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31.
有限变形弹性动力学的非传统Gurtin型变分原理 总被引:5,自引:2,他引:5
根据古典阴阳互补和现代对偶互补的基本思想,通过作者早已提出的一条简单而统一的途径,系统地建立了有限变形弹性动力学的各类非传统Gurtin型变分原理,给出一个以卷积表示的重要关系式,可以认为,该式是有限变形动力学的广义虚功原理的表式。从该式出发,不仅能得到有限变形动力学的虚功原理,而且通过给出的一系列广义Legendre变换,还能系统地成对导出5类变量,3类变量,2类变量和1类变量非传统Gurtin型变分原理的互补泛函。通过这条途径还能清楚地阐明这些原理之间的内在联系。 相似文献
32.
The mechanical behavior of rock under uniaxial tensile loading is different from that of rock under compressive loads. A micromechanics-based model was proposed for mesoscopic heterogeneous brittle rock undergoing irreversible changes of their microscopic structures due to microcrack growth. The complete stress-strain relation including linear elasticity, nonlinear hardening, rapid stress drop and strain softening was obtained. The influence of all microcracks with different sizes and orientations were introduced into the constitutive relation by using the probability density function describing the distribution of orientations and the probability density function describing the distribution of sizes. The influence of Weibull distribution describing the distribution of orientations and Rayleigh function describing the distribution of sizes on the constitutive relation were researched. Theoretical predictions have shown to be consistent with the experimental results. 相似文献
33.
A new nonlinear evolution equation is derived for surface solitary waves propagating on a liquid-air interface where the wave motion is induced by a harmonic forcing. Instead of the traditional approach involving a base state of the long wave limit, a base state of harmonic waves is assumed for the perturbation analysis. This approach is considered to be more appropriate for channels of length just a few multiples of the depth. The dispersion relation found approaches the classical long wave limit. The weakly nonlinear dispersive waves satisfy a KdV-like nonlinear evolution equation with steeper nonlinearity. 相似文献
34.
Feng Xiqiao Yu Shouwen 《Acta Mechanica Solida Sinica》1995,8(2):121-132
By using the concept of domain of microcrack growth(DMG),themicromechanisms of damage in quasi-brittle materials subjected to triaxial either tensileor compressive loading are investigated and the complete strew-strain relation includingfour stages is obtained from micromechanical analysis.The regime of pre-peaknonlinear hardening corresponds to the distributed damage,i.e.the stable propagationof microcracks.After the attainment of the ultimate strength of load-bearing capacity,some microcracks experience the second unstable growth and the distributed damage istransmitted to the localization of damage.These analyses improve our understanding ofthe hardening and softening behaviors of quasi-brittle materials. 相似文献
35.
钛合金TC-4在高应变率下的动态本构关系 总被引:1,自引:0,他引:1
利用分离式Hopkinson扭杆对钛合金TC-4进行了高应变率下动态剪切本构关系的实验研究。结果表明TC-4对应变率高度敏感,对应变率的敏感性随应变率的提高而增加。其动态应力应变关系呈线性强化形式。但动态强化模量随应变率的提高而略有减少。采用Malvern给出的过应力模式_p={exp[(1/)(-f())]-1}/b可以较好地描述TC-4的动态剪切本构关系。 相似文献
36.
Anna Vainchtein 《Continuum Mechanics and Thermodynamics》2003,15(1):1-19
In this paper we derive an explicit formula for a kinetic relation governing the motion of a phase boundary in a bilinear
thermoelastic material capable of undergoing solid-solid phase transitions. To obtain the relation, we study traveling wave
solutions of a regularized problem that includes viscosity, heat conduction and convective heat exchange with an ambient medium.
Both inertia and latent heat of transformation are taken into account. We investigate the effect of material parameters on
the kinetic relation and show that in a certain range of parameters the driving force becomes a non-monotone function of the
interface velocity. The model also predicts a nonzero resistance to phase boundary motion, part of which is caused by the
thermal trapping.
Received: November 15, 2001 / Published online September 4, 2002
RID="*"
ID="*" e-mail: annav@math.pitt.edu
Communicated by Lev Truskinovsky, Minneapolis 相似文献
37.
In this paper, by capturing the atomic information and reflecting the behaviour governed by the nonlinear potential function,
an analytical molecular mechanics approach is proposed. A constitutive relation for single-walled carbon nanotubes (SWCNT’s)
is established to describe the nonlinear stress-strain curve of SWCNT’s and to predict both the elastic properties and breaking
strain of SWCNT’s during tensile deformation. An analysis based on the virtual internal bond (VIB) model proposed by P. Zhang
et al. is also presented for comparison. The results indicate that the proposed molecular mechanics approach is indeed an
acceptable analytical method for analyzing the mechanical behavior of SWCNT’s.
The project supported by the National Natural Science Foundation of China (10121202, 90305015 and 10328203), the Key Grant
Project of Chinese Ministry of Education (0306) and the Research Grants Council of the Hong Kong Special Administrative Region,
China (HKU 7195/04E). 相似文献
38.
开采沉陷工程岩体本构关系研究 总被引:1,自引:0,他引:1
传统开采沉陷理论存在对采动岩体本构关系研究不够的问题, 本文在运用现代工程地质学理论和现代数学力学理论相结合, 对采动岩体本构关系进行深入研究的基础上, 提出了用“黑箱”问题“灰箱”化的全息反分析法, 确定采动工程岩体本构关系及其有关参数。实例分析表明, 对于复杂岩体结构的开采沉陷问题, 能够取得满意的结果。 相似文献
39.
J. M. Wiest 《Rheologica Acta》1989,28(1):4-12
A modification of the Giesekus constitutive equation is derived by incorporating (approximately, via the Peterlin approximation) the finite extensibility of polymer molecules into dumbbell kinetic theory along with the anisotropic hydrodynamic drag suggested by Giesekus. The constitutive equation that is obtained retains much of the simplicity of Giesekus' constitutive equation, but it involves terms that are cubic in the stress as well as those that are quadratic. It is shown that the constitutive equation quantitatively describes the steady elongational viscosity of the IUPAC polymer melt A (including the strain softening of the melt), but it cannot describe the elongational and shear viscosities simultaneously. It is also shown that the constitutive equation satisfies the Lodge-Meissner relation for shear strains less than unity. 相似文献
40.
Phase transformational shakedown of a structure refers to a status that plastic strains cease developing after a finite number of loading cycles, and subsequently the structure undergoes only elastic deformation and alternating phase transformations with limited magnitudes. Due to the intrinsic complexity in the constitutive relations of shape memory alloys (SMA), there is as yet a lack of effective methods for modeling the mechanical responses of SMA structures, especially when they develop both phase transformation and plastic deformation. This paper is devoted to present an algorithm for analyzing shakedown of SMA structures subjected to cyclic or varying loads within specified domains. Based on the phase transformation and plastic yield criteria of von Mises-type and their associated flow rules, a simplified three-dimensional phenomenological constitutive model is first formulated accounting for different regimes of elastic–plastic deformation and phase transformation. Different responses possible for SMA bodies exposed to varying loads are discussed. The classical Melan shakedown theorem is extended to determine a lower bound of loads for transformational shakedown of SMA bodies without necessity of a step-by-step analysis along the loading history. Finally, a simple example is given to illustrate the application of the present theory as well as some basic features of shakedown of SMA structures. It is interesting to find that phase transformation may either increase or decrease the load-bearing capacity of a structure, depending upon its constitutive relations, geometries and the loading mode. 相似文献