastic and viscoelastic sub‐components. The viscoelasticity is described by introducing pseudo potentials, and the ratchetting is considered by the viscoplastic flow which is derived by the codirectionality hypotheses. The capability of the proposed model to describe the nonlinear and time‐dependent deformation of polymers is then verified by comparing the simulations with the corresponding experimental results of polycarbonate (PC) polymer. It is shown that the nonlinear and time‐dependent stress–strain responses of the PC can be reasonably predicted by the proposed model. POLYM. ENG. SCI., 56:1375–1381, 2016. © 2016 Society of Plastics Engineers     

A thermodynamically consistent, nonlinear viscoelastic approach for modeling glassy polymers

A thermodynamically consistent nonlinear viscoelastic constitutive theory is derived to capture the wide range of behavior observed in glassy polymers, including such phenomena as yield, stress/volume/enthalpy relaxation, nonlinear stress-strain behavior in complex loading histories, and physical aging. The Helmholtz free energy for an isotropic, thermorheologically simple, viscoelastic material is constructed, and quantities such as the stress and entropy are determined from the Helmholtz potential using Rational Mechanics. The constitutive theory employs a generalized strain measure and a material clock, where the rate of relaxation is controlled by the internal energy that is likewise determined consistently from the viscoelastic Helmholtz potential. This is perhaps the simplest model consistent with the basic requirements of continuum physics, where the rate of relaxation depends upon the thermodynamic state of the polymer. The predictions of the model are compared with extensive experimental data in the following companion paper.     

Nonlinear viscoelastic modeling of soft polymers

A one‐dimensional phenomenological constitutive model, representing the nonlinear viscoelastic behavior of polymers is developed in this study. The proposed model is based on a modification of the well‐known three element standard solid model. The linear dashpot is replaced by an Eyring type one, while the nonlinearity is enhanced by a nonlinear, strain dependent spring constant. The new constitutive model was proved to be capable of capturing the main aspects of nonlinear viscoelastic response, namely, monotonic and cyclic loading, creep and stress relaxation, with the same parameter values. Model validation was tested on the experimental results at various modes of deformation for two elastomeric type materials, performed elsewhere. A very good agreement between model simulations and experimental data was obtained in all cases. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 42141.     

Prediction of the relationship between the rate of deformation and the rate of stress relaxation in glassy polymers

Kim, et al. (Polymer, 54(15), 3949, 2013) recently reported on the unexpected relaxation behavior of an amorphous polymer in the T_g-region, where the rate of stress relaxation increased with deformation at a strain rate of 1.5 × 10⁻⁴ s⁻¹ but decreased at a strain rate of 1.2 × 10⁻⁵ s⁻¹. This inversion in the ordering with strain rate challenges the underlying structure of the existing nonlinear viscoelastic and viscoplastic constitutive models, where the key nonlinearity is a deformation dependent material clock. The nonlinear stress relaxation predictions of a recently developed stochastic constitutive model, SCM, (Medvedev, et al., J. Rheology, 57(3), 949, 2013) that acknowledge dynamic heterogeneity of the glass have been investigated. The SCM predicts the inversion in the ordering of the mobility with the loading strain rate as reported by the stress relaxation response. The change in perspective on the nonlinear viscoelastic behavior of glassy polymers engendered by the SCM is discussed.     

On Mooney and Mooney stress relaxation. II. A nonlinear viscoelastic description: Experimental and numerical results

It has been investigated whether the stress build‐up and the stress relaxation involved in a Mooney test, with subsequent Mooney stress relaxation, can be described by nonlinear viscoelastic theory, more particularly the Wagner constitutive model. For this purpose, the viscoelastic behavior of three nonvulcanized EPDM materials, with similar Mooney viscosity but varying elasticity, has been studied. Relaxation time spectra were obtained from dynamic mechanical experiments, from which the step‐strain stress‐relaxation modulus was calculated. Stress build‐up experiments were performed with a cone and plate system in order to obtain the so‐called damping function (a measure for the deformation sensitivity) of the materials. Using these material functions, the Mooney test was successfully described with the Wagner constitutive model. Experimental and theoretical Mooney stress‐relaxation rates are in close agreement. The predicted Mooney viscosity is up to 25% lower than the measured value. This may be due to nonideal conditions during the Mooney test, such as inhomogeneous heating and secondary flows, and to inaccuracy of the damping function. The model calculations confirm the strong experimental dependence of Mooney measurements on small variations in instrumental conditions such as geometry, rotation speed, and so forth. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 74: 1220–1233, 1999     

Effects of loading rate on viscoplastic properties of polymer geosynthetics and its constitutive modeling

On the basis of the special tensile test results under various loading histories, the rate‐dependent behaviors of three polymer geosynthetics due to their viscous properties have been investigated. All the investigated polymer geosynthetics show significant loading rate effects, creep deformation, and stress relaxation. Except for the polyester geogrid showing the combined viscosity, all the investigated polymer geosynthetics exhibit the isotach viscosity. An elasto‐viscoplastic constitutive model described in a nonlinear three‐component model framework is developed to simulate the rate‐dependent behaviors of polymer geosynthetics. The developed constitutive model is verified by comparing its simulated results with the experimental data of polymer geosynthetics presented in this study and those available from the literature. The comparison indicates that the developed model can reasonably interpret the rate‐dependent behaviors of polymer geosynthetics under arbitrary loading histories, including the step‐changed strain rate loading, creep, and stress relaxation applied during otherwise monotonic loading (ML). POLYM. ENG. SCI., 2010. © 2009 Society of Plastics Engineers     

Nonlinear mechanical response of high density polyethylene. Part I: Experimental investigation and model evaluation

The nonlinear behavior of high density polyethylene (HDPE) is investigated for samples cut from thick-walled HDPE pipe. Extensive experimental work has been performed to characterize the non-linear time-dependent response of the material tested under uniaxial compression. Tests were conducted under conditions of constant strain rate, creep, stress relaxation, constant loading rate, abrupt change of strain rate, creep-recovery, cyclic strain rate, and various combinations of these loading conditions. Creep and stress relaxation response after strain reversal and the effect of the transient response on the following stress-strain behavior is examined. Permanent strains for the test specimens and their dependence on loading histories are investigated. Specimens cut at various orientations from the pipe are used to quantify the small amounts of local anisotropy in the pipe specimen. The experimental work has been used to develop both nonlinear viscoelastic (NVE) and viscoplastic (VP) constitutive models in a companion paper. Both the test results and the corresponding model predictions are reported in this paper. It is found that the VP model reproduces the nonlinear viscoelastic-viscoplastic behavior of HDPE very well provided that the current strain is not below the maximum strain imposed (there is no strain reversal). The NVE model predicts the material behavior reasonably well for some loading conditions, but inadequately for others.