橡胶材料的非线性黏弹性本构方程

橡胶是一种非线性黏弹性材料,准确描述其非线性黏弹性力学响应的本构方程是橡胶材料及制品设计优化的关键。文中基于超弹性模型和并行流变模型(PRF)描述了橡胶材料的非线性黏弹性响应特征,重点探讨了由实验数据确定PRF本构方程材料参数的方法。首先通过单轴拉伸实验数据拟合得到超弹性模型,将应力松弛实验数据拟合得到表征材料线性黏弹性的模型-Prony级数,再将Prony级数转化为初始的PRF模型,进而不断优化得到PRF模型的准确材料参数,最后进行实验验证。结果表明,PRF模型计算的不同应变下的应力松弛数据与实验数据之间的误差仅为0.067%,PRF能准确地描述橡胶材料非线性响应的应力松弛行为。     

玄武岩纤维混凝土的冲击力学行为及本构模型

采用Φ100mm分离式霍普金森压杆(SHPB)试验装置研究了玄武岩纤维混凝土在不同应变率下的冲击力学行为,并将其与基体混凝土进行对比分析;采用朱-王-唐(ZWT)模型,在试验研究的基础上,建立了考虑纤维三维随机分布效应的玄武岩纤维混凝土非线性粘弹性本构模型,并与SHPB试验结果进行比较。结果表明:玄武岩纤维混凝土的冲击压缩强度与能量吸收能力,较素混凝土有明显提高,具备优异的冲击力学性能;本构模型提供的理论曲线与试验曲线比较接近,改进后的ZWT模型可以较为准确地描述玄武岩纤维混凝土的高应变率力学行为。     

三维正交机织玻璃纤维/环氧树脂复合材料动态力学性能的实验和理论研究

通过实验系统研究了三维正交机织玻璃纤维/环氧树脂复合材料厚度方向和面内方向的动、 静态压缩力学性能。结果表明, 动、 静态压缩载荷作用下该材料响应表现出明显的各向异性、 非线性和应变率敏感性。针对三维正交机织玻璃纤维/环氧树脂复合材料高速变形过程中不同形式的内部缺陷和微损伤的演化, 提出了一个依赖应变、 应变率的宏观损伤量, 建立了一种含损伤的非线性黏弹性本构模型。采用数据处理方法拟合了其本构方程材料参数, 在加载过程中, 模型计算值与实验结果吻合较好。     

泡沫塑料包装衬垫缓冲性能建模

本文从非线性粘弹性物质的多重积分型本构方程出发,引入塑性应变,推导了粘弹塑性物质的微分型本构方程.进一步考虑材料的损伤特性,建立了泡沫塑料包装衬垫的缓冲性能模型.根据在一种跌落高度、衬垫厚度和静态应力组合条件下的国产可发聚苯乙烯沫泡塑料的连续多次跌落冲击试验数据,识别了其缓冲性能模型参数.动力学计算与试验结果的比较表明,该模型能较好地反映可发聚苯乙烯泡沫塑料包装衬垫在连续多次跌落冲击过程中的加速度、速度、位移变化,冲击能量的吸收性和塑性变形等基本特性.并且仅根据在一种组合条件下的试验数据所识别的这一模型,在其它组合条件下其缓冲性能与试验结果也吻合较好.     

轴向运动黏弹性梁横向非线性受迫振动

运用微分求积法数值研究不同边界条件下轴向运动黏弹性梁受到简谐外激励的横向受迫     

Time integration in linear viscoelasticity—a comparative study

One of the key tasks in computational viscoelasticity is the time integration of the constitutive equation. It is important that the behaviour of the integrators is well understood since they are used in a variety of applications. In the present paper, the performance of conventional semi-analytical methods and implicit Runge-Kutta methods for the integral model of linear viscoelasticity with Prony series is evaluated analytically and numerically. Although a linear viscoelastic constitutive equation is considered, the analyzed integrators can be extended to handle also Schapery-type nonlinear constitutive equations. Numerical examples involving a simple uniaxial problem and multiaxial simulations are presented in order to analyze and compare the time integrators.     

