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1.
Derivatives and Rates of the Stretch and Rotation Tensors 总被引:2,自引:0,他引:2
Luciano Rosati 《Journal of Elasticity》1999,56(3):213-230
General expressions for the derivatives and rates of the stretch and rotation tensors with respect to the deformation gradient
are derived. They are both specialized to some of the formulas already available in the literature and used to derive some
new ones, in three and two dimensions. Essential ingredients of the treatment are basic elements of differential calculus
for tensor valued functions of tensors and recently derived results on the solution of the tensor equation A X + XA= H in the unknown X.
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
4.
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
5.
6.
Jovo P. Jaric 《Journal of Elasticity》1998,51(1):73-79
This note provides short proof of the representation of a symmetric isotropic 4-tensor in an n-dimensional real Euclidean
space.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
7.
8.
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
9.
10.
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
11.
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
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.
14.
With the help of Cayley-Hamilton theorem we have obtained two sets of complete invariance algorithms for calculating the stretches
and rotation in the polar decomposition of finite deformation gradient in this paper. Furthermore, the representation theorem
as well as its perturbation form for various strains in common use is presented.
This paper had been reported at the Congress of the East China Association for Solid Mechanics (1985). 相似文献
15.
有限谱ENO格式及其应用 总被引:2,自引:0,他引:2
首先对王健平提出的有限谱法^[1-3]做了进一步的理论研究,发现了一些新的有限谱法的插值基函数组,并互将有限谱法应用在ENO格式中,构造了有限谱ENO计算格式,然后通过对一维Euler方程的几个经典的模型问题和二维湍流与弱激波相互作用问题的数值计算,并且与理论解或准精确解进行比较分析,从而表明了此格式对于激波和其他间断具有较高的分辨率,在激波附近基本上没有明显的数值振荡,而且对于流场中的细致结构也具有相当高的精度。 相似文献
16.
M. Hayes 《Journal of Elasticity》1997,49(3):285-288
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. 相似文献
17.
The draping behavior of fabric is simulated by using four node quadrilateral thin plate elements with finite rotation. The
finite element formulation is based on the total Lagrangian approach. An exact representation of finite rotation is introduced.
The strain energy function accounting for the material symmetry is obtained by the tensor representation theory. To avoid
shear locking, the assumed strain technique for transverse shear is adopted. The conjugate gradient method with a proposed
line search algorithm is employed to minimize energy and reach the final shape of fabric. The draping behavior of a rectangular
piece of fabric over a rectangular table is simulated. 相似文献
18.
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
19.
New results are presented here for finite volume (FV) methods that use flux vector splitting (FVS) along with higher‐order reconstruction schemes. Apart from spectral accuracy of the resultant methods, the numerical stability is investigated which restricts the allowable time step or the Courant–Friedrich–Lewy (CFL) number. Also the dispersion relation preservation (DRP) property of various spatial and temporal discretization schemes is investigated. The DRP property simultaneously fixes space and time steps. This aspect of numerical schemes is important for simulation of high‐Reynolds number flows, compressible flows with shock(s) and computational aero‐acoustics. It is shown here that for direct numerical simulation applications, the DRP property is more restrictive than stability criteria. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
20.
C.S. Jog 《Journal of Elasticity》2002,66(2):159-169
A method for the explicit determination of the polar decomposition (and the related problem of finding tensor square roots) when the underlying vector space dimension n is arbitrary (but finite), is proposed. The method uses the spectral resolution, and avoids the determination of eigenvectors when the tensor is invertible. For any given dimension n, an appropriately constructed van der Monde matrix is shown to play a key role in the construction of each of the component matrices (and their inverses) in the polar decomposition. 相似文献