一种新的橡胶材料弹性本构模型

橡胶类材料本构关系对于科学研究和工程应用具有重要意义,但已有的橡胶模型的拟合能力和可靠性需要进一步提高.为解决此问题,本文提出了一种新的橡胶材料的各向同性、不可压缩柯西弹性模型.研究了橡胶材料本构关系的模型形式,基于平面应力变形状态,提出了一种以较大的两个伸长率为自变量、适用于一般变形状态的橡胶材料弹性本构模型形式;研究了橡胶材料在侧面受约束条件下的变形规律,分析了橡胶材料本构关系需要满足的约束条件;在此基础上,结合一个可以通过实验确定的描述平面拉伸变形状态下的橡胶材料力学特性函数,提出一种将该函数拓展为平面应力状态一般模型的方法,并给出了一个具体的函数形式,形成了一个新的不可压缩、各向同性的橡胶材料弹性本构模型.使用5组包含3种类型实验的数据和一组较全面的双轴测试数据对该模型进行了参数拟合,结果表明:该模型具有很好的拟合精度和更高的可靠性,仅用一种类型实验数据,如单轴拉伸或者平面拉伸等,也能获得较好的拟合结果.      

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.      

炭黑填充橡胶材料的修正三链模型和Mullins模型

本文探讨了炭黑颗粒填充橡胶材料的本构模型。考虑到橡胶单个分子链与周围分子网络的约束作用和炭黑颗粒对橡胶的补强作用,提出了一种修正三链模型,用Edwards管模型描述分子链之间的相互作用和约束,采用应变放大因子来考虑炭黑含量的影响。并在修正三链模型的基础上,利用橡胶分子网络重构理论,提出了一种适合表征橡胶Mullins现象的本构模型。通过与实验数据比较分析,修正三链模型可较准确地表征未填充橡胶材料不同变形模式的力学性能和炭黑颗粒填充橡胶材料的单向拉伸力学行为,Mullins模型也可较好地描述橡胶材料的Mullins现象。     

橡胶弹性材料的一种混合本构模型

该文探讨不可压缩橡胶弹性材料的本构模型.考虑到小变形时分子链的端矢分布符合高斯函数,而大变形时符合非高斯函数,提出一个混合模型,用高斯链网络模型来描述小变形而用8链网络模型来描述大变形.引入权重函数,使小变形和大变形情况下混合模型分别退化或趋于高斯链网络模型和8链网络模型.由Treloar拉伸实验数据拟合得到模型参数,通过这些材料参数混合模型对等双轴拉伸和纯剪切变形模式的预测结果与Tre-loar实验数据基本吻合,说明混合模型具有同时描述不同变形模式的能力.通过比较分析,混合模型的总体预测精度均优于高斯链网络模型和8链网络模型,特别是对剪切变形.     

炭黑填充橡胶材料改进Mooney模型

本文讨论了炭黑填充橡胶材料的唯象本构模型。考虑到Mooney模型无法表征橡胶类材料大变形阶段的力学特性,首先利用实验数据,对Mooney模型进行了分析,讨论了炭黑含量与Mooney模型准确表征橡胶材料应变区间大小的关系,Mooney模型对纯剪切和等比双向拉伸等复杂变形的预测能力,同时也分析了材料参数对Mooney模型的影响。最后在Mooney模型的基础上添加了一个修正项,且改进后的Mooney模型满足Treloar和Ogden六项假设。通过与实验数据对比分析,改进Mooney模型可以较好地描述橡胶材料大变形阶段的应力应变关系,同时提高了预测橡胶材料复杂变形的能力。     

超弹-粘弹-损伤仿射微球模型及其应用

硅胶弹性体PDMS,在多个领域有着广泛的应用。为了提高PDMS的力学性质,近期我们在PDMS材料中加入微米尺寸的玻璃微珠,这有效地提高了PDMS的模量。然而,玻璃微珠填充的PDMS材料在循环变形过程中,在第一个加卸载周期出现大的滞回圈,表现出明显的损伤行为,且后续加载过程中仍有稳定的较小的滞回圈,显示出一定的粘弹性特性,此外,卸载后材料有明显的残余应变。针对上述实验发现,本文建立了一个基于仿射假设的微球模型,分子链在各个方向上初始均匀分布,当受到加载后,各个方向上的分子链发生损伤行为和粘弹性松弛机制,导致不同方向的各向异性变形行为。该五参数的本构模型能够描述玻璃微珠填充弹性体的实验现象,包括不同周次循环加载的滞回圈形状以及残余应变的大小。该理论模型能描述各类软材料体系的复杂力学行为,有望为软材料的力学行为的预测提供有力的支撑。     