A thermodynamic study of materials representable by integral expansions

A thermodynamic formulation is developed for nonlinear compressible viscoelastic materials and is used to quantitatively study the thermodynamic states associated with fracture. The Helmholtz free energy is assumed to be approximated by a fourth order multiple integral expansion on the histories of the Lagrangian strain tensor and temperature, and the first and second laws are then utilized to develop a constitutive equation and dissipation function for the material. Simplified expressions are obtained for the special cases of slow motions and long term steady flows. An experimental study is then made on equi-temperature metamorphosed snow, a nonlinear viscoelastic material, to determine the states associated with fracture for a variety of deformation paths. In view of the experimental study, the author is able to conclude that this approach to fracture investigation can produce much insight on the strength properties and may be instrumental in the formulation of a useful fracture criterion of materials for which the fracture condition is history dependent. Additionally, due to the thermodynamic nature of this approach, the information gathered could be useful in investigations of crack growth in nonlinear viscoelastic materials such as snow or even in the formulation of structural constitutive equations.     

正弦型黏弹性拱的非线性动力学行为研究

利用分数导数的本构关系建立了粘弹性拱的控制方程,采用Galerkin方法简化了拱的数学模型。提出一种求解含分数算子的非线性方程的数值方法,并利用该方法对控制方程进行求解。考察载荷参数、材料参数对拱动力响应的影响。运用非线性动力学中各种经典的分析方法,如时程曲线、功率谱、相图、庞加莱截面等,判别并揭示了粘弹性拱的丰富的动力学行为。     

新型碳酚醛材料动静态力学性能和本构关系研究

研究了碳纤维增强酚醛复合材料在不同温度下的动静态压缩力学性能，碳酚醛材料不但是应变率敏感材料，也是温度相关材料；提出了一个非线性粘弹性本构方程，通过对实验应力-应变曲线的拟合给出了本构方程的材料参数，讨论了温度对本构方程参数的影响；分析了材料力学行为的时温等效性，给出了不同加载条件下的时温等效曲线。     

具有几何和物理非线性粘弹性梁的混沌运动

建立了描述具有几何和物理非线性均匀梁动力学行为的偏微分－积分方程,梁的材料满足Leaderman非线性本构关系。对于两端简支的情形,采用Galerkin方法简化为常微分－积分方程;然后通过引进附加变量的方法进一步简化为常微分方程;最后利用相平面图、功率谱和Lyapunov指数等非线性动力学中的数值方法识别梁的动力学行为。结果表明梁的运动呈现混沌性态。     

Nonlinear constitutive equations for transient creep of viscoelastic polymers including the effect of hydrostatic pressure

The behaviour of polymers is known to be significantly influenced by the hydrostatic pressure in creep deformation or elastic-plastic deformation. The effect of the third stress invariant on the nonlinear viscoelastic deformation is much smaller than that of the hydrostatic pressure. In this paper, a constitutive equation for transient creep is proposed, which includes the effect of the hydrostatic pressure on the yield function. The creep and plastic strains or the creep strain rate converge to zero with increasing hydrostatic pressure. The proposed constitutive equation is in good agreement with the actual creep data of cellulose nitrate and cellulose acetate, under various combinations of superimposed tensile and hydrostatic loadings.     

Micro-Macro Analysis of Viscoelastic Unidirectional Laminated Composite Plates Using DR Method

The Dynamic Relaxation (DR) technique together with finite difference discritization is used to study the bending behavior of Mindlin composite plate including geometric nonlinearity. The overall behavior of the unidirectional composite is obtained from a three-dimensional (3D) micromechanical model, in any combination of normal and shear loading conditions, based on the assumptions of Simplified Unit Cell Method (SUCM). The composite system consists of nonlinear viscoelastic matrix reinforced by transversely isotropic elastic fibers. A recursive formulation for the hereditary integral of the Schapery viscoelastic constitutive equation in multiaxial stress state is used to model the nonlinear viscoelastic matrix material in the material level. The creep tests data is used for verification of the predicted response of the current approach. Under uniform lateral pressure, the laminated plate deformation with clamped and hinged edged constraints is predicted for various time steps.     

