基于横观各向同性超弹性理论的短纤维增强橡胶本构模型的建立与应用Establishment and application of short fiber reinforced rubber constitutive model based on transversely isotropic hyperelastic theory

提出了一种能够表征短纤维增强橡胶的横观各向同性超弹性本构模型,并结合试验体系,对其在数值分析中的应用方法和效果进行了研究。基于连续介质力学理论,建立了横观各向同性材料的应变能函数,推导得到不同变形形式下的应力应变关系,给出材料参数辨识试验方法,并成功应用于某短纤维增强橡胶测试中,得到表征其超弹性特性的相关材料参数。利用有限元软件ANSYS对不同纤维排布方向的单轴拉伸和平行纤维方向的平面拉伸进行仿真计算,并对比相应试验数据,以验证材料参数的可靠性。最后基于已验证的本构模型,建立了某铣槽装备减振环仿真模型,并对其进行了校核计算。研究结果表明,本文提出的本构模型能够有效表征短纤维增强橡胶的静态力学特性并且方便嵌入现有的有限元软件中,具有材料参数少、测试简便和结果准确等特点,工程实用性强。     

土本构关系的尖点突变模式

本文首次应用突变理论的尖点突变模型分析土的本构特性,建立了土相应的统一本构关系方程。该方程可以考虑软化土的应力路径,亦可分析硬化土的应力路径,统一本构方程通过试验检验是令人满意的。     

岩土介质横观各向同性的模拟

评述了岩土介质横观各向同性模拟的进展状况，包括横观各向同性弹塑性及其屈服准则的模拟，并给出了相应的力学模型及其数学表达式．     

一种横观各向同性强度准则及变换应力空间

考虑岩土介质在自然形成过程中产生的原生各向异性性质,将其简化为一种横观各向同性岩土材料.基于已提出的a强度准则,根据沉积面与有效滑移面在物理空间中位置的相互关系,采用两面的空间夹角作为度量岩土材料原生各向异性在加载条件下发挥强度作用的影响变量.并根据有效滑移面的物理概念,当沉积面与有效滑移面夹角越大,则摩擦特性潜力发挥的越充分,此时对应更高的强度应力比,反之则对应越小的强度应力比.基于上述思想,建立了考虑原生各向异性的强度应力比公式,将其用于修正a准则,进而得到了横观各向同性a准则公式.采用上述横观各向同性a准则公式向各向同性Von-Mises准则公式转换的变换思路,在横观各向同性a准则公式基础上,推导得到了变换应力公式,该公式可由横观各向同性应力空间转变为各向同性应力空间,利用所提出的变换应力方法,可方便的将传统的在偏平面上以Von-Mises准则为基础的二维模型转换为可考虑原生各向异性的三维模型.通过对岩土材料的强度以及真三轴条件下的应力应变关系试验数据预测,验证了所提的横观各向同性a准则及其变换应力公式的有效性及适用性.      

基于t准则的各向异性强度准则及变换应力法

岩土材料通常呈现出成层水平分布特点, 即可将其视为横观各向同性材料, 横观各向同性对于岩土材料的变形以及强度值都会产生显著的影响. 基于已提出的t强度准则, t强度准则是基于各向同性单元体中存在有效滑移面来构建的, 并根据该空间有效滑移面上主剪应力与主法向应力的比值达到一定阈值为破坏条件. 在空间中存在有效滑移面与物理沉积面, 基于上述两个面在空间的位置关系, 用两面夹角作为表征横观各向同性对剪切强度影响程度的参量, 并假定当该夹角值越大, 则各向异性对强度贡献程度越大, 对应更大的应力比强度值, 反之, 则对应更小的应力比强度值. 基于上述思路并类比将其推广为正交三维各向异性准则, 基于三维各向异性材料的三维沉积面, 提出了三维特征沉积面的概念, 并基于空间滑移面与三维特征沉积面之间的夹角作为度量各向异性程度的变量, 提出了基于两面角作为参量考虑原生各向异性的应力比强度公式, 并利用该应力比强度公式来修正已提出的t强度准则, 最终建立了考虑各向异性影响的t准则公式. 在上述准则基础上, 考虑将各向异性应力空间转换为各向同性应力空间的思路, 在各向异性t准则基础上, 推导得到了基于各向异性强度t准则的变换应力公式, 利用变换应力公式可以将传统的以p, q为变量的各向同性本构模型转变为可考虑各向异性的三维本构模型. 通过对岩土材料的强度以及真三轴条件下的应力应变关系试验数据预测, 验证了所提的各向异性t准则及其变换应力公式的有效性及适用性.      

形状记忆合金的热力学本构方程

利用形状记忆因子,直观地描述了形状记忆合金(SMA)实现其超弹性与形状记忆效应的热力学宏观过程.根据热力学基本原理并假设SMA为各向同性材料,建立了描述复杂应力状态下SMA热力学行为的三维本构方程.该本构方程具有直观的表述形式且所含材料常数均可以通过宏观实验测定,克服了现存SMA三维本构方程由于表述形式复杂和材料参数不...     

