玻璃态高聚物PMMA的非线性粘弹-塑性本构方程

对航空有机玻璃(聚甲基丙烯酸甲酯,PMMA)实验测定了不同应变率下单轴压缩加卸载循环的应力-应变曲线,讨论了应力促进热激活塑性变形的活化粘壶理论,提出由标准线性体或Maxwell体与考虑应变硬化效应的活化粘壶作串联耦合的粘弹-塑性本构模型,给出了完备的微分和积分形式的本构方程组,用于拟合实测加卸载循环的应力-应变曲线,获得良好吻合的结果。对应变软化效应提出一种新的起因于粘弹变形滞后效应的理论说明,并对屈服后加载应力-应变曲线的走向特征作了理论解释。     

沥青混合料一维非线性粘弹本构方程

本文根据Green-Rivlin提出的Frechet级数,提出了一个兼具长时粘流效应及短时粘弹效应的一维非线性本构方程,并对一种沥青混合料采用蠕变试验方式拟合了本构方程的参数向量。拟合结果表明:这一本构方程形式简洁,物理意义清晰,易于拟合,并对不同应力历史下的应变响应具有广泛的适用性。     

扰动本构方程及粘弹流体拉伸流动不稳定性

提出“准衰退记忆”新概念,发展了非牛顿流体扰动本构理论,并研究了粘弹流体拉伸流动的不稳定性规律     

弹／粘塑性三维应力的参数变换

对符合Ｂｒｉｄｇｍａｎ假设和简单加载条件的弹／粘塑性材料，本文引用坐标变换的三个参数σｍ、μσ、ｊ′２将非线性弹／粘塑性本构方程线性化。用这些参数构造三维基本方程，用Ｌａｐｌａｃｅ变换方法可以求解。本文用这一方法分析了弹／粘塑性力学典型问题。     

材料的弹粘塑性本构关系和应力波的演化

试验表明，大多数工程材料在冲击载荷作用之下的变形一般都同时包含有可恢复的瞬态性弹性变形和不可恢复的粘滞性塑性变形，即其本构关系可以用弹粘塑性模型来描述。本文从内变量理论出发，探讨了时率相关材料的弹粘塑性本构关系的一般特性，建立了增量型的弹粘塑性本构关系的一般理论框架和普适的表达式，并且对两种最常用的本构模型——Bodner-Partom模型和Johnson-Cook模型给出了在一维应变条件下的具体形式。通过计算和讨论一维应变粘塑性靶板中冲击波的衰减机制和应力波的演化规律，特别是考察各种粘塑性本构模型中的材料参数对冲击波的衰减和应力波的演化的影响，得出了一些可以直接应用或具有一定借鉴价值的结果，为研究应力波的其他衰减机制以及在人防工程中智能防护层设计时新材料的选取奠定了基础。     

软岩三维非线性统一弹粘塑性本构模型有限元分析

在作者已建立的软岩三维非线性统一弹粘塑性软化本构模型基础上,讨论了软岩三维非线性统一弹粘塑性本构模型有限元分析过程,即推导了软岩三维非线性统一弹粘塑性屈服面(破坏面)的流动矢量表达式,便于编程与通用的有限元程序接口,进行二次开发;利用张量求导的原则,导出了流动矢量对应力求导公式中关键矩阵的具体表达式,并结合平面应力、平面应变和轴对称问题的特点进行了简化,得出了适合于分析二维问题的关键矩阵的表达式;采用流动矢量奇异性的统一处理方法,有效地处理了各种角点奇异性问题;最后给出了有限元分析的流程图,便于编制有限元程序.     

