金属基复合材料单向和循环变形行为的数值模拟研究

利用晶体细观力学模型，依据组元材料的单晶体变形性质，以Ａｌ－Ａｌ２Ｃｕ自生复合材料为模型材料，用数值法模拟其拉伸和循环拉伸变形过程，得到了与有关实验结果相符的应力－应变曲线，研究了增强相间距和循环加载过程对复合材料变形行为的影响，通过考虑变形过程中组元相及其界面的应力分布规律，分析研究了循环变形过程中基体Ｂａｕｓｃｈｉｎｇｅｒ效应对于复合材料微观变形与损伤机制的作用，结果表明，晶体细观力学模拟计算     

硬质聚氨酯泡沫塑料本构关系的研究

介绍用大尺寸分离式Ｈｏｐｋｉｎｓｏｎ压杆对四种密度的硬质聚氨酯泡沫塑料进行高应变率实验，完整地给出了这种材料在１０３／ｓ高应变率下的包括弹性区、屈服区和致密区变形全过程的动态应力应变曲线，并提出了包括应力、应变、应变率和密度等参量的本构关系．     

应变率对Gr/Al金属基复合材料力学性能的影响

利用自行研制的冲击拉伸实验装置对单向石墨纤维增强铝基复合材料实施了不同应变率下的拉伸实验。获得了材料在００００５～１３００ｓ－１应变率范围内完整的应力应变曲线。结果表明Ｇｒ／Ａｌ的应力应变曲线可分为两个部分:非线性弹脆性变形以及材料失稳后的残余变形。实验结果还表明Ｇｒ／Ａｌ是一种应变率敏感材料,随着应变率的提高,材料的拉伸强度、失稳应变以及剩余应力均相应提高。根据不同应变率下的实验结果,提出了计及应变率强化效应的复合丝束统计本构模型,模型拟合的结果与实验结果吻合得很好。拟合结果还表明,特征纤维统计分布的Ｗｅｉｂｕｌ参数（尺度参数与形状参数）均是与应变率无关的,复合材料的应变率效应主要是由基体的应变率强化效应引起的。     

帘线/橡胶复合材料各向异性黏-超弹性本构模型

帘线/橡胶复合材料广泛应用于轮胎等重要工程领域,为了描述其在服役条件下的大变形、非线性、各向异性和高应变率等材料力学行为,基于纤维增强复合材料连续介质力学理论,提出了一种考虑应变率效应的帘线/橡胶复合材料各向异性黏-超弹性本构模型. 该模型中单位体积的应变能被解耦为便于参数识别的基体等容变形能、帘线拉伸变形能、剪切应变能和黏性应变能四部分. 给出了模型参数的确定方法,并通过拟合文献中单轴拉伸、偏轴拉伸实验数据,得到了模型参数. 利用该模型预测了不同加载和变形条件下的力学行为,并将预测结果与实验结果对比分析. 结果表明, 考虑黏性模型和不考虑黏性模型对不同应变率变形条件下的预测结果相差很大,且考虑黏性模型的预测结果与实验结果吻合很好. 因此,与不考虑黏性模型相比,所提出的各向异性黏-超弹性本构模型能更好地表征帘线/橡胶复合材料在大变形、高应变率条件下的力学特性.      

Comp.B复合炸药动态压缩力学性能和本构关系的研究

本文利用自制的含能材料变温动态压缩实验装置，采用准静态应变速率（１０－４／ｓ）和中等应变速率（３／ｓ），对国产复合炸药Ｃｏｍｐ．Ｂ进行了动态压缩实验。测试了Ｃｏｍｐ．Ｂ在不同温度、不同应变速率条件下的杨氏模量、断裂强度等力学性能参数。实验结果证明，Ｃｏｍｐ．Ｂ具有明显的应变率相关和温度效应。采用Ｊｏｈｎｓｏｎ提出的温度、应变率相关的本构模型，根据实验数据拟合了Ｃｏｍｐ．Ｂ材料的本构关系，分析表明该本构模型可以很好地描述材料的应变率和温度效应。这些基础研究为含能材料动态力学性能的研究和炸药早爆机理的理论分析提供了依据。     