混凝土材料宏观力学特性分析的细观单元等效化模型

提出了一种混凝土材料宏观力学特性分析的新方法—细观单元等效化模型。该方法从描述混凝土材料的细观尺度入手,采用Monte Carlo法生成由骨料颗粒及砂浆基质组成的混凝土试件的随机骨料模型;然后,依据混凝土材料特征单元尺度来剖分有限元网格并投影到建立的随机骨料模型上,各细观单元的有效力学特性则采用复合材料等效化方法来确定。本文方法体现了材料非线性宏观力学特性源于其内在的不均匀性这一认识,而对不均匀性的描述则是以网格剖分是否影响其宏观力学特性为准则。因此,本文方法较其他细观力学方法最大的优点在于极大地减小了体系自由度数目（特别是对于三维问题）,从而提高了计算效率。算例分析初步验证了本文方法的高效性。     

骨骼肌生物力学特性多尺度建模与仿真

针对肌纤维微观结构模型与显微镜下观察的图像存在一定差异、微观组分生物力学模型无法有效捕获骨骼肌剪切变形时的力学行为、骨骼肌多尺度数值模型计算成本高的问题,本文从实验、多尺度建模和仿真的角度研究骨骼肌被动力学特性,提出以曲边泰森多边形作为肌纤维截面形状,并建立骨骼肌微观尺度代表性体元RVE;提出新的生物力学模型(MMA模型),并将MMA模型作为肌纤维和结缔组织生物力学模型,MMA模型采用完全的应变不变量I₄, I₅, I₆和I₇,使骨骼肌的剪切行为从材料属性层面得以体现;结合骨骼肌力学实验结果、RVE模型、肌纤维和结缔组织的生物力学模型,建立骨骼肌多尺度数值模型.根据实验结果确定生物力学模型参数,通过多尺度均匀化方法实现微观尺度和宏观尺度之间的连接,最终获得骨骼肌宏观力学行为,通过纵向拉伸、横向拉伸、平面外纵向剪切和平面内剪切4种变形形式的仿真结果验证骨骼肌多尺度数值模型的收敛性.研究了生物力学模型中模型参数、肌纤维体积分数和肌纤维结构对骨骼肌宏观力学行为的影响,最后通过实验验证多尺度数值模型的有效性...     

黏弹性材料等效分数阶微观结构标准线性固体模型

从黏弹性材料微观链结构出发,以橡胶基黏弹性材料超弹性理论分子网链高斯(Gauss)统计模型和黏滞流动理论为基础,研究黏弹性材料的微观结构、填料等对黏弹性性能的影响.用温频等效原理描述温度对黏弹性材料力学性能的影响,建立了可以有效描述黏弹性材料耗能特性的等效分数阶微观结构标准线性固体模型.采用动态热机械分析仪(DMA)对高聚物黏弹性材料力学性能、耗能能力进行测试.试验表明:在低温区域,储能模量较大,随着温度的升高,储能模量下降显著;能量损耗因子在高温和低温区域数值较小,在玻璃化转变温度附近数值较高.根据测试数据对所提等效分数阶微观结构标准线性固体模型进行验证,该力学模型能够较好地描述黏弹性材料储能模量和能量损耗因子随温度的变化趋势.用9050A和ZN22黏弹性材料对模型的有效性进一步验证,结果表明:9050A和ZN22黏弹性材料具有较好的耗能能力,所提出的等效分数阶微观结构标准线性固体模型能够准确地描述微观结构和填料对黏弹性材料宏观性能的影响,能够准确地描述黏弹性材料在不同温度和频率下的动态力学性能.     

