显式模拟类橡胶材料Mullins效应滞回圈

通过显式、直接的方法提出一个多轴可压缩应变能函数,用来模拟类橡胶材料在加载-卸载作用下,由于Mullins效应而产生的应力-应变滞回圈.本文的创新点在于将表征能量耗散的变量引入到应变能函数.新的弹性势具有以下两个特点:第一,在加载情况下,新引入的变量不会对弹性势产生任何影响,因此,只要给出合适的形函数显式表达,3个基准实验,包括单轴拉伸和压缩,等双轴拉伸和压缩,以及平面应变,都可精确模拟;第二,新引入的变量在卸载情况下将被激活.在不同的卸载应力下,变量将发生改变,从而影响弹性势,使其最终产生不同的应力-应变关系卸载曲线,与对应的加载曲线共同构成应力-应变滞回圈.通过对Mullins效应实验数据进行分析和研究,得出了卸载形函数在不同卸载应力下变化的规律,并预测不同卸载应力下的应力-应变关系.最后,我们将得到精确匹配实验数据的数值模拟结果,从而证明本文方法不仅可以精确匹配至少3个基准实验,还可以模拟和预测类橡胶材料在加载-卸载作用下由于Mullins效应而产生的滞回圈.     

N330炭黑增强天然橡胶材料力学性能的实验研究

为了研究炭黑对橡胶材料力学性能的影响,对9种不同体积含量的炭黑填充橡胶材料进行了准静态力学实验研究。利用循环拉伸加卸载实验分析了炭黑对橡胶Mullins效应及能量损耗的影响,通过单轴拉伸实验研究了炭黑对橡胶材料刚度和起始模量的影响,采用多步松弛拉伸加卸载实验研究了炭黑对橡胶材料应力行为的应变历史相关性的影响。实验结果表明:炭黑填充量越高,橡胶材料的刚度越大,初始模量越大,Mullins效应也越明显;随着炭黑填充量的增加,橡胶在加卸载循环中所产生的迟滞损耗、Mullins效应相对能量损耗以及残余应变都呈现出非线性增长趋势;随着炭黑填充量的升高,橡胶在加卸载过程中的应力松弛现象越明显,其平衡态迟滞损耗以及与时间相关部分的迟滞损耗也越大。     

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。     

显式模拟类橡胶材料应力软化引起的不可恢复变形及其各向异性特征

类橡胶材料在经过初次加载后会产生应力软化现象, 也就是Mullins效应. 实验证明应力软化现象会导致材料产生不可恢复变形, 同时引入各向异性特征. 本文基于对数应变构造一个多轴可压缩应变能函数, 先引入耗散来表征应力软化现象, 再引入依赖耗散大小的不可恢复变形量以及各向异性特征量, 使得新模型既可以表征Mullins效应, 又能模拟应力软化作用下产生的不可恢复变形和各向异性特征. 本文在各向同性形函数的基础上, 通过球坐标系的思想, 进一步发展并提出了一个任意方向适用的各向异性形函数. 新模型在材料尚未发生软化(耗散为0)的情况下, 表现出各向同性; 一旦发生应力软化(耗散大于0), 则变为各向异性. 随着加载?卸载循环的累积, 耗散逐渐变大, 不可恢复变形也随之变大直到达到一个稳定的值, 各向异性特性也逐渐变得明显. 新方法得到的结果可以精确匹配经典的实验数据, 并预测不同方向的应力软化现象以及由此产生的不可恢复变形和各向异性特征.      

炭黑颗粒对丁苯橡胶材料力学性能的影响

利用电子万能材料试验机,对不同体积分数的炭黑填充丁苯橡胶复合材料进行了单向拉伸和循环拉伸加卸载等准静态力学试验,研究了炭黑填充橡胶材料单向拉伸应力应变关系、Mullins效应、调制应变相关性和拉伸断裂力学行为等.试验结果表明:调制应变越大,橡胶材料的刚度越小,橡胶的非线性应力应变关系越明显;炭黑含量越高,橡胶材料的初始模量和刚度越大,应力反翘现象和Mullins效应越显著;同时,随着炭黑体积分数的增加,炭黑填充丁苯橡胶材料的拉伸强度和断裂伸长率将呈现先增大后减小的趋势.     