材料非线性粘弹性本构关系的神经网络模拟

对Green-Rivlin非线性粘弹本构方程给出了用一个三层时延前馈神经网络表示的等价关系,从而利用该网络可以求解G-R方程中的各阶核函数,并给出了根据有机玻璃的一组实验数据计算核函数的应用实例,由此指出神经网络方法可广泛应用于材料本构关系的研究。     

热粘塑性体的积分—微分型本构关系

应用ИЛЪЮШИН关于应力是五维偏应变空间变形历史的泛函的概念和Ｖａｌａｎｉｓ有关内时理论的描述，本文提出，对热粘塑性体，应力可设为应变、应变率和温度历史泛；并应用Ｍｉｌｌｅｒ和其它一些作者有关内变量演化方程的描述，由此建立了热粘塑性体的积分－微分型本构方程这一积分－微分型本构关系大体和Ｍｉｌｌｅｒ微分型模型等价。对１０２０钢的单轴本构响应进行了数值模拟，和Ｔａｎａｋａ与Ｍｉｌｌｅｒ的分析及一些实     

描述非线性动力响应的砂质土本构模型

本文提出描述非线性响应的砂擀土本构模型，由本构模型计算所得到的理论曲线与实验曲线发接近此模型能广泛地用于土工问题的弹一塑性有限元分析中。     

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。     

Ein nichtlineares Stoffgesetz für die ebene photoviskoelastische Spannungsanalyse

On the basis of a phenomenological theory of photoviscoelasticity which is guided by the results on the macroscopic behaviour of materials, nonlinear constitutive equations in the form of a single-integral representation are derived, being valid for homogeneous, isotropic, and non-aging, amorphous plastics, including large deformations. They yield the basic equations of two-dimensional nonlinear photoviscoelasticity which are used for the experimental analysis of plane states of stresses in polymeric structures under static or quasistatic isothermal loading. The example of an unsaturated polyester material labeled Leguval E 81 shows how to determine the material functions in the constitutive equations. The results allow us to make some simplifications which reduce the amount of numerical calculations when applying the proposed non-linear photoviscoelastic method.     

Uniaxial wave propagation in a nonlinear thermoviscoelastic medium with temperature dependent properties

The problem of finite wave propagation in a nonlinearly thermoviscoelastic thin rod whose viscoelastic properties are temperature dependent is considered. The rod is subjected to mechanical or thermal time-dependent loading. The coupled equations of motion and heat conduction are based on a constitutive theory of nonisothermal nonlinear viscoelasticity which is described by single-integral terms only. This theory is reformulated here for the uniaxial motion of a compressible rubbery material. The solution of the field equations is obtained by a numerical procedure which is developed for the present case and is able to handle successfully shock waves whenever they built up in the nonlinear material.     

Viscoelastic response of a unidirectional composite containing two viscoelastic constituents

Viscoelastic response of a unidirectional aramid fiber-reinforced epoxy was measured. Procedures to measure all five time-dependent material properties necessary to describe behavior of a transversely isotropic continuous-fiber unidirectional lamina were implemented. The Iosipescu shear method was used to measure in-plane and interlaminar shear viscoelastic response. Applicability of the Schapery single-integral nonlinear viscoelastic constitutive model to describe time-dependent mechanical behavior of a laminated composite material containing two viscoelastic phases was explored. Linear and nonlinear viscoelastic parameters for this two-viscoelastic constituent composite were measured and data summaries are presented in the paper. The time-dependent behavior of this two-viscoelastic constituent composite material was found to be complex, but the Schapery nonlinear viscoelastic model did adequately fit the response of such a composite to uniaxial applied loads.Paper was presented at the 1988 SEM Spring Conference on Experimental Mechanics held in Portland, OR on June 5–10.     

Coupled nonlinear constitutive models for rarefied and microscale gas flows: subtle interplay of kinematics and dissipation effects

The constitutive relations of gases in a thermal nonequilibrium (rarefied and microscale) can be derived by applying the moment method to the Boltzmann equation. In this work, a model constitutive relation determined on the basis of the moment method is developed and applied to some challenging problems in which classical hydrodynamic theories including the Navier–Stokes–Fourier theory are shown to predict qualitatively wrong results. Analysis of coupled nonlinear constitutive models enables the fundamentals of gas flows in thermal nonequilibrium to be identified: namely, nonlinear, asymmetric, and coupled relations between stresses and the shear rate; and effect of the bulk viscosity. In addition, the new theory explains the central minimum of the temperature profile in a force-driven Poiseuille gas flow, which is a well-known problem that renders the classical hydrodynamic theory a global failure.     

