多孔硅橡胶有限变形的弹性行为

针对孔隙度较大 (孔隙度大于 5 0 % )的硅橡胶材料在压缩情况下的大变形 ,提出了可描述此类可压橡胶材料力学行为的应变能密度函数 ,推导了硅橡胶材料的本构方程。利用硅橡胶材料的单轴压缩实验进行了材料参数拟合 ,讨论了多孔硅橡胶的孔隙度和体积变形对压缩性能的影响     

粘弹性材料的变形动力学模型

粘弹性材料的变形动力学模型周建平（长沙国防科技大学，４１００７３）关键词粘弹性，本构关系，内变量，老化１引言许多工程材料，特别是聚合物材料的应力应变关系具有粘弹性特征，使得材料或结构在受力过程中发生蠕变或应力松弛现象．从微观上讲，这种粘弹性变形是由于...     

超弹性材料本构关系的最新研究进展

超弹性材料是工程实际中的常用材料, 具有在外力作用下经历非常大变形、在外力撤去后完全恢复至初始状态的特征. 超弹性材料是典型的非线性弹性材料, 其性能可通过材料的应变能函数予以表征. 近几十年来, 围绕应变能函数形式的构造, 已提出许多超弹性材料本构关系研究的数学模型和物理模型, 但适用于多种变形模式和全变形范围的完全本构关系仍是该领域期待解决的重要问题. 本文从3个不同角度, 对超弹性材料本构关系研究的最新进展进行了总结和分析: (1)不同体积变化模式, 包含不可压与可压两种; (2)多变形模式, 包含单轴拉伸、剪切、等双轴以及复合拉剪等多个种类; (3)全范围变形程度, 包含小变形、中等变形到较大变形范围. 超弹性材料本构关系研究的最新进展表明, 为了全面描述具体材料的实验数据并在实际问题中应用超弹性材料, 需要建立适合于多种变形模式和全变形范围的可压超弹性材料的完全本构关系. 对实际超弹性材料完全本构关系的建立及可压超弹性材料应变能函数的构造, 笔者还提出了相应的实施步骤和研究方法.      

在有限变形条件下损伤粘弹性梁的动力学行为

本文在有限变形条件下，根据损伤粘弹性材料的一种卷积型本构关系和温克列假设，建立了粘弹性基础上损伤粘弹性Timoshenko梁的控制方程。这是一组非线性积分——偏微分方程。为了便于分析，首先利用Galerkin方法对该方程组进行简化，得到一组非线性积分一常微分方程。然后应用非线性动力学中的数值方法，分析了粘弹性地基上损伤粘弹性Timoshenko梁的非线性动力学行为，得到了简化系统的相平面图、Poincare截面和分叉图等。考察了材料参数和载荷参数等对梁的动力学行为的影响。特别，考察了基础和损伤对粘弹性梁的动力学行为的影响。     

96.5Sn-3.5Ag钎料合金的时相关单轴应变循环变形行为及其本构关系研究

在室温下对96.5Sn-3.5Ag钎料合金进行了不同加载波形下的单轴应变循环实验。研究了在具有不同保持时间、不同应变率、不同应变幅值及其历史对材料的循环变形行为的影响。基于材料时相关变形行为,提出了统一粘塑性本构模型,并对该材料的变形行为进行本构模拟。实验结果表明:该钎料合金单轴变形行为具有应变率、保持时间以及应变幅值依赖性。本构关系的预言结果与实验结果吻合得一致性说明该种模型能够很好地描述材料的单轴应变循环变形行为。     