求解一类非线性粘弹性问题的弹性回复对应原理

本文提出了一个全新的粘弹性理论体系,它把传统的线粘弹性理论作为特殊情况包括在内。其主要结果是两个用于求解一类物理非线性粘弹性问题的弹性回复对应原理。利用它,只要知道相应的非线性弹性问题的解,就可以求出非线性粘弹性问题的解答。对应原理不是基于本构关系的相似性,而是基于从粘弹性现时响应到瞬时弹性响应的可回复性[1]。首先找到非线性粘弹性与非线性弹性本构关系之间的对应,然后导出了两个弹性回复对应原理。通过对改性聚丙烯材料的实验验证了该对应原理的正确性和对此类材料的实用性。     

纵向振动粘弹性桩的分叉和混沌运动

研究了轴向周期载荷作用下非线性粘弹性嵌岩桩纵向振动的混沌运动。假定桩和土体分别满足Leaderman非线性粘弹性本构关系和线性粘弹性本构关系,得到的运动方程为非线性积分-偏微分方程;利用Galerkin方法将方程简化,并进行了数值计算。数值结果表明纵向振动的非线性粘弹性桩可以通过准周期分叉的方式进入混沌运动。     

泡沫EPS非线性粘弹性本构模型在LS-DYNA空调跌落仿真中的研究

目的 研究泡沫EPS非线性粘弹性本构模型对空调跌落仿真精度的影响。方法 通过动态压缩试验获得泡沫EPS在不同应变率下的应力-应变结果,使用LS-DYNA中的非线性粘弹性本构模型Fu-Chang泡沫准确模拟泡沫在不同应变率下的力学性能,并通过空调跌落仿真进行验证。结果 使用不同应变率下的泡沫EPS非线性粘弹性本构模型进行仿真,空调不同位置的仿真加速度曲线和实际试验加速度曲线相似度在90%以上。结论 不同应变率下的泡沫EPS非线性粘弹性本构模型可以准确模拟EPS泡沫在动态冲击下的材料力学性能,可以更加准确地模拟跌落工况中空调结构的动态反应及泡沫失效状态,提高仿真精度。     

Numerical study on the nonlinear oscillations of a torsion absorber filled with a viscoelastic fluid

Summary. Results are presented concerning the mechanical behavior of a torsion absorber filled with a viscoelastic fluid. As regards the nonlinear constitutive equation of the viscoelastic filling, a multi-mode fluid model is used, leading to a set of coupled ordinary differential equations, which were solved numerically. The influence of different excitation strengths and frequencies on the energy dissipated per cycle in the periodic stage, as well as the resulting shear in the transient and fully developed stages are given and discussed. The findings for small excitation amplitude were compared to those resulting from linear theory.     

Nonlinear compressive deformation of viscoelastic porous materials

Two nonlinear viscoelastic solutions are presented for a porous, foam type material. The first is for the hydrostatic compression of the foam, while the second is for the one-dimensional compression of an infinite slab of the material. Relative to the particular viscoelastic constitutive equation employed, the first solution is exact, whereas the second, obtained through the use of a physical hypothesis, is approximate. Both solutions predict the macroscopic, average stress in the foam, required by the corresponding deformation processes. The theoretical results are compared with experimental measurements on a foam material at a porosity of 48.5%. The effect of material hysteresis is revealed and discussed.     

A nonlinear constitutive relationship for asphalt binders

A nonlinear constitutive relationship was developed for asphalt binders. Two binders, one polymer modified and one unmodified, were tested in shear using creep and recovery loading. Five different stress levels and four loading times were considered, to capture the response of the binders in the linear and nonlinear viscoelastic range. The creep response of the binders was successfully modeled with a nonlinear power law function. The modified superposition principle was unable to predict the recovery phase of the testing data. A nonlinear constitutive relationship composed of a nonlinear viscous part plus a linear viscoelastic part was developed. The constitutive relationships successfully predicted the binders’ response in creep and recovery. The predictions of the constitutive relationships matched accurately the response of the binders subjected to the Multiple Stress Creep and Recovery loading pattern.     

VPF粘性介质粘弹性本构关系研究

为研究粘性介质的力学性能对板材变形的影响,通过剪切蠕变-回复和松弛试验分析了甲基乙烯基粘性介质的流变性能.实验结果表明粘性介质可以简化为线性粘弹性材料.建立了粘性介质的积分型粘弹性本构方程,并结合剪切蠕变-回复过程的有限元分析确定了方程中的材料参数.利用该本构方程对粘性介质压力胀形过程进行了有限元分析,模拟结果与试验结果对比表明,所建立的本构方程可以较好的预测板材的变形过程.     

高分子材料非线性粘弹性问题的解法

尽管实验限制在小变形范围之内，高分子材料仍表现出明显的非线性粘弹性性能。目前由于分析上的困难，通常只好采用线粘弹性假设。基于前文，提出了一个求解高分子材料物理非线性（含线性）粘弹性问题的新原理，通过对改性聚丙烯材料的实验表明了该原理的正确性和对于此类材料的实用性。