橡胶楔体与刚性缺口接触大变形分析

利用Ｋｕｏｗｌｅｓ与Ｓｔｅｒｎｂｅｒｇ提出的非线性弹性大变形应变能函数,对橡胶楔体与刚性缺口接触问题进行大变形渐近分析,推导了楔体尖端场的渐近方程,得到楔体尖端附近的应力应变场及应力的奇异性指数与橡胶楔体角度、刚性缺口角度及材料常数有关的表达式;楔尖附近同一半径上应力分量为常数,同时,利用非线性有限元理论编制了大变形有限元程序,考虑楔体尖端与缺口接触边界条件,计算得到了与分析解一致的结论,当缺口角     

变形—损伤耦合的超塑性恒压轴对称充模胀形的有限元模拟

采用大变形刚粘塑性有限元法模拟超塑性恒压轴对称充模胀形过程，分析了模具几何参数及材料参数对胀形过程中材料的流变行为、胀形制件厚度分布和成形时间的影响规律，给出了质点的流动轨迹，不同时刻制件的剖面形状及应力、应变分布；基于修正的Ｇｕｒｓｏｎ粘塑性势推导了内部空洞体积分数累积增大模型并据此进行了变形－损伤耦合计算。     

载重子午线轮胎三维非线性有限元分析

建立了一个轮胎结构有限元分析模型，考虑了轮胎变形的几何非线性，轮胎与地面和轮胎与轮辋的大变形非线性接触，轮胎材料的非均匀性，橡胶材料的不可压缩性和物理非线性及橡胶基复合材料的各向异性。结果表明，该模型有效可靠。     

复合材料柱管撞击分析中的有限元方法

建立了复合材料柱管结构在撞击状态下的有限元分析模型,考虑了撞击大变形引起的几何非线性、撞击接触的非线性、纤维树脂复合材料的各向异性及材料的物理非线性．给出了利用该有限元方法分析玻璃环氧柱管撞击吸能特性,并与试验进行了比较,得到了较好的吻合结果,表明该有限元方法是有效的．此外,还讨论了纤维的铺设角度对复合材料管的吸能性能的影响．     

纤维复合材料的弹粘塑性行为体分比与应变率的影响

利用微观力学方法研究了纤维增复合材料的弹塑性行为，着重分析了纤维体分比和加载应变率对以金属基为主的复合材料应力－应变关系的影响。给出了不同体分比的Ｇｒａｐｈｉｔｅ／Ｔｉｔａｎｉｕｍ复合材料在不同常应变率下的应力－应变关系曲线，对这两种因素的影响进行了比较分析。     

An improved Jones-Nelson nonlinear material model and rubber composite lamina analysis

A Jones-Nelson model has been applied to depict nonlinear stress-strain relations of composite laminae, where mechanical properties were expressed by strain energy density. The nonlinear material matrix is only a function of the strain energy density. Then a material model could be conveniently applied under complex stress condition. In this paper, by introducing large displacement stress-strain measurement and varying-Poisson's ratio idea, an improved Jones-Nelson material model is presented, where the expanding problem of material properties and convergence problems are overcome. Meanwhile a discuss of the reorientation of fiber and a material nonlinear analysis of rubber composite lamina under super large deformation conditions are made. The prediction results of improved material model are in fairly good agreement with those of the experiments.     

General stress-strain relations in non-linear theory of viscoelasticity for large deformations