填充橡胶温度依赖的非弹性力学行为实验研究

填充橡胶具有复杂的非弹性力学行为，主要包括应变率依赖的粘弹性效应和变形历史依赖的Mullins效应。当前大多数对填充橡胶的实验研究集中于室温条件，针对以上问题，本文通过单轴压缩实验系统地研究了温度对氟橡胶粘弹性和Mullins效应这两种非弹性行为的影响。首先采用多次循环加载获得了完全消除了Mullins效应的预处理试样。通过对原试样和预处理试样的单轴加卸载实验应力响应进行对比，发现Mullins效应不受变形温度和应变率的影响。通过对消除Mullins效应橡胶材料应力松弛实验结果分析，发现粘弹性行为不仅与变形的温度、应变率相关，还受加载应变的影响，表现为较大的加载应变会抑制氟橡胶的应力松弛。     

加载速度对两种缓冲包装材料静态压缩特性的影响

聚苯乙烯和聚乙烯缓冲包装材料是粘弹性材料．本文的实验研究表明，当应变速度在一定范围内变化时此类材料与时间有关的应力可分离为一个时间函数与一个应变函数的乘积．分析结果还表明，测定此类材料的静态压缩特性时，加载速度在一定范围内的变化对试验结果的影响可以略去不计．     

基于变形动力学模型的黏弹性材料本构关系

本文从分子运动学理论出发建立了表征材料粘弹性变形的内变量演变方程,从不可逆过程热力学的基本方程和该内变量演变方程导出了积分型线性粘弹性应力应变关系。     

近似不可压软材料动力分析的完全拉格朗日物质点法

物质点法(MPM)在模拟非线性动力问题时具有很好的效果, 其已被广泛应用于许多大变形动力问题的分析中. 然而传统的MPM在模拟不可压或近似不可压材料的动力学行为时会产生体积自锁, 极大地影响模拟精度和收敛性. 本文针对近似不可压软材料的大变形动力学行为, 提出一种混合格式的显式完全拉格朗日物质点法(TLMPM). 首先基于近似不可压软材料的体积部分应变能密度, 引入关于静水压力的方程; 之后将该方程与动量方程基于显式物质点法框架进行离散, 并采用完全拉格朗日格式消除物质点跨网格产生的误差, 提升大变形问题的模拟精度; 对位移和压强场采用不同阶次的B样条插值函数并通过引入针对体积变形的重映射技术改进了算法, 提升算法的准确性. 此外, 算法通过实施一种交错求解格式在每个时间步对位移场和压强场依次进行求解. 最后, 给出几个典型数值算例来验证本文所提出的混合格式TLMPM的有效性和准确性, 计算结果表明该方法可以有效处理体积自锁, 准确地模拟近似不可压软材料的大变形动力学行为.      

类橡胶材料变形直到破坏的显式本构模型

本文通过直接、显式的方法提出一个多轴可压缩应变能弹性势来模拟类橡胶材料受载荷直到软化破坏的变形行为．首先，我们提出一个多轴可压缩应变能函数；其次，通过特定的不变量，该多轴应变能函数在单轴拉伸，平面应变和等双轴拉伸三个基准实验的情况下，可以退化为各自的单轴形函数形式；再次，我们显式给出带有软化破坏特性的形函数；最后，模型结果和试验数据可以精确匹配，同时可以预测材料临近破坏以后，接下来的变形行为．     

一种适合橡胶类材料的非线性粘弹性本构模型

借助非线性流变模型建立大变形情况非线性粘弹材料的本构关系,考虑到大多数橡胶类材料具有的几乎不可压缩性,以及体积响应和剪切响应的流变性能不同,将变形梯度乘法分解为等容部分和体积变形部分,给出了一种适合橡胶类材料的非线性粘弹性本构模型,并模拟了粘滞效应。对于极快或极慢的过程,该模型退化为橡胶弹性理论;在小变形情况下退化为经典的广义Maxwell粘弹性材料。模型与热力学第二定律相容,适合于大规模数值分析。     