非线性横观各向同性弹性材料的本构方程及其势函数

研究了非线性Green弹性材料弹性张量独立分量,归纳推导出横观各向同性Green弹性材料、各向同性非线性弹性材料独立的弹性常数个数.从张量函数出发,用含有高阶弹性张量的张量多项式,推导出四阶非线性横观各向同性,各向同性材料Green弹性材料本构方程及其势函数.并将本构方程及其势甬数用张量不变量,标量不变量表示.证明了方程是完备的,不可约的,满足张量函数表示定理.     

一种土的非线性弹性本构模型参数的反演方法

旨在提出一种土的非线性弹性本构模型参数反演的方法。以现今普遍实行的地基载荷试验为基础,依据遗传算法的组合优化理论,采用正演计算和遗传算法优化相结合的方式,建立了土层非线性弹性本构模型参数反演的方法;并依据某黄土场地地基载荷试验数据,实施了黄土土层非线性弹性本构模型参数反演的全过程。计算结果表明,所建立的方法可以实现土层非线性弹性本构模型中相互关联的多个参数的组合优化,并在对初始值要求较低的情况下,可以获得良好的参数反演精度。从而为土的变形特性分析和土与其中及相邻结构的共同作用分析,提供了较好的土体本构模型参数的确定方法。     

动脉壁静态非线性力学性质的实验和理论研究

在动脉血管壁力学实验及已有的拟弹性理论研究基础上,提出了一个理论模型来分析具有残余应力动脉壁的非线性力学性质． 在动脉壁被模拟为均质、正交各向异性、不可压缩和具有初应力材料的前提下,建立了一个表达有残余应力动脉壁静态三维非线性拟弹性性质的ｅ指数型本构方程． 动脉壁本构方程中的十个拟弹性参数是用我们的动脉实验数据及所发展的多曲线联合逼近算法数据拟合来确定．     

横观各向同性饱和土中柱面载荷的动力Green函数

基于饱和介质的三维波动理论的Biot模型,利用Fourier展开和Hankel变换,并借助算子理论,给出了圆柱坐标系下横观各向同性饱和土波动方程的非轴对称通解;利用通解,建立了饱和土层及饱和半空间的精确动力刚度矩阵;借助刚度矩阵,给出层状横观各向同性饱和地基中,作用沿土层深度方向分布的竖向和水平柱面载荷时的动力Green函数,进而解决了利用间接边界元法分析桩-饱和土动力相互作用的关键问题.     

Cyclic stress-softening model for the Mullins effect in compression

This paper models the cyclic stress softening of an elastomer in compression. After the initial compression the material is described as being transversely isotropic. We derive non-linear transversely isotropic constitutive equations for the elastic response, stress relaxation, residual strain, and creep of residual strain in order to model accurately the inelastic features associated with cyclic stress softening. These equations are combined with a transversely isotropic version of the Arruda–Boyce eight-chain model to develop a constitutive relation that is capable of accurately representing the Mullins effect during cyclic stress softening for a transversely isotropic, hyperelastic material, in particular a carbon-filled rubber vulcanizate. To establish the validity of the model we compare it with two test samples, one for filled vulcanized styrene–butadiene rubber and the other for filled vulcanized natural rubber. The model is found to fit this experimental data extremely well.     

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对薄层单元的基本假设和简化进行了探讨并得到如下结论：薄层单元的本构方程可 通过横观各向同性体本构方程采用合理简化得到;薄层单元受拉开裂的本构关系可 采用分布裂缝模型模拟开裂简化得到;薄层单元采用的基本假 设能在一定程度上保证计算精度及简化计算.     

An explicit formulation of a three-dimensional material damping model with transverse isotropy

A constitutive three-dimensional (3D) damping model is derived for transversely isotropic material symmetry, using the augmented Hooke's law [Intl. J. Solids Struct. 32 (1995) 2835] as a starting point. The proposed material model is tested numerically, via finite-element techniques, on a laminate structure built from stacked aluminium and Plexiglas plates. Effective 3D transversely isotropic material properties are given in terms of homogeneous material damping functions in connection with homogenised elastic laminate properties. Comparisons made between the results from the elastic (undamped) eigenvalue problem of the detailed (layerwise) model of the laminate and the effective 3D elastic model show that the homogenised model is reasonably accurate, in terms of predicted elastic eigenfrequencies for the first 20 modes. The dynamic homogenisation process, with damping included, is evaluated in terms of forced vibration response for the laminate structure, using effective transversely isotropic frequency dependent material properties. The dynamic 3D effective homogeneous material model is found to simulate very closely the detailed model in the studied frequency interval for the numerical test case.     