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．     

考虑缠结效应的超弹性本构模型

经典熵弹性模型, 如 Neo-Hookean模型和Arruda-Boyce八链模型, 被广泛应用于预测橡胶等软材料的超弹性力学行为. 然而, 大量实验结果也显示仅采用一套模型参数, 这类模型不能同时准确地描述橡胶在多种加载模式下的应力响应. 为了克服上述模型的不足, 本文在熵弹性的模型基础上引入缠结约束效应. 微观上, 采用Langevin统计模型来表征熵弹性变形自由能, 通过管模型(tube model)引入缠结约束自由能, 并基于仿射假设, 建立微观变形与宏观变形之间的映射关系. 在宏观上, 所建立的超弹性模型的Helmholtz自由能同时包含熵弹性和缠结约束两部分, 其中熵弹性自由能与经典的Arruda-Boyce八链模型一致, 依赖于柯西-格林应变张量的第一不变量, 而缠结约束自由能依赖于柯西-格林应变张量的第二不变量. 与文献中的实验结果对比发现, 该三参数模型能准确地预测实验中所测得的橡胶材料在单轴拉伸、纯剪切和等双轴拉伸变形条件下的应力响应, 也能较好地描述不同预拉伸比条件下双轴拉伸实验结果. 最后, 本文比较了所建立的基于应变不变量的缠结约束模型与文献中相关的缠结约束模型在多种加载模式下自由能的异同. 总的来说, 本文所建立的本构理论能准确模拟橡胶等软材料的大变形力学行为, 对其工程应用有促进作用.      

形状记忆合金伪弹性行为模拟

基于对伪弹性形状记忆合金(SMA)典型应力-应变曲线的特征分析,在原Graesser本构模型中增加简洁多项式来描述SMA应力诱发马氏体相变完成后在变形马氏体相下继续加载阶段的变形特征;并引入应变幅值与混相下SMA弹性模量的关系来改进不同应变幅值下卸载时SMA的应力-应变关系,从而提出了一种新的SMA一维本构关系模拟其伪弹性力学行为。该模型对直径为0.5mm的NiTi合金丝的拉伸加载、卸载试验曲线的模拟结果表明:改进本构模型与原Graesser模型相比,其能够准确地模拟SMA在不同应变幅值下加载和卸载应力-应变关系。此外,通过研究SMA本构模型的物理关系,推导出了控制SMA滞回曲线特征的关键参数fT与相变临界应力、弹性常数之间的明确关系,可利用该关系直接确定参数fT,摆脱了只靠试算获取该参数的传统做法,其准确性得到了试验验证。     

高弹态未硫化橡胶在不同变形模式下的循环加卸载力学行为

对高弹态未硫化橡胶实施了不同变形模式(单轴拉伸和压缩)的循环力学实验，以考察其黏超弹性响应以及应变率对力学行为的影响。结果表明，材料的拉伸、压缩性能与加载速率和变形历史均有着显著的相关性。对于循环拉伸变形，应力-应变曲线的非线性特征较为明显，材料表现出类似于屈服的性质，且随着循环次数和变形量增加，迟滞损耗的积累趋势逐渐减弱；而对于循环压缩变形，应力-应变关系接近线弹性，且随着循环次数和变形量增加，材料刚度和迟滞损耗积累的趋势都逐渐增强。针对上述实验结果，在经典的Bergstrom-Boyce模型中引入损伤变量，对未硫化橡胶的应变率相关性和Mullins效应进行表征。理论计算结果表明，这种非线性黏超弹模型能够较好地描述未硫化橡胶在不同载荷条件下的变形响应与应力软化特征。     