Adequacy of a nonlinear theory of viscoelasticity

Some features of the behavior of viscoelastic materials whose existence leads to the choice of nonlinear constitutive relations are discussed. A classification of such constitutive relations is given and a number of requirements imposed by practice on their adequacy are formulated. A nonlinear theory of viscoelasticity is proposed; this theory offers the advantages over the theory in which stresses are expressed in terms of strains by integral operators of increasing multiplicity. By a one-dimensional example, it is shown that the constitutive operator relations are reciprocal.     

Microstructure-dependent couple stress theories of functionally graded beams

A microstructure-dependent nonlinear Euler-Bernoulli and Timoshenko beam theories which account for through-thickness power-law variation of a two-constituent material are developed using the principle of virtual displacements. The formulation is based on a modified couple stress theory, power-law variation of the material, and the von Kármán geometric nonlinearity. The model contains a material length scale parameter that can capture the size effect in a functionally graded material, unlike the classical Euler-Bernoulli and Timoshenko beam theories. The influence of the parameter on static bending, vibration and buckling is investigated. The theoretical developments presented herein also serve to develop finite element models and determine the effect of the geometric nonlinearity and microstructure-dependent constitutive relations on post-buckling response.     

Nonlinear strain gradient elastic thin shallow shells

The governing equilibrium equations for strain gradient elastic thin shallow shells are derived, considering nonlinear strains and linear constitutive strain gradient elastic relations. Adopting Kirchhoff’s theory of thin shallow structures, the equilibrium equations, along with the boundary conditions, are formulated through a variational procedure. It turns out that new terms are introduced, indicating the importance of the cross-section area in bending of thin plates. Those terms are missing from the existing strain gradient shallow thin shell theories. Those terms highly increase the stiffness of the structures. When the curvature of the shallow shell becomes zero, the governing equilibrium for the plates is derived.     

On Pitteri Neighborhoods Centered at Hexagonal Close-Packed Configurations

I study the structure of Pitteri neighborhoods centered at hexagonal close-packed configurations of monatomic crystals using my previously introduced X-ray theory. The theory is generalized to cover some effects of magnetism. I give an alternative formulation of X-ray theory that makes comparison to conventional continuum theories more transparent. I study the influence of lattice symmetry on the constitutive relations of nonlinear thermoelasticity and thermomagnetoelasticity, consistent with the existence of a Pitteri neighborhood.     

两相混合流体的非线性本构理论

本文从连续介质力学的基本原理出发,建立了微极流体与经典流体两相流动的非线性扩散理论。给出了混合流体本构方程的一般形式。对单相流体、单相微极流体及稀悬浮体三种特殊情形,得到了具体形式的二阶非线性本构方程,并同已有的理论进行了比较。     

Restrictions on nonlinear constitutive equations for elastic shells

Constitutive equations for the resultant forces and moments applied to a shell-like body necessarily couple the influences of the shell geometry and the constitutive nature of the three-dimensional material from which the shell is constructed. Consequently, even when the nonlinear constitutive equation of the three-dimensional material is known, the complicated influence of the shell geometry on the constitutive response of the shell is not known. The main objective of this paper is to develop restrictions on the constitutive equations of nonlinear elastic shells which ensure that exact solutions of the shell equations are consistent with exact nonlinear solutions of the three-dimensional equations for homogeneous deformations. Since these restrictions are nonlinear in nature they provide valuable general theoretical guidance for specific constitutive assumptions about the coupling of material and geometric properties of shells. Examples of the linear theories of a plate and a spherical shell are considered.