Conclusion General phenomenoligical stress-strain relations in non-linear theory of visco-elasticity for large deformations have been presented.In the first place, according to V. V. Novozhilov 1 we express the generalized equilibrium equation for large deformations in the Lagrange representation, and we apply the generalized Hamilton's principle to the equation of energy conservation, which denotes that the sum of the elastic energy and the dissipative energy is equal to the work done by the body force and the surface on the substance; so that we obtain the required general stress-strain relations in comparison with the above two equations.On the condition that the elastic potential is a function only of the strain, and the dissipation function is a function of the rate of strain and of strain; such a substance is reduced to the Voigt material necessarily, and the stresses which act on the substance are given by the sum of elastic- and viscous stresses, and the stress-strain relations are reduced to the so-called Lagrangian form.If elongations, shears and angles of rotation are small and also the strains and rates of strain are sufficiently small, the stress-strain relations are expressed by a linear Voigt model constituting a Hookian spring in parallel with a Newtonian dashpot.Non-linearity in the theory is classified into two groups i. e. the geometrical non-linearity and the physical non-linearity. The former is introduced into the theory through the definition of the generalized strain and of the generalized stress and through the equilibrium equation for large deformation, and the latter through the general stress-strain relations.The main result of this paper is that the general stress-strain relations in viscoelasticity are deduced necessarily from the physically appropriate assumptions.     

A composites-based hyperelastic constitutive model for soft tissue with application to the human annulus fibrosus

This paper presents a composites-based hyperelastic constitutive model for soft tissue. Well organized soft tissue is treated as a composite in which the matrix material is embedded with a single family of aligned fibers. The fiber is modeled as a generalized neo-Hookean material in which the stiffness depends on fiber stretch. The deformation gradient is decomposed multiplicatively into two parts: a uniaxial deformation along the fiber direction and a subsequent shear deformation. This permits the fiber-matrix interaction caused by inhomogeneous deformation to be estimated by using effective properties from conventional composites theory based on small strain linear elasticity and suitably generalized to the present large deformation case. A transversely isotropic hyperelastic model is proposed to describe the mechanical behavior of fiber-reinforced soft tissue. This model is then applied to the human annulus fibrosus. Because of the layered anatomical structure of the annulus fibrosus, an orthotropic hyperelastic model of the annulus fibrosus is developed. Simulations show that the model reproduces the stress-strain response of the human annulus fibrosus accurately. We also show that the expression for the fiber-matrix shear interaction energy used in a previous phenomenological model is compatible with that derived in the present paper.     

A pattern-based method for bounding the effective response of a nonlinear composite

This paper deals with the prediction of the effective properties of nonlinear composites. Rather than bounding the effective energy, this work aims at bounding directly the effective stress-strain response, by extending a method originally introduced by Milton and Serkov (J. Mech. Phys. Solids 48 (2000) 1295) and recently refined by Talbot and Willis (Proc. Roy. Soc. 460 (2004) 2705). In this paper, bounding the effective response is achieved by introducing a linear comparison composite with the same micro-geometry as the given nonlinear composite, as Ponte Castañeda (J. Mech. Phys. Solids 39 (1991) 45) did for the energy. It is found that any lower bound for the energy of the linear comparison composite generates a corresponding bound for the stress-strain response of the nonlinear composite. A selection of examples is presented to illustrate the method and compare the bounds obtained with existing results.     

On the unilateral contact problem of structures with a non quadratic strain energy density

The analysis of structures with “unilateral contact” boundary conditions is considered. The stress-strain relations are nonlinear and they are derived from a non quadratic strain energy density by “subdifferentiation”. It is proved that for the inequality constrained boundary value problem the “principles” of virtual and of complementary virtual work hold in an inequality form constituting a variational inequality. The theorems of minimum potential and complementary energy are proved to be valid to account for this type of boundary conditions. These theorems are used to formulate the analysis as a nonlinear programming problem. A numerical example of a structure having the “unilateral contact” boundary condition illustrates the theory.     

Solution of a Riemann problem for elasticity

This paper describes a numerical algorithm for the Riemann solution for nonlinear elasticity. We assume that the material is hyperelastic, which means that the stress-strain relations are given by the specific internal energy. Our results become more explicit under further assumptions: that the material is isotropic and that the Riemann problem is uniaxial. We assume that any umbilical points lie outside the region of physical relevance. Our main conclusion is that the Riemann solution can be obtained by the iterative solution of functional equations (Godunov iterations) each defined in one- or two-dimensional spaces.Supported in part by AFOSR-88-0025.     