基于有理插值方法模拟可压缩类橡胶材料多轴变形行为

提出一个多轴应变能函数来模拟可压缩类橡胶材料在载荷作用下的大变形行为。首先,基于对数应变构造三个不变量,使得应变能函数分别具备可压缩功能、多轴有效功能以及适用于多个变形模式的功能;其次,利用有理插值方法构造单轴形函数,并结合前面引入的三个不变量,通过哈密顿插值方法构建统一的应变能函数;最后,在单轴情况下,应变能函数通过对Hencky应变求导,可以得到对应变形模式下的应力-应变关系。本文通过调节泊松比的大小来控制体积变化从而实现模型的可压缩性;此应变能函数可以模拟单轴拉伸压缩、平面应变以及等双轴拉伸等至少三个基准试验。新方法得到的伸长比-应力关系、伸长比-体积比关系与经典试验数据结果作比较,进而证明方法的准确性和有效性。     

显式方法精确模拟形状记忆聚合物热力学行为

通过构建一个热耦合的多轴可压缩应变能函数,得到应力-应变、应力-温度和应变-温度之间的函数关系,建立形状记忆聚合物的本构方程.本文引入三个基于对数应变的不变量使得模型（i）可以模拟可压缩情况;（ii）适用于单轴拉伸和等双轴拉伸至少两个基准实验;（iii）多轴有效.通过显式方法（i）给出自由能和熵的具体表达,证明模型热力学定律;（ii）给出应变-应力,温度-应力以及,温度-应变的形函数具体表达.多轴模型在特定的情况下可以自动退化到各自的单轴情况. 通过调节形函数的参数,最终得到的模型结果和实验结果能够精确匹配.新方法建立的本构模型得到的结果能更加准确地指导形状记忆聚合物的工程设计。     

显式方法精确模拟形状记忆聚合物热力学行为

通过构建一个热耦合的多轴可压缩应变能函数，得到应力-应变、应力-温度和应变-温度之间的函数关系，建立形状记忆聚合物的本构方程.本文引入三个基于对数应变的不变量使得模型（i）可以模拟可压缩情况；（ii）适用于单轴拉伸和等双轴拉伸至少两个基准实验；（iii）多轴有效.通过显式方法（i）给出自由能和熵的具体表达，证明模型热力学定律；（ii）给出应变-应力，温度-应力以及，温度-应变的形函数具体表达.多轴模型在特定的情况下可以自动退化到各自的单轴情况. 通过调节形函数的参数，最终得到的模型结果和实验结果能够精确匹配.新方法建立的本构模型得到的结果能更加准确地指导形状记忆聚合物的工程设计。     

在弹-粘塑性材料中平面波传播的初步研究

在材料的应力应变关系中,本文对剪切部分的线性弛豫近似和线性硬化效应作了简化讨论,其中对动态和静态的加载、卸载过程讨论的更多一些,从而得到一个适合于弹-粘塑性材料以及加载、卸载过程都可用的本构关系,并将其用于一维平面波的传播过程,计算了飞板碰靶后应力、应变的分布,结果同等人的工作相符。     

Rate dependent finite strain constitutive model of polyurea

Continuous loading and unloading experiments are performed at different strain rates to characterize the large deformation behavior of polyurea under compressive loading. In addition, uniaxial compression tests are carried out with multistep strain history profiles. The analysis of the experimental data shows that the concept of equilibrium path may not be applied to polyurea. This finding implies that viscoelastic constitutive models of the Zener type are no suitable for the modeling of the rate dependent behavior of polyurea. A new constitutive model is developed based on a rheological model composed of two Maxwell elements. The soft rubbery response is represented by a Gent spring while nonlinear viscous evolution equations are proposed to describe the time-dependent material response. The eight material model parameters are identified for polyurea and used to predict the experimentally-measured stress-strain curves for various loading and unloading histories. The model provides a good prediction of the response under monotonic loading over wide range of strain rates, while it overestimates the stiffness during unloading. Furthermore, the model predictions of the material relaxation and viscous dissipation during a loading-unloading cycle agree well with the experiments.     