微振激励下黏弹性阻尼器微观链结构力学模型

减小微振动对高精密仪器至关重要,利用黏弹性阻尼器进行微振动抑制是一个新兴而又具有挑战性的课题.本文采用分子链网络模型方法分析了黏弹性材料的微观分子链结构,综合考虑材料分子链结构中的网络链和自由链对黏弹性材料力学性能的影响,提出一种基于材料微观分子链结构的微振激励下黏弹性阻尼器力学模型.模型分别采用标准线性固体模型和Maxwell模型来描述网络链和自由链中单个链的力学性能,并分别采用8链网络模型和3链网络模型考虑两种类型分子链的综合效应,引入温频等效原理描述温度对微振激励下黏弹性阻尼器力学性能的影响.该模型能够描述温度和频率对黏弹性阻尼器动态力学性能的影响,并能够反映黏弹性材料的微观结构与材料力学性能的关系.为验证所提模型的有效性及考察黏弹性阻尼器在微振激励下的耗能能力和动态力学性能,在微振条件下对黏弹性阻尼器进行了动态力学性能试验.研究结果表明黏弹性阻尼器具有较好的微振耗能能力,其动态力学性能受温度和频率影响较大,所提的力学模型能够精确地描述微振激励下黏弹性阻尼器动态力学性能随温度和频率的变化关系.      

Spherical indentation of incompressible rubber-like materials

In recent years, indentation tests have been proven very useful in probing mechanical properties of small volumes of materials. However, a class of materials that very little has been done in this direction is rubber-like materials (elastomers). The present work investigates the spherical indentation of incompressible rubber-like materials. The analysis is performed in the context of second-order hyperelasticity and is accompanied by finite element computations and an extensive experimental program with spherical indentors of different radii. Uniaxial tensile tests were also performed and it was found that the initial elastic modulus correlates well with the indentation response. The experiments suggest stiffer indentation response than that predicted by linear elasticity, which is somehow counter-intuitive, if the uniaxial material response is to be considered. Regarding the uniqueness of the inverse problem, that is to establish material properties from spherical indentation tests, the answer is disappointing. We prove that the inverse problem does not give unique answer regarding the constitutive relation, except for the initial stiffness.     

Biaxial Mechanical Evaluation of Planar Biological Materials

A fundamental goal in constitutive modeling is to predict the mechanical behavior of a material under a generalized loading state. To achieve this goal, rigorous experimentation involving all relevant deformations is necessary to obtain both the form and material constants of a strain-energy density function. For both natural biological tissues and tissue-derived soft biomaterials, there exist many physiological, surgical, and medical device applications where rigorous constitutive models are required. Since biological tissues are generally considered incompressible, planar biaxial testing allows for a two-dimensional stress-state that can be used to characterize fully their mechanical properties. Application of biaxial testing to biological tissues initially developed as an extension of the techniques developed for the investigation of rubber elasticity [43, 57]. However, whereas for rubber-like materials the continuum scale is that of large polymer molecules, it is at the fiber-level (∼1 μm) for soft biological tissues. This is underscored by the fact that the fibers that comprise biological tissues exhibit finite nonlinear stress-strain responses and undergo large strains and rotations, which together induce complex mechanical behaviors not easily accounted for in classic constitutive models. Accounting for these behaviors by careful experimental evaluation and formulation of a constitutive model continues to be a challenging area in biomechanics. The focus of this paper is to describe a history of the application of biaxial testing techniques to soft planar tissues, their relation to relevant modern biomechanical constitutive theories, and important future trends. This revised version was published online in July 2006 with corrections to the Cover Date.     

Spherical void expansion in rubber-like materials: The stabilizing effects of viscosity and inertia

Dynamic cavitation is known to be a typical failure mechanism in rubber-like solids. While the mechanical behaviour of these materials is generally rate-dependent, the number of theoretical and numerical works addressing the problem of cavitation using nonlinear viscoelastic constitutive models is scarce. It has been only in recent years when some authors have suggested that cavitation in rubber-like materials is a dynamic fracture process strongly affected by the rate-dependent behaviour of the material because of the large strains and strain rates that develop near the cavity. In the present work we further investigate previous idea and perform finite element simulations to model the dynamic expansion of a spherical cavity embedded into a rubber-like ball and subjected to internal pressure. To describe the mechanical behaviour of the rubber-like material we have used an experimentally calibrated constitutive model which includes rate-dependent effects and material failure. The numerical results demonstrate that inertia and viscosity play a fundamental role in the cavitation process since they stabilize the material behaviour and thus delay failure.     

