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	1. The Simulation of crack propagation with Discrete Element Method
	Xia Shengxu ,Yu Tiantang
	Mechanics 26 October 2009
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	Abstract:In this paper, the discrete element method (DEM) was used to study how cracks propagate in rocks subjected to a uniaxial compressive stress. In order to obtain immediate response to the loading, the convergence of DEM is firstly discussed with respect to the mass scaling method. Secondly, the bonded crack propagation criterion based on Mohr-Coulomb criterion is suggested. Thirdly, the DEM results were compared with those obtained in laboratory samples. The laboratory tests used rock samples with two cracks inclined at varying angles with respect to the compressive stress. The DEM and the laboratory results compared very well. Also, the results show that the DEM is a very successful approach for the visualization of secondary crack formations and its propagation in the simulated samples.
	TO cite this article:Xia Shengxu ,Yu Tiantang . The Simulation of crack propagation with Discrete Element Method[OL].[26 October 2009] http://en.paper.edu.cn/en_releasepaper/content/36127


	2. A micro scale Timoshenko beam model based on strain gradient elasticity theory
	Wang Binglei,Zhou Shenjie ,Zhao Junfeng
	Mechanics 22 June 2009
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	Abstract:A micro scale Timoshenko beam model is developed based on strain gradient elasticity theory. Governing equations, initial conditions and boundary conditions are derived simultaneously by using Hamilton’s principle. The new model incorporated with Poisson effect contains three material length scale parameters and can consequently capture the size effect. This model can degenerate into the modified couple stress Timoshenko beam model or even the classical Timoshenko beam model if two or all material length scale parameters are taken to be zero respectively. In addition, the newly developed model recovers the micro scale Bernoulli–Euler beam model when shear deformation is ignored. To illustrate the new model, the static bending and free vibration problems of a simply supported micro scale Timoshenko beam are solved respectively. Numerical results reveal that the differences in the deflection, rotation and natural frequency predicted by the present model and the other two reduced Timoshenko models are large as the beam thickness is comparable to the material length scale parameter. These differences, however, are decreasing or even diminishing with the increase of the beam thickness. In addition, Poisson effect on the beam deflection, rotation and natural frequency possesses an interesting “extreme point” phenomenon, which is quite different from that predicted by the classical Timoshenko beam model.
	TO cite this article:Wang Binglei,Zhou Shenjie ,Zhao Junfeng. A micro scale Timoshenko beam model based on strain gradient elasticity theory[OL].[22 June 2009] http://en.paper.edu.cn/en_releasepaper/content/33331


	3. On The Lagrangian Finite Plasticity Theory
	Wen Zhicheng,Fu Mingfu,Chen Liangsen
	Mechanics 08 January 2009
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	Abstract:In the present paper, the Lagrangian finite plasticity theory is discussed based on the theory of materials with elastic range by the assumptions of the existence of a yield functional and a flow rule, to generalize the framework of A.E. Green, P.M. Naghdi and J. Casey (see Naghdi(1990), Brown et al (2003)), so that it can describe better the mechanical behaviors of anisotropic elastic-plastic materials and the strain induced anisotropy. Here the plastic strain, also called intermediate strain, is defined by the plastic stress, and the elastic response functional is assumed to be a functional of plastic strain history. As a result of this definition of intermediate strain, the elastic response functional has a special form, the normal flow rule of generally accepted Il’yushin’s Postulate is the evolution law for the plastic stress. If the plastic stress is also defined to describe the kinematical hardening, it is the kinematical hardening law. The definitions of strain, plastic strain and elastic strain are discussed from a geometric point of view. It is shown that Green-Naghdi elastic strain is the Lagrange elastic strain. The discussion of the consequences of Il’yushin’s Postulate has detailed, the necessary and sufficient condition is obtained. The rate-form of this theory is obtained. The material symmetry and strain induced anisotropy are also discussed in detail. Finally an example of isotropic elastic plastic materials is given. It has been shown that in general this model can satisfy the basic conditions such as Il’yushin postulate and uniqueness and existence of solution of flow rule for any plastic deformation.
	TO cite this article:Wen Zhicheng,Fu Mingfu,Chen Liangsen. On The Lagrangian Finite Plasticity Theory[OL].[ 8 January 2009] http://en.paper.edu.cn/en_releasepaper/content/27486