Compressible rubber materials: experiments and simulations

Porous rubber materials are often used in automotive industries. In this paper, a carbon black-filled one is investigated, which is used, for example, as sealing. Such materials are distinguished by viscoelastic behaviour and by a structural compressibility induced by the porous structure. To identify the material behaviour, uniaxial tension tests and hydrostatic compression tests are performed. Therein the main focus of attention lies on the basic elasticity and on the viscoelasticity in the whole loading range. An important observation of these tests is the viscoelastic behaviour under hydrostatic compression, which has to be included in the material model. Because of the two-phase character of cellular rubber, the theory of porous media is taken into account. To model the structural compressibility, a volumetric–isochore split of the deformation gradient is used. Therein the volumetric part includes the aspect of the point of compaction. Finally, the concept of finite viscoelasticity is applied introducing an intermediate configuration. Because of the viscoelastic behaviour under hydrostatic compression, the volumetric–isochore split is taken into account for the nonequilibrium parts, too. Nonlinear relaxation functions are used to model the process-dependent relaxation times and the highly nonlinear behaviour with respect to the deformation and feedrate. The material parameters of the model are estimated using a stochastic identification algorithm.     

柔性硅泡沫薄片的短时松弛行为研究

根据多孔硅泡沫材料的单轴压缩和应力松弛实验,利用最小二乘法的LM法拟合得到硅泡沫材料的本构关系.基于上述模型开展了组合结构中多孔泡沫薄片应力松弛行为的数值模拟,得到了短时松弛过程中硅泡沫结构件的应力变化规律.     

Heat capacities and volumetric changes in the glass transition range: a constitutive approach based on the standard linear solid

A novel approach to represent the glass transition is proposed. It is based on a physically motivated extension of the linear viscoelastic Poynting–Thomson model. In addition to a temperature-dependent damping element and two linear springs, two thermal strain elements are introduced. In order to take the process dependence of the specific heat into account and to model its characteristic behaviour below and above the glass transition, the Helmholtz free energy contains an additional contribution which depends on the temperature history and on the current temperature. The model describes the process-dependent volumetric and caloric behaviour of glass-forming materials, and defines a functional relationship between pressure, volumetric strain, and temperature. If a model for the isochoric part of the material behaviour is already available, for example a model of finite viscoelasticity, the caloric and volumetric behaviour can be represented with the current approach. The proposed model allows computing the isobaric and isochoric heat capacities in closed form. The difference \(c_\mathrm{p} -c_\mathrm{v} \) is process-dependent and tends towards the classical expression in the glassy and equilibrium ranges. Simulations and theoretical studies demonstrate the physical significance of the model.     

Finite telescopic shear of a compressible hyperelastic tube

Finite telescopic shear of a compressible hyperelastic tube is considered. It is shown that solutions with isochoric deformation fields exist for a class of strain energy functions. A numerical method is proposed for the analysis of the problem when a solution with an isochoric deformation field does not exist. Numerical results obtained by using a programmable desk calculator are presented graphically for two strain energy functions.     

Constitutive modeling of isotropic hyperelastic materials in an exponential framework using a self-contained approach

In this paper, an exponential framework for strain energy density functions of elastomers and soft biological tissues is proposed. Based on this framework and using a self-contained approach that is different from a guesswork or combination viewpoint, a set strain energy density functions in terms of the first and second strain invariants is rebuilt. Among the constructed options for strain energy density, a new exponential and mathematically justified model is examined. This model benefits from the existence of second strain invariant, simplicity, stability of parameters, and the state of being accurate. This model can capture strain softening, strain hardening and is able to differentiate between various deformation-state dependent responses of elastomers and soft tissues undergoing finite deformation. The model has two material parameters and the mathematical formulation is simple to render the possibility of numerical implementations. In order to investigate the appropriateness of the proposed model in comparison to other hyperelastic models, several experimental data for incompressible isotropic materials (elastomers) such as VHB 4905 (polyacrylate rubber), two various silicone rubbers, synthetic rubber neoprene, two different natural rubbers, b186 rubber (a carbon black-filled rubber), Yeoh vulcanizate rubber, and finally porcine liver tissue (a very soft biological tissue) are examined. The results demonstrate that the proposed model provides an acceptable prediction of the behavior of elastomers and soft tissues under large deformation for different applied loading states.