数据驱动梯度结构材料弹塑性本构

梯度结构材料因其优异的力学性能被广泛应用于工程结构中。本文整合塑性理论和人工神经网络技术,发展了一种构建梯度结构材料弹塑性本构模型的新方法。该方法基于梯度结构材料不同位置的微结构,构建不同代表性体积单元,进而生成应力应变数据,应用生成的数据训练人工神经网络,建立基于神经网络的材料本构模型。应用该方法,本文开展了针对实际工程结构件的计算,算例结果表明,该方法可快速计算梯度功能复合材料在循环载荷反向载荷状态下的宏观响应,且较为准确。该方法为模拟含复杂梯度结构材料的结构件弹塑性力学响应提供了新的工具。     

Localization and stability in damageable amorphous solids

In the present article, based on a recently proposed model (De Tommasi et al. in J Rheol 50:495–512, 2006; Phys Rev Lett 100:085502, 2008), we analyze the influence of the microstructure properties on the damage behavior of amorphous materials. In accordance with the experimental observations, different scenarios of damage nucleation and evolution are associated to different material distributions at the microscale. In particular, we observe the possibilities of uniform or localized damage and strain geometries with a macroscopic behavior that may range from brittle to ductile or rubber-like. To describe the possibility of extending our stability analysis to three-dimensional damageable amorphous bodies we consider a simple boundary value problem of engineering interest.     

Cosserat modeling of cellular solidsModélisation des solides cellulaires selon Cosserat

Cellular solids inherit their macroscopic mechanical properties directly from the cellular microstructure. However, the characteristic material length scale is often not small compared to macroscopic dimensions, which limits the applicability of classical continuum-type constitutive models. Cosserat theory, however, offers a continuum framework that naturally features a length scale related to rotation gradients. In this paper a homogenization procedure is proposed that enables the derivation of macroscopic Cosserat constitutive equations based on the underlying microstructural morphology and material behavior. To cite this article: P.R. Onck, C. R. Mecanique 330 (2002) 717–722.     

Mechanism-based multi-surface plasticity model for ideal truss lattice materials

The mechanical behavior of ideal truss lattice materials is controlled by the so-called direct action mechanism at the microscale which involves the uniform stretching and compressing of individual truss members. Standard homogenization techniques have been employed to develop a general micromechanics-based finite-strain constitutive model for truss lattice materials. Furthermore, a specialized small-strain plasticity model has been derived. Both models have been implemented in a finite-element program and used to simulate the anisotropic plastic behavior of the octet-truss lattice material in various applications including cyclic uniaxial loading, pure shear, and three-point bending. The constitutive model predictions agree well with the results obtained from discrete finite element models. Regarding the plasticity of the octet-truss lattice material, it has been found that the elastic domain is constrained by twelve pairwise parallel hyperplanes in the six-dimensional stress space. Moreover, the mechanism-based small-strain formulation reveals that the direction of plastic flow is normal to the pressure-dependent macroscopic yield surfaces.     

考虑微结构连接性的双尺度结构自然频率拓扑优化

多孔材料因具有轻量化、高孔隙率和减振/散热等优良多物理特性,在航空航天等领域具有广阔应用前景。采用拓扑优化方法对含多种多孔材料的结构进行结构与材料微结构构型一体化设计,有助于获得具有优良力学性能的结构设计。然而,传统逆均匀化微结构设计方法无法确保不同多孔材料微结构之间的连接性,设计结果不具备可制造性。本文面向含多种多孔材料的双尺度结构基频最大化设计问题,考虑不同微结构之间的连接性,协同设计多孔材料的微结构构型及其在宏观尺度下的布局。采用均匀化方法计算多孔材料的宏观等效力学性能,通过对不同多孔材料微结构单胞的边界区域采用相同的拓扑描述确保双尺度优化过程中任意空间排布下不同微结构的连接性,并通过优化算法确定微结构间的连接形式及微结构拓扑。在宏观尺度,提出结合离散材料插值模型和RAMP插值模型RAMP (Rational Approximation of Material Properties)的多孔材料各向异性宏观等效刚度及质量插值模型,获得清晰的多孔材料宏观尺度布局并减轻优化过程中伪振动模态的影响。建立以双尺度结构基频最大化为目标,以材料用量为约束的优化列式,推导灵敏度表达式,并基于梯度优化算法求解双尺度结构拓扑优化问题。数值算例表明,采用本文优化方法能够有效确保基频最大化双尺度结构设计中不同多孔材料微结构之间的连接性,增强优化设计结果的可制造性。