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	1. Chen Rational Mechanics IV. Constitutive Equations
	Xiao Jianhua
	Mechanics 06 February 2007
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	Abstract: The way to derive elastic constitutive equations is applied to elastoplastic deformation. Two measurable plasticity parameters are introduced. The obtained constitutive equation improves the classical elastoplastic constitutive equation in that it takes the maximum loading point as the reference point, while the classical elastoplastic constitutive equation takes the last plastic configuration as reference. Further more, the constitutive equations for incremental deformation is given for the multiplicative decomposition of plasticity and elasticity and the integral form of deformation.
	TO cite this article:Xiao Jianhua. Chen Rational Mechanics IV. Constitutive Equations[OL].[ 6 February 2007] http://en.paper.edu.cn/en_releasepaper/content/11071


	2. Chen Rational Mechanics III. Deformation Decomposition and Strain Definition
	Xiao Jianhua
	Mechanics 06 February 2007
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	Abstract:Firstly, Chen additive decomposition of deformation gradient is formulated. By this formulation, the Eringen-Truesdell polar decomposition are formulated by explicit formulation of displacement field. Then the strain introduced by the multiplicative decomposition and the strain introduced by the additive decomposition are formulated explicitly with displacement gradient. This formulation clears the intrinsic contents of strains defined by taking the Eringen-Truesdell polar decomposition. After that, it shows that the plastic deformation can be expressed as the irreversible local average rotation. For initial isotropic simple elastic material, the path-dependent feature of classical plasticity theory is naturally expressed in Chen strain definition.
	TO cite this article:Xiao Jianhua. Chen Rational Mechanics III. Deformation Decomposition and Strain Definition[OL].[ 6 February 2007] http://en.paper.edu.cn/en_releasepaper/content/11064


	3. Chen Rational Mechanics II. Geometrical Equations
	Xiao Jianhua
	Mechanics 31 January 2007
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	Abstract:Using material coordinators, deformation has two senses: distance variation and area variation. Starting from the geometrical invariant quantities in tensor theory, the macro deformation is described by the distance base vector transformation and the area base vector transformation. For pure elastic deformation, the area base vector transformation is the inverse of the distance base vector transformation. Only in this special case, the deformation is equivalent with coordinator transformation. For arbitral deformation, the area base vector transformation is plastic volume variation dependent and the distance base vector transformation is the deformation gradient. Therefore, for large deformation problem, two deformation tensors should be introduced. Some remarks are made for related theoretic results which are viewed as widely accepted.
	TO cite this article:Xiao Jianhua. Chen Rational Mechanics II. Geometrical Equations[OL].[31 January 2007] http://en.paper.edu.cn/en_releasepaper/content/10973


	4. Chen Rational Mechanics I. Introduction to Rational Mechanics
	Xiao Jianhua
	Mechanics 30 January 2007
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	Abstract:Rational mechanics is raised by Truesdell. Although this research clears many deformation concepts, its true physical and mathematic bases are not real strong. When many kinds of new materials are made out and the traditional materials is used in near extreme conditions, the finite deformation mechanics faces real problems which may appear as how to constructive constitutive equations, how to evaluate the damage or fatigue of materials, or how to understand the internal mechanism for instability and non-linearity. To attack theses new problems raised by industrial application, the theoretic problem of finite deformation mechanics must be re-examined. Tracing back to the basic concept of rational mechanics becomes a valuable thing for the study of finite deformation mechanics. In this paper, the basic idea of deformation transformation, tensor decomposition, motion equation, and experiment results will be simply reviewed.
	TO cite this article:Xiao Jianhua. Chen Rational Mechanics I. Introduction to Rational Mechanics[OL].[30 January 2007] http://en.paper.edu.cn/en_releasepaper/content/10958


	5. dependence of nanosolid elasticity and its derivatives on extensibility, Debye temperature, and heat capacity: a broken bond rule
	Sun Changqing
	Mechanics 11 August 2006
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	Abstract:With the miniaturization of a solid down to nanometers scale, the elasticity, extensibility, Debye temperature, and the specific heat capacity are no longer constant but change with variation of size. The trends of change of these quantities also depend on temperature of measurement and the nature of chemical bond involved. Mechanism behind the intriguing tunability and the interdependence of these quantities are yet unclear. A set of analytical solutions is presented herewith showing that the observed trends could be reproduced by taking the fact of bond order deficiency into effect. Agreement between predictions and observations clarifies that the shortened and strengthened surface bonds dictate the observed variations intrinsically yet atoms in the core interior remain as they are in the bulk.
	TO cite this article:Sun Changqing. dependence of nanosolid elasticity and its derivatives on extensibility, Debye temperature, and heat capacity: a broken bond rule [OL].[11 August 2006] http://en.paper.edu.cn/en_releasepaper/content/7888


	6. Intermediate processes, critical phenomena: theory, method, progress of fractional operators and its applications to modern mechanics
	Xu Mingyu,Tan Wenchang
	Mechanics 27 February 2006
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	Abstract:From point of view of physics, especially of mechanics, we briefly introduce fractional operators (with emphasis on fractional calculus and fractional differential equations) used for describing intermediate processes and critical phenomena in physics and mechanics, and their progress in theory and methods, and applications to modern mechanics. Some authors’ researches in this area in recent years are included. Finally, prospects and evaluation for this subject are made.
	TO cite this article:Xu Mingyu,Tan Wenchang. Intermediate processes, critical phenomena: theory, method, progress of fractional operators and its applications to modern mechanics[OL].[27 February 2006] http://en.paper.edu.cn/en_releasepaper/content/5390

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