横观各向同性饱和地基上无限板的稳态振动

研究了横观各向同性饱和土地基上无限板的稳态振动问题. 基于直角坐标系下横观各向同性饱和介质Biot波动方程的一般解，采用双重Fourier积分变换技术，建立了饱和地基与无限矩形板相互作用的动力方程，利用数值方法求解该方程，得到任意谐振荷载作用下饱和半空间体上无限板稳态响应的一般解. 数值结果表明，横观各向同性饱和地基上无限板的振动与各向同性饱和地基上的无限板的振动特性存在明显差异.     

横观各向同性层状场地中的单桩横向动力阻抗函数

本文采用横观各向同性层状弹性模型，模拟半空间上的层状场地，用阻尼器模拟透射边界代替半空间以吸收能量。利用薄层元素法和于结构法，并利用在这种边界下受水平简谐荷载作用下的格林函数，推导了这种场地中竖直单桩在水平—摇摆简谐荷载作用下的横向动力阻抗函数，并用实例计算了不同横观各向同性性质场地下的动力阻抗函数，并由此分析了场地的横观各向同性性质的强弱对单桩的横向动力阻抗函数所将产生的影响。计算表明：弱横观各向同性场地对阻抗函数的影响很小，以至可以忽略这种影响；而强横观各向同性场地对阻抗函数的影响较大，必须考虑其影响。另外，桩头约束的存在与否，对单桩的横向阻抗函数值也有较大的影响，桩头有约束的阻抗函数值要明显大于无约束的阻抗函数值。     

Wave propagation in a transversely isotropic solid cylinder of arbitrary cross-sections immersed in fluid

The wave propagation in an infinite, transversely isotropic solid cylinder of arbitrary cross-section immersed in fluid is studied using the Fourier expansion collocation method, within the framework of the linearized, three-dimensional theory of elasticity. The equations of motion of solid and fluid are respectively formulated using the constitutive equations of a transversely isotropic cylinder and the constitutive equation of an inviscid fluid. Three displacement potential functions are introduced to uncouple the equations of motion along the radial, circumferential and axial directions. The frequency equations of longitudinal and flexural (symmetric and antisymmetric) modes are analyzed numerically for an elliptic and cardioidal cross-sectional transversely isotropic solid cylinder of arbitrary cross-section immersed in fluid. The computed non-dimensional wavenumbers are presented in the form of dispersion curves for the material zinc. The general theory can be used to study any kind of cylinder with proper geometric relations.     

Static analysis of simply supported functionally graded and layered magneto-electro-elastic plates

In this article, static analysis of functionally graded, anisotropic and linear magneto-electro-elastic plates have been carried out by semi-analytical finite element method. A series solution is assumed in the plane of the plate and finite element procedure is adopted across the thickness of the plate such a way that the three-dimensional character of the solution is preserved. The finite element model is derived based on constitutive equation of piezomagnetic material accounting for coupling between elasticity, electric and magnetic effect. The present finite element is modeled with displacement components, electric potential and magnetic potential as nodal degree of freedom. The other fields are calculated by post-computation through constitutive equation. The functionally graded material is assumed to be exponential in the thickness direction. The numerical results obtained by the present model are in good agreement with available functionally graded three-dimensional exact benchmark solutions given by Pan and Han [Pan, E., Han, F., in press. Green’s function for transversely isotropic piezoelectric functionally graded multilayered half spaces. Int. J. Solids Struct.]. Numerical study includes the influence of the different exponential factor, magneto-electro-elastic properties and effect of mechanical and electric type of loading on induced magneto-electro-elastic fields. In addition further study has been carried out on non-homogeneous transversely isotropic FGM magneto-electro-elastic plate available in the literature [Chen, W.Q., Lee, K.Y., Ding, H.J., 2005. On free vibration of non-homogeneous transversely isotropic magneto-electro-elastic plates].     

On some connections between equivalent single material and mixture theory models for fiber reinforced hyperelastic materials

There are two approaches that can be used to model the large strain mechanical response of material systems in which elastic fibers are embedded in an elastic matrix. In the first approach, a fiber reinforced material undergoing large deformation is homogenized in the sense that it is assumed to act as an equivalent single material that is transversely isotropic and hyperelastic. Both constituents then share a common reference configuration, which is typically assumed to be a natural or stress-free configuration for the equivalent single material. The stress depends on a single deformation gradient defined with respect to the natural configuration.In the second approach, the fiber/matrix system is treated as a mixture, with the matrix and the fibrous constituents having their own reference configurations and material symmetries. The total stress depends on the deformation gradients and material symmetries for both constituents, defined with respect to their reference configurations.Under appropriate assumptions, the constitutive theory developed using mixture theory can coincide with the constitutive theory assuming an equivalent single material that is transversely isotropic and hyperelastic. This paper explores the connection between the two approaches by considering the various reference configurations and material symmetries.