共查询到20条相似文献,搜索用时 140 毫秒
1.
2.
非线性正交各向异性弹性材料的本构方程及其势函数 总被引:1,自引:0,他引:1
研究了非线性Green弹性材料弹性张量独立分量,归纳推导出各向异性Green弹性材料、具有一个对称面Green弹性材料、 正交各向异性非线性弹性材料独立的弹性常数个数.从张量函数出发,用含有高阶弹性张量的张量多项式,推导出三阶非线性正交各向异性Green弹性材料本构方程及其势函数.并将本构方程及其势函数用张量不变量,标量不变量表示.证明了方程是完备的,不可约的,满足张量函数表示定理.详细研究Green弹性材料势函数存在的充分和必要条件,给出并证明了具有普适性的势函数存在定理. 相似文献
3.
结构钢本构关系的精度直接影响分析结果的可靠度.根据能量等效性假设、热力学第二定律,推出损伤材料的弹性本构方程;采用混合强化准则,考虑Bauschinger效应、屈服平台、硬化(软化)效应及损伤和损伤演化影响,建立了的结构钢弹塑性各向异性损伤本构关系.结合构建的本构关系,采用八节点超参数壳体单元,推导了用U.L.格式及Cauchy应力描述的板壳双重非线性有限元方程,并编制了计算程序.利用U.L.格式的壳体大挠度双重非线性有限元分析方法,对钢方管截面短柱进行面内拉压循环荷载作用下的滞回性能分析. 相似文献
4.
5.
6.
增量型各向异性损伤理论与数值分析 总被引:6,自引:1,他引:5
考虑到目前各向异性损伤理论存在一些不足,该文在增量型各向异性损伤理论的框架下,引入二阶对称张量,构造四阶对称有效损伤张量,建立了有效应力方程.类似于塑性流动分析方法,定义了增量弹性应力.应变关系.利用von Mises塑性屈服准则,并考虑各向异性损伤效应,推导出四阶对称的弹.塑性变形损伤刚度张量,其对称性反映了材料的固有特性.根据物体的变形和现时损伤状态,构造了材料损伤演化方程,方程中各项具有明确的物理意义.通过对A12024-T3金属薄板单向拉伸的有限元分析,确定了损伤演化参数,验证了损伤演化方程的正确性.此外还对含孔口薄板做有限元模拟,讨论了反力—位移曲线的变化规律以及它所揭示变形性质,给出了损伤场的分布规律。 相似文献
7.
本文在几何非线性三维弹性理论的基础上,通过量级分析导出了考虑横向剪切效应的正交各向异性纤维增强复合材料扁壳的基本方程,并应用伽略金方法求得了四边可动简支正交各向异性圆柱形扁壳后屈曲变形和非线性自由振动问题的数值解。计算结果表明:对于复合材料而言,横向剪切效应是值得注意的。 相似文献
8.
含基体横向损伤的黏弹性板的蠕变后屈曲分析 总被引:2,自引:0,他引:2
基于Schapery三维黏弹性损伤本构关系,引入沈为和Kachanov损伤演化方程,建立了基体横向损伤的纤维单一方向铺设黏弹性板的损伤模型;应用von Karman板理论,导出了考虑损伤效应的具初始挠度的纤维单一方向铺设黏弹性矩形板的非线性压屈平衡方程. 对未知变量在空间上采用差分法离散,时间上采用增量算法和Newton-Cotes积分法离散,控制方程被迭代求解. 算例中讨论了损伤以及有关参数对黏弹性复合材料板后屈曲行为的影响,且与已有文献的结果进行了比较. 数值结果表明:随着外载荷或者初始挠度的增大,板后屈曲趋于稳定时的挠度就愈大,损伤的影响愈明显;而随着长宽比的增大,板后屈曲趋于稳定时的挠度愈小,损伤的影响却随之增大. 相似文献
9.
动脉壁静态非线性力学性质的实验和理论研究 总被引:1,自引:0,他引:1
在动脉血管壁力学实验及已有的拟弹性理论研究基础上,提出了一个理论模型来分析具有残余应力动脉壁的非线性力学性质. 在动脉壁被模拟为均质、正交各向异性、不可压缩和具有初应力材料的前提下,建立了一个表达有残余应力动脉壁静态三维非线性拟弹性性质的e指数型本构方程. 动脉壁本构方程中的十个拟弹性参数是用我们的动脉实验数据及所发展的多曲线联合逼近算法数据拟合来确定. 相似文献
10.
