共查询到20条相似文献,搜索用时 31 毫秒
1.
By means of Sylvester's spectral representation of tensor-valued functions, a representation is derived for the finite stretch
and rotation associated with the polar decomposition of a given deformation gradient.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
2.
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. 相似文献
3.
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. 相似文献
4.
5.
Time Rates of Hill's Strain Tensors 总被引:4,自引:0,他引:4
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. 相似文献
6.
变形梯度张量极分解中转动张量的直接表示及其应用 总被引:1,自引:0,他引:1
本文通过变分途径建立了变形梯度张量的极分解和加法分解之间的联系.采用工程界通常采用的变形梯度张量的加法分解形式,得到了三维空间中极分解的转动张量和伸长张量的直接表示,即实现了转动和变形的分离.由这些直接表示,可以得到各种有用的近似表示. 相似文献
7.
8.
C. S. Jog 《Journal of Elasticity》2006,82(2):175-192
We present a solution for the tensor equation TX + XT
T
= H, where T is a diagonalizable (in particular, symmetric) tensor, which is valid for any arbitrary underlying vector space dimension n. This solution is then used to derive compact expressions for the derivatives of the stretch and rotation tensors, which in turn are used to derive expressions for the material time derivatives of these tensors. Some existing expressions for n = 2 and n = 3 are shown to follow from the presented solution as special cases. An alternative methodology for finding the derivatives of diagonalizable tensor-valued functions that is based on differentiating the spectral decomposition is also discussed. Lastly, we also present a method for finding the derivatives of the exponential of an arbitrary tensor for arbitrary n. 相似文献
9.
In this study, we considered the extended polar decomposition using a more general approach than the one provided by Boulanger and Hayes [Int. J. Non-Linear Mech. 36 (2001) 399–420]. We showed that the procedure of the decomposition could be simplified by considering its rotation tensor. Our method is illustrated by examples. 相似文献
10.
Dui Guan-Suo 《Journal of Elasticity》1998,50(3):197-207
An explicit representation for the rotation tensor which contains the lower powers of deformation gradient is proposed and
used to evaluate the angle and axis of the rotation tensor. Some related equations about the rotation tensor are established.
Through the approximate analysis, the relation between the S-R decomposition and the polar decomposition is examined.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
11.
By using Cayley-Hamilton theorem, two kinds of explicit representation for the rotation tensor are proposed. One contains
the lower powers of deformation gradient, by which the formula of the principal rotation angle and the explicit representation
of principal axis are obtained; the other, a high efficient method to obtain the rotation tensor, does not contain the complicated
coefficients and uses few variables. Some properties about the principal rotation angle and the principal rotation axis are
obtained. 相似文献
12.
本文应用超弹性材料的有限变形理论分析了在面内等双向拉伸死载荷作用下不可压热超弹性方形薄板发生非对称变形的分岔及其稳定性问题.给出了方板变形的分岔曲线和临界载荷,发现对受面内等双向拉伸载荷作用的均匀方板,当拉伸载荷值较小时,方板双向等伸长变形,发生对称的拉伸变形;但当此载荷值大于某一临界值时,从方板的对称拉伸变形中分岔出非对称的变形,方板在两个方向的变形不再相等.通过变形发生分岔前后的能量比较发现,分岔后的对称变形是不稳定的,而非对称变形是稳定的.同时,给出了板中的应力分布曲线,并由不同温度下变形的分岔曲线和应力分布曲线讨论了温度对方板变形和板中的应力分布的影响. 相似文献
13.
Surface Impedance Tensors of Textured Polycrystals 总被引:1,自引:0,他引:1
A formula for the surface impedance tensors of orthorhombic aggregates of cubic crystallites is given explicitly in terms
of the material constants and the texture coefficients. The surface impedance tensor is a Hermitian second-order tensor which,
for a homogeneous elastic half-space, maps the displacements given at the surface to the tractions needed to sustain them.
This tensor plays a fundamental role in Stroh's formalism for anisotropic elasticity. In this paper we account for the effects
of crystallographic texture only up to terms linear in the texture coefficients and give an explicit formula for the terms
in the surface impedance tensor up to those linear in the texture coefficients.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
14.
Cristina Padovani 《Journal of Elasticity》2000,58(3):257-268
An explicit expression of the derivative of the square root of a tensor is provided, by using the expressions of the derivatives
of the eigenvalues and eigenvectors of a symmetric tensor. Starting from this result, the derivatives of the right and left
stretch tensor U, V and of the rotation R with respect to the deformation gradient F, are calculated. Expressions for the material time derivatives of U, V and R are also given.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
15.
C. S. Jog 《Journal of Elasticity》2006,85(2):119-124
We present a new proof of the representation theorem for fourth-order isotropic tensors that does not assume the tensor to have major or minor symmetries at the outset. 相似文献
16.
赵祖武 《应用数学和力学(英文版)》2001,22(1):89-95
1 IntroductionandPreliminaryWhentheplasticconstitutiveequationatfinitestrainisdiscussed ,thefirstthingtodoistodefineareasonableplasticstrainratewhichisconnectedwiththeproblemofdecompositionofdeformationintoelasticandplasticparts .Inthelatestyearstherea… 相似文献
17.
18.
Through a variational approach, an explicit connection between the additive and the polar decompositions of deformation gradient has been established. An exact formula for determining the rotation tensor in polar decomposition is obtained. The formula is fundamental in continuum mechanics and can be used to separate the rotation and the pure strain in deformation, by which various approximate expressions can be easily obtained. 相似文献
19.
The paper presents a general methodology of introducing the shell-type variables which is based on the rotation constraint-equation
(RC-equation). The RC-equation is proven to be equivalent to the polar decomposition of the deformation gradient formula,
and the rotations which it yields are interpreted in terms of rotations of vectors of an ortho-normal basis. The deformation
function and rotations are assumed as polynomials of the thickness coordinate ζ, and in this form used in the RC-equation.
Solving this equation, we can express the coefficients of the quadratic deformation function in terms of the following shell-type
variables: (a) the mid-surface position x
0, (b) the constant rotation Q
0, (c) the rotation vector ψ
* for the ζ-dependent rotations, and (d) the normal components U
33
0 and U
33
1 of the right stretching tensor. This new methodology (i) ensures that all shell kinematical variables are consistent with
the RC-equation, which is justified on 3D grounds, (ii) provides a general framework from which various Reissner-type hypotheses
can be obtained by suitable assumptions. As an example, two generalized Reissner hypotheses are derived: one with two normal
stretches, and the other with the in-plane twist and the bubble-like warping parameters.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
20.
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. 相似文献