Moderately large flexural vibrations of composite plates with thick layers

In this paper moderately large amplitude vibrations of a polygonally shaped composite plate with thick layers are analyzed. Three homogeneous and isotropic layers with a common Poisson’s ratio are perfectly bonded and their arbitrary thickness and material properties are symmetrically disposed about the middle plane. Mindlin–Reissner kinematic assumptions are implemented layerwise, and as such model both the global and local response. Geometric nonlinear effects arising from longitudinally constrained supports are taken into account by Berger’s approximation of nonlinear strain–displacement relations. Overall cross-sectional rotations are defined and subsequently a correspondence of this complex problem to the simpler case of a homogenized shear-deformable nonlinear plate with effective stiffness and hard hinged boundary conditions is found. The nonlinear steady-state response of composite plates subjected to a time-harmonic lateral excitation is investigated and the phenomena of nonlinear resonance are studied and evaluated.     

Influence of fiber’s shape and size on overall elastoplastic property for micropolar composites

A general micromechanical method is developed for a micropolar composite with ellipsoidal fibers, where the matrix material is idealized as a micropolar material model. The method is based on a special micro–macro transition method, and the classical effective moduli for micropolar composites can be determined in an analytical way. The influence of both fiber’s shape and size can be analyzed by the proposed method. The effective moduli, initial yield surface and effective nonlinear stress and strain relation for a micropolar composite reinforced by ellipsoidal fibers are examined, it is found that the prediction on the effective moduli and effective nonlinear stress and strain curves are always higher than those based on classical Cauchy material model, especially for the case where the size of fiber approaches to the characteristic length of matrix material. As expected, when the size of fiber is sufficiently large, the classical results (size-independence) can be recovered.     

NEPE推进剂低高应变率下改进的黏-超弹本构模型

为研究低高应变率条件下NEPE推进剂的力学特性,通过电子万能试验机和分离式霍普金森杆装置,对NEPE推进剂进行了准静态和冲击实验,得到了不同应变率下（1.667×10?4～4 500 s?1）的应力-应变曲线。实验结果表明NEPE推进剂具有明显的非线性弹性和应变率敏感性,随着应变率的增加,材料的强度、屈服应力和弹性模量显著增加,与低应变率相比,高应变率条件下材料的应变率敏感性更高。在高速冲击下材料内部瞬间产生大量热量无法及时散发出去,使得材料内部温度升高,导致材料出现软化效应,力学性能降低。本文建立了一个非线性黏超弹本构模型,其中采用Rivlin应变能函数来描述稳态超弹响应部分,采用积分型本构模型来描述材料的动态黏弹性响应部分,考虑到松弛时间具有应变率相关性,本文采用了一个率相关松弛函数来替代传统的Prony级数形式。使用极慢速压缩实验数据对本构模型中的超弹部分进行拟合获得超弹参数,然后用准静态和动态实验数据对本构模型进行拟合得出其他参数。不同应变率下的预测曲线与实验曲线具有较好的重合度,证明了该模型可以很好地描述低高应变率下NEPE推进剂的力学特性。     

Nonlinear low-velocity impact on damped and matrix-cracked hybrid laminated beams containing carbon nanotube reinforced composite layers

This paper investigates the low-velocity impact response of a shear deformable laminated beam which contains both carbon nanotube reinforced composite (CNTRC) layers and carbon fiber reinforced composite (CFRC) layers. The effect of matrix cracks is considered, and a refined self-consistent model is selected to describe the degraded stiffness caused by the damage. The beam including damping effects rests on a two-parameter elastic foundation in thermal environments. Based on a higher-order shear deformation theory and von Kármán nonlinear strain–displacement relationships, the motion equations of the beam and impactor are established and solved by means of a two-step perturbation approach. The material properties of both CFRC layers and CNTRC layers are assumed to be temperature-dependent. To assess engineering application of this hybrid structure, two conditions for outer CNTRC layers and outer CFRC layers are compared. Besides, the effects of the crack density, volume fraction of carbon nanotube, temperature variation, the foundation stiffness and damping on the nonlinear low-velocity impact behavior of hybrid laminated beams are also discussed in detail.