On Unsheared Tetrads

Assuming the existence of genuine unsheared triads, we examine the possibility of having unsheared tetrads, particularly unsheared genuine tetrads.     

A novel internal dissipation inequality by isotropy and its implication for inelastic constitutive characterization

In the present work a novel inelastic deformation caused internal dissipation inequality by isotropy is revealed. This inequality has the most concise form among a variety of internal dissipation inequalities, including the one widely used in constitutive characterization of isotropic finite strain elastoplasticity and viscoelasticiy. Further, the evolution term describing the difference between the rate of deformation tensor and the “principal rate” of the elastic logarithmic strain tensor is set, according to the standard practice by isotropy, to equal a rank-two isotropic tensor function of the corresponding branch stress, with the tensor function having an eigenspace identical to the eigenspace of the branch stress tensor. Through that a general form of evolution equation for the elastic logarithmic strain is formulated and some interesting and important results are derived. Namely, by isotropy the evolution of the elastic logarithmic strain tensor is embodied separately by the evolutions of its eigenvalues and eigenprojections, with the evolution of the eigenprojections driven by the rate of deformation tensor and the evolution of the eigenvalues connected to specific material behavior. It can be proved that by isotropy the evolution term in the present dissipation inequality stands for the essential form of the evolution term in the extensively applied dissipation inequality.     

A Note on Maximum Shear

The problem of the determination at any point P in a body of that pair of infinitesimal material line elements which suffers the maximum shear in a deformation has been solved [1]. Here that problem is revisited and a short proof, of geometrical type, of the result is presented. This revised version was published online in July 2006 with corrections to the Cover Date.     

Central Circular Sections of the Strain Ellipsoids

A simple direct proof is given of the known result that in any deformation x = x(X), the planes of the central circular sections of the material strain-ellipsoid at X are deformed into the planes of the spatial strain-ellipsoid at x. This revised version was published online in August 2006 with corrections to the Cover Date.     

QUASI-PRINCIPAL AXIS METHOD IN FINITE DEFORMATION

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Shear instability direction at a crack-tip in a thermoviscoplastic body

Deformation fields near a crack tip are analyzed for a thermoviscoplastic body deformed either in an antiplane shear or in plane strain. The effects of inertia forces and heat conduction are considered, but those of material elasticity are neglected. By assuming that a shear band initiating from the crack-tip propagates in the direction of the maximum effective stress. It is found that a shear band propagates along the crack ligament in the body deformed in an antiplane shear. For a body undergoing plane strain deformations, the direction of the propagation of the shear band depends upon the mode-mixity parameter and agrees with that observed by Kalthoff.     

On Pure Shear

Following on the work of Belik and Fosdick, an extremely elementary proof is given for a fundamental theorem concerning pure shear.     

INVESTIGATIONS ON THE MECHANICAL CHARACTERISTICS OF NANOBEAMS BASED ON THE NONLOCAL STRAIN GRADIENT THEORY1)

基于非局部应变梯度理论,建立了一种具有尺度效应的高阶剪切变形纳米梁的力学模型. 其中,考虑了应变场和一阶应变梯度场下的非局部效应. 采用哈密顿原理推导了纳米梁的控制方程和边界条件,并给出了简支边界条件下静弯曲、自由振动和线性屈曲问题的纳维级数解. 数值结果表明,非局部效应对梁的刚度产生软化作用,应变梯度效应对纳米梁的刚度产生硬化作用,梁的刚度整体呈现软化还是硬化效应依赖于非局部参数与材料特征尺度的比值. 梁的厚度与材料特征尺度越接近,非局部应变梯度理论与经典弹性理论所预测结果之间的差异越显著.     

广义双重抗侧力结构体系的统一位移计算理论

在广义概念上将建筑结构视为由同时考虑弯曲变形、剪切变形的两种子结构组成的双重抗侧力结构体系, 提出弹性阶段广义双重结构水平位移的统一的计算方法. 子结构单独承受水平外载荷时其内力与变形的关系服从Timoshenko剪切梁基本理论, 在子结构协同工作的基础上, 采用水平变形连续化的计算方法, 建立了广义双重抗侧力结构体系的统一位移微分方程, 以结构承受均布载荷作用为例推导出两个子结构的弯曲变形、剪切变形及结构总水平位移的通用解析表达式. 对框架-剪力墙结构与广义双重结构的位移微分方程式、微分方程特解、水平位移解析解进行了全面对比分析, 证明了框架-剪力墙结构是隶属于广义双重结构体系的一种具体表现形式; 算例分析表明, 对于一般中高层双重抗侧力结构, 采用解析法计算所得的位移结果能够满足一般工程设计的精度要求.      