非局部弹性直杆振动特征及Eringen常数的一个上限 总被引:5,自引:0,他引:5
应用非局部连续介质理论推导了弹性直杆的振动方程,并采用分离变量法
进行求解,得到了振动方程的本征方程、模态函数及通解. 结果表明:非局部连续介质弹性
直杆的自振频率因非局部效应而降低,降低的幅度不仅与材料内禀长度相关,还与振动频率
的阶次相关;而且频率大小存在极限值,显示了与晶格点阵相同特性. 通过与Brillouin格
波结果比较,给出了Eringen非局部理论中材料常数的一个上限. 相似文献
11.
EIGEN THEORY OF VISCOELASTIC MECHANICS FOR ANISOTROPIC SOLIDS 总被引:4,自引:0,他引:4
Guo Shaohua 《Acta Mechanica Solida Sinica》2001,14(1):74-80
Anisotropic viscoelastic mechanics is studied under anisotropic subspace. It is proved that there also exist the eigen properties
for viscoelastic medium. The modal Maxwell's equation, modal dynamical equation (or modal equilibrium equation) and modal
compatibility equation are obtained. Based on them, a new theory of anisotropic viscoelastic mechanics is presented. The advantages
of the theory are as follows: 1) the equations are all scalar, and independent of each other. The number of equations is equal
to that of anisotropic subspaces, 2) no matter how complicated the anisotropy of solids may be, the form of the definite equation
and the boundary condition are in common and explicit, 3) there is no distinction between the force method and the displacement
method for statics, that is, the equilibrium equation and the compatibility equation are indistinguishable under the mechanical
space, 4) each model equation has a definite physical meaning, for example, the modal equations of order one and order two
express the volume change and shear deformation respectively for isotropic solids, 5) there also exist the potential functions
which are similar to the stress functions of elastic mechanics for viscoelastic mechanics, but they are not man-made, 6) the
final solution of stress or strain is given in the form of modal superimposition, which is suitable to the proximate calculation
in engineering. 相似文献
12.
We construct a mixture theory which describes a porous elastic anisotropic solid with inclusions. Thermal effects are taken into account. The theory is in accord with classical thermodynamics. Fully nonlinear isotropic and anisotropic materials are considered, and field equations are also given for a nontrivial special case which, though nonlinear, is controlled by a few material functions. When properly specialized, the theory reduces to the P- model, a model widely used to describe porous solids.This work is dedicated to Jerald L. Ericksen on the occasion of his 60th birthday 相似文献
13.
George Herrmann 《Archive of Applied Mechanics (Ingenieur Archiv)》2007,77(2-3):123-133
This contribution presents the foundations of a thermodynamic theory of damage in elastic solids, developed in collaboration
with the late J. Kestin and with E. Honein and T. Honein. The theory is rooted in the so-called conservative or conventional
thermodynamics of irreversible processes, where the concept of a local thermodynamic state plays a prominent role. An elastic
body prone to damage is regarded as a thermodynamic system characterized by a set of extensive variables that can be defined
in both equilibrium and nonequilibrium states and assigned approximately the same values in both the physical space and the
abstract state space (i.e., the Gibbsian phase space of constrained equilibria). The extensive variables introduced include
internal parameters which describe the damaged state of the body and whose conjugate intensive variables, or affinities, constitute
a generalization of Eshelby’s concept of a “force on an elastic singularity”. The local state approximation is applied by
assigning to the entropy and temperature in physical space local values which can be calculated in the Gibbsian phase space
by the well-established methods of equilibrium thermodynamics. This leads to an explicit expression for the entropy production.
The rate equations for the damage are then postulated in such a way as to conform to the second part of the second law of
thermodynamics. The resulting theory captures many features of real inorganic material behavior in which no mass loss is sustained.
By contrast, damage of organic materials, such as compact bone subject to osteoporosis, is accompanied by bone mass loss.
This feature can be accommodated in the theory proposed by a suitable adjustment of the expression of the Gibbs free energy. 相似文献
14.
为描述岩石加速蠕变阶段的非线性变形规律,在广义开尔文体基础上串联一个村山体,基于Kachanov损伤率理论,建立了损伤变量D与蠕变时间的函数关系,并根据Lemaitre应变等效原理将村山体中的无损模型参数p用有效模型参数p(1-D)代替,以此来表征岩石加速蠕变阶段的非线性,建立了一种新的非线性损伤蠕变模型;根据广义塑性力学理论给出了该模型的三维蠕变方程;采用Levenberg-Marquardt非线性优化最小二乘法对红砂岩和绿片岩常规三轴压缩蠕变试验数据进行拟合,反演得到这两种岩石的蠕变模型参数。拟合结果表明:拟合曲线与试验曲线的拟合相关系数R2分别为0.999和0.992,说明该蠕变模型能较好地反映这两种岩石各阶段的蠕变曲线特征。 相似文献
15.