	4. On the yield functionals in Lagrangian stress space of elastic-plastic materials with internal constraints
	Fu Mingfu,Chen Liangsen
	Mechanics 02 January 2007
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	Abstract:In the present paper it is shown that the elastic range in the second Piola-Kirchhoff stress space can be chosen in a hyperplane perpendicular to the direction related to the simple internal constraint if the determinate stress response of the elastic-plastic material with simple internal constraints with the condition (2.30) is correctly chosen, otherwise, it is in general in a hypersurface and the normal flow rule by Il’yushin’s postulate will have an indeterminate part( [8]). The choice of determinate stress response is probable because of its indeterminacy ([1]). Therefore the yield functional should be a function of the second Piola-Kirchhoff stress lying in the hyperplane so that it is more simple and the back stress as the geometric center of the elastic range in general is inside the elastic range. Finally some examples are concerned.
	TO cite this article:Fu Mingfu,Chen Liangsen. On the yield functionals in Lagrangian stress space of elastic-plastic materials with internal constraints[OL].[ 2 January 2007] http://en.paper.edu.cn/en_releasepaper/content/10562


	5. The Correlation between Fractal Dimension of Fracture Surfaces and Mechanical Properties
	Liu Haishun,Yin Chunhao,Miao Xiexing
	Mechanics 24 October 2006
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	Abstract:The literature on metal fatigue and fracture based on fractal theory is reviewed, focusing on the fractal character of metal fracture surfaces and the approaches to measure the fractal dimension. The correlations between the fractal dimension of fracture, various fractal models of metal fatigue crack propagation and fracture are analyzed and compared, and the physical signification of fractal dimension are also discussed. It seems there is still further research necessary to improve theoretical method and to reveal the physical nature of fractal dimension. We expect this paper could make the fractal theory understood comprehensively, and could expand fractal application properly in more and more fields.
	TO cite this article:Liu Haishun,Yin Chunhao,Miao Xiexing. The Correlation between Fractal Dimension of Fracture Surfaces and Mechanical Properties[OL].[24 October 2006] http://en.paper.edu.cn/en_releasepaper/content/8936


	6. Two-dimensional sliding frictional contact mechanics of functionally graded materials with arbitrary spatial variations of material properties
	Liao-Liang Ke,Yue-Sheng Wang
	Mechanics 14 December 2005
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	Abstract:A multi-layered model for sliding frictional contact analysis of functionally graded materials (FGMs) with arbitrarily varying elastic modulus under plane strain-state deformation has been developed. Based on the fact that an arbitrary curve can be approached by a series of continuous but piecewise linear curves, the FGM is divided into several sub-layers and in each sub-layers the shear modulus is assumed to be a linear function while the Possion’s ratio is assumed to be a constant. On the contact area, it is assumed that the friction is one of Coulomb type. With this model the fundamental solutions for concentrated forces acting perpendicular and parallel to the FGMs layer surface are obtained. Then the sliding frictional contact problem of a functionally graded coated half-space is investigated. The transfer matrix method and Fourier integral transform technique are employed to cast the problem to a Cauchy singular integral equation. The contact stresses and contact area are calculated for various moving stamps by solving the equations numerically.
	TO cite this article:Liao-Liang Ke,Yue-Sheng Wang. Two-dimensional sliding frictional contact mechanics of functionally graded materials with arbitrary spatial variations of material properties[OL].[14 December 2005] http://en.paper.edu.cn/en_releasepaper/content/4373

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