混凝土剪切应力-应变曲线的研究

本文利用自行设计的混凝土剪切试件对混凝土剪切强度、剪切应力一应变曲线进行了研究,为混凝土结构的分析提供了必要的力学模型．     

On several new methods to polar decomposition computation

In this paper, the polar decomposition of a deformation gradient tensor is analyzed in detail. The four new methods for polar decomposition computation are given: (1) the iterated method, (2) the principal invariant's method, (3) the principal rotation axis's method, (4) the coordinate transformation's method. The iterated method makes it possible to establish the nonlinear finite element method based on polar decomposition. Furthermore, the material time derivatives of the stretch tensor and the rotation tensor are obtained by explicit and simple expressions. The authors gratefully acknowledge the support rendered by the National Natural Science Foundation of China and the Natural Science Foundation of Jiangxi of China in 1998.     

关于几种新的极分解计算方法

对变形梯度极分解的计算方法进行了分析,给出极分解计算的四种新方法：（１）增量叠加法;（２）基于伸长张量不变量（近似）计算法;（３）确定主转动轴计算法;（４）坐标变换法．增量叠加极分解计算方法将为建立以伸长张量为应变度量的大变形大转动有限元分析方法提供基础．本文还给出了伸长张量物质时间导数的简洁表达式     

Derivation of the general form of elasticity tensor of the transverse isotropic material by tensor derivate

SymbolsU--FunchonofstrainenergyQ--OrthonormaltensorE--StraintensorEar--ComponentsofthestraintensorE,i,j=l,2,3n--VectorofthesymmetricaamsofthetransverseisotropicmaterialU*,E.,n*--FormsofU,EandninanothercoordinatesystemJf--MaininvariantsofstraintensorE,i=l,2,3Jf'n--InvariantsofstraintensorEconnectingwithvectorn,i=4,5Ji--TheabbreviatedformsofJf,Jf,Jf,Jf,",Jf,",i=l,2,3,4,5fi--ConstantsindependentonE,n,i=l,2,3,4,5el,e"--Thecovariantandcontravariantofthonormalbasisoftheusedcoordinatesyste…     

用高阶位移模式分析复合材料层合板的自由振动

建立一种新的高阶位移模式：分层假设复合材料层合板的位移场，利用各层间应力及位移的连续性条件，导出了作为整体的层合板控制微分方程。最后，采用这一高阶剪切理论来分析复合材料矩形层合板的自由振动。数值计算采用有限差分法，并编制了计算程序，计算得出了六种不同边界条件、不同铺层、不同宽厚比工况下的矩形层合板的自振频率。同经典理论解进行比较，可以看出本文方法简便易行，且精度较高，可以在微机上实用。     

Basic Issues Concerning Finite Strain Measures and Isotropic Stress-Deformation Relations

It is indicated that the commonly-used Rivlin–Ericksen representation formula for isotropic tensor functions exhibits some properties that might be undesirable for its reasonable and effective applications. Towards clarification and improvement, a set of three mutually orthogonal tensor generators is introduced to achieve an alternative representation formula for isotropic symmetric tensor-valued functions of a symmetric tensor. This representation formula enables us to express the unknown representative coefficients in terms of simple, explicit tensorial inner products of the argument tensor and the value tensor without involving their eigenvalues. In particular, the tensorial interpolation expressions thus obtained assume a unified form for the three different cases of coalescence of the eigenvalues of the argument tensor. Moreover, each summand in the alternative representation formula is shown to inherit the continuity and differentiability properties of the represented isotropic tensor function. These results are used to study some basic issues concerning finite strain measures and stress-deformation relations of isotropic materials, such as continuity and differentiability properties of the representation, determination of the representative coefficients in terms of experimental data for stress and deformation tensors, and computations of finite strain measures. This revised version was published online in June 2006 with corrections to the Cover Date.     

连续介质力学中变形梯度张量客观性表述的分歧

张量的客观性是连续介质力学中一个重要的概念,但现有文献对张量客观性的定义不一致导致有关变形梯度张量客观性的表述存在分歧.本文主要基于张量的逆及功共轭角度分析了不同客观性定义的差别,旨在加深对张量客观性,特别是对变形梯度等两点张量客观性的认识.     

极分解计算的非线性消除法

变形梯度的极分解在平面问题中得到了很好解决,在三维空间问题中一直认为是相当困难,利用Cayley-Hamilton公式和U的三个不变量求解是目前普遍采用的方法,文章利用正交矩阵的特性,介绍了非线性逐次消除的方法,给出了右极分解的计算式.     

Time Rates of Hill's Strain Tensors

Based on Hill's principal components formulae, two kinds of basis-free time rate formulae for Hill's strain tensors are proposed in this paper, which are obtained for the cases of distinct stretches, double coalescence and triple coalescence. Furthermore, relations between the coefficients in the representation for the strain tensor and its time derivative are disclosed. This revised version was published online in August 2006 with corrections to the Cover Date.