韩玉英 《应用数学和力学(英文版)》1983,4(2):283-290
The conditions for fracture of anisotropic bodies and theirgeometry in stress space are proposed in this paper.The an-alytical formulae expressing the fracture conditions are es-tablished from the viewpoint of energy theory for crack pro-pagation.In stress space the limiting surface corresponding to thefracture conditions derived for anisotropic solids is quadra-tic.It is an ellipsoid in case the mean stress is greaterthan zero and it is hyperboloid in case the mean stress is smal-ler than zero.The conclusions formed by the author in the present paperhave certain generality.Some results obtained by predeces-sors appear to be special cases with respect to the presenttheory. 相似文献
16.
Considering the pore fluid, the energy singular propagation in open-cell anisotropic porous solids is studied with the aim to provide a reference in the energy design and application of porous materials. Firstly, based on Biot’s theory, the perturbed eigenvalue problem that arises when the nearly pure modes are propagated is considered. Then, by using the obtained perturbed eigenvalues, the evolution conditions on the elastic parameters of solid skeleton materials are established for the existence of various systems of folds in the wave front. The emphasis is placed on the slow wave, which is particular for the porous material with the pore fluids. The critical conditions for the pattern transformation in the parameter space are given for the first time. Finally, the special situation (zero porosity) is discussed and the comparison with respect to the results for pure solids is made. The results show that the situation in the pure solids is a degenerated case of the present discussion. 相似文献
17.
In this paper, a nonlinear theory of nonlocal asymmetric, elastic solids is developed on the basis of basic theories of nonlocal continuum fieM theory and nonlinear continuum mechanics. It perfects and expands the nonlocal elastic fiteld theory developed by Eringen and others. The linear theory of nonlocal asymmetric elasticity developed in [1] expands to the finite deformation, We show that there is the nonlocal body moment in the nonlocal elastic solids. The noniocal body moment causes the stress asymmetric and itself is caused by the covalent bond formed by the reaction between atoms. The theory developed in this paper is applied to explain reasonably that curves of dispersion relation of one-dimensional plane longitudinal waves are not similar with those of transverse waves. 相似文献
18.
平行微裂纹损伤模型被用于构建各向异性损伤理论.当施加在代表性体积单元上的边界条件满足Hill条件时,基于平均场理论论证了由平行穿透裂纹损伤的弹性体仅有6个独立有效弹性常数.除了原各向同性基体的2个弹性常数外,与损伤相关的另外4个常数中,3个描述有效弹性常数的折减,1个描述损伤导致的拉剪耦合效应.结合单胞模型和有限元方法分析了双周期阵列平行裂纹问题,数值结果显示:裂纹呈一般双周期阵列时,拉剪耦合参数相比其它模量小很多;当裂纹密度一定时,改变裂纹的排列形式,面内剪切模量和面外剪切模量的折减呈现出不同的规律. 相似文献
19.
《International Journal of Plasticity》2005,21(3):397-434
The objective of this contribution is the formulation and algorithmic treatment of a phenomenological framework to capture anisotropic geometrically nonlinear inelasticity. We consider in particular the coupling of viscoplasticity with anisotropic continuum damage whereby both, proportional and kinematic hardening are taken into account. As a main advantage of the proposed formulation standard continuum damage models with respect to a fictitious isotropic configuration can be adopted and conveniently extended to anisotropic continuum damage. The key assumption is based on the introduction of a damage tangent map that acts as an affine pre-deformation. Conceptually speaking, we deal with an Euclidian space with respect to a non-constant metric. The evolution of this field is directly related to the degradation of the material and allows the modeling of specific classes of elastic anisotropy. In analogy to the damage mapping we introduce an internal variable that determines a back-stress tensor via a hyperelastic format and therefore enables the incorporation of plastic anisotropy. Several numerical examples underline the applicability of the proposed finite strain framework. 相似文献
20.
A new damage model for microcrack-weakened brittle solids 总被引:1,自引:0,他引:1
In the present paper, a micromechanically based damage model for microcrack-weakened solids is developed. The concept of the
domain of microcrack growth (DMG) is defined and used to describe the damage state and the anisotropic properties of brittle
materials. After choosing an appropriate fracture criterion of microcrack, we obtain the analytical expression of DMG under
a monotonically increasing proportional plane stress. Under a complex loading path, the evolution equation of DMG and the
overall effective compliance tensor of damaged materials are given.
The project supported by National Natural Science Foundation of China 相似文献