Stress–softening effect of SBR/nanocomposites by a phenomenological Gent–Zener viscoelastic model

An experimental study of a tensile loading–unloading procedure, as well as multi-cyclic response in a strain-controlled program of a Styrene-Butadiene (SBR) elastomer reinforced with four different weight fractions of carbon nanotubes (CNTs) has been performed. The Mullins effect features, namely hysteresis, damage and residual strain, exhibited by the SBR/nanocomposites were analyzed by a modified Gent–Zener rheological model, and a damage function. Especially for the multi-cyclic stress–strain curves, phenomenological equation of the model parameters evolution with strain were also introduced. The same loading procedure was applied in pre-stressed materials, revealing a different stress–strain response due to strain prehistory. The model has been proven to accurately capture the loading–unloading behavior, the residual strain, hysteresis loops as well as the multi-cyclic behavior of the SBR/CNT nanocomposites.     

A constitutive model for carbon black filled rubber: Experimental investigations and mathematical representation

Abspract The stress-strain behavior of carbon black filled rubber is recognized to be nonlinearly elastic in its main part (see e.g. Gent [1]). In addition, inelastic effects occur under monotonic and cyclic processes. The inelastic behavior includes nonlinear rate dependence as well as equilibrium hysteresis. Moreover, the first periods of a stress-strain curve differ significantly from the shape of subsequent cycles; a characteristic feature, which is called the Mullins effect, because it has been pointed out by Mullins [2]. All inelastic phenomena are strongly influenced by the volume fraction of the filler particles (see e.g. Payne [3], So and Chen [4], Meinecke and Taftaf [5]).The aim of the present paper is to design a constitutive model, representing this kind of material behavior as a phenomenological theory of continuum mechanics. In order to motivate the basic structure of the constitutive theory, a series of uniaxial experiments between 100% in tension and 30% in compression are presented and analyzed. First of all, monotonic strain controlled experiments show the nonlinear rate dependence of the stress response. Then, a series of inserted relaxation periods at constant strain yields the monotonic equilibrium stress-strain curve, which is strongly nonlinear and unsymmetric with respect to the origin. Finally, cyclic experiments under strain control display pronounced hysteresis behavior. The hysteresis effects are mainly rate dependent, but there exists also a weak equilibrium hysteresis (compare to similar observations of Orschall and Peeken [6]). The Mullins effect corresponds to a softening phenomenon during the first few cycles. By means of an appropriate preprocess, this effect was excluded during the above experiments. Apart from the Mullins effect, neither hardening nor significant softening phenomena were observed in the context of cyclic loadings.These results motivate the structure of a constitutive model of finite strain viscoplasticity: The total stress is decomposed into an equilibrium stress and an overstress, where the overstress is a rate dependent functional of the strain history. The overstress represents the rate dependence of the material behavior and tends asymptotically to zero during relaxation processes. The nonlinearity of the rate dependence is incorporated by means of a stress dependent relaxation time. The equilibrium stress is assumed to be a rate independent functional of the strain history. For this quantity, we make use of an arclength representation, which was originally introduced by Valanis [7]. In case of vanishing equilibrium hysteresis and vanishing rate dependence our constitutive model reduces to finite strain hyperelasticity, which is the first approximation of the constitutive properties. In more general cases the main shape of a stress-strain curve is determined by hyperelasticity, superimposed by rate dependent and equilibrium hysteresis. The representation of the Mullins effect is incorporated by a continuum damage model.Some numerical simulations at the end of the paper demonstrate that the presented theory is able to represent the observed phenomena qualitatively and quantitatively with sufficient approximation.     

非均质结构PBX炸药的动态压缩过程模拟

采用离散元方法,构建了考虑PBX炸药晶体颗粒与黏结剂非均匀性的计算模型,通过在炸药试样两端采用相向飞片加载、将原SHPB实验的应力边界替代为速度边界的方法,开展了PBX炸药的动态压缩数值模拟研究,再现了考虑PBX炸药非均质特性的SHPB实验过程,获得了不同加-卸载路径下炸药应力应变曲线以及相应的损伤破坏图像。模拟结果表明:在动态压缩过程中,虽然PBX炸药处于整体应力平衡,由于PBX高度非均质性,内部应力分布并不均匀,晶体间应力以应力桥形式传递;应力曲线为试样整体平均,试样内局部所受真实应力可能高于曲线峰值应力;出现卸载回滞曲线的试样发生局部损伤破坏,而完全软化曲线的试样发生整体失稳破坏。