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Science China(Physics,Mechanics & Astronomy) 2018年第6期61卷 50-61页

作者： Dake Yi tzuchiang wang College of Mechanics and Materials Hohai University The State Key Laboratory of Nonlinear Mechanics Institute of Mechanics Chinese Academy of Sciences

In the paper, a new procedure is proposed to investigate three-dimensional fracture problems of a thin elastic plate with a long through-the-thickness crack under remote uniform tensile loading. The new procedure includes a new analytical method and high accurate finite element simulations. In the part of theoretical analysis, three-dimensional Maxwell stress functions are employed in order to derive three-dimensional crack tip fields. Based on the theoretical analysis, an equation which can describe the relationship among the three-dimensional J-integral J(z), the stress intensity factor K(z) and the tri-axial stress constraint level Tz(z) is derived first. In the part of finite element simulations, a fine mesh including 153360 elements is constructed to compute the stress field near the crack front, J(z) and Tz(z). Numerical results show that in the plane very close to the free surface, the K field solution is still valid for in-plane stresses. Comparison with the numerical results shows that the analytical results are valid.

关键词： three-dimensional fracture analysis out-of-plane constraint three-dimensional J-integral

Total energy equation leading to exchange-correlation functional

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Science China(Physics,Mechanics & Astronomy) 2015年第5期58卷 93-98页

作者： LIU Feng wang tzuchiang State Key Laboratory of Nonlinear Mechanics Institute of Mechanics Chinese Academy of Sciences

By solving the total energy equation, we obtain the formula of exchange-correlation functional for the first time. This functional is usually determined by fitting experimental data or the numerical results of models. In the uniform electron gas limit, our exchangecorrelation functional can exactly reproduce the results of Perdew-Zunger parameterization from the jellium model. By making use of a particular solution, our exchange-correlation functional could take into accotmt the case of non-uniform electron density, and its validity can be confirmed through comparisons of the band structure, equilibrium lattice constant, and bulk modulus of aluminum and silicon. The absence of mechanical prescriptions for the systematic improvement of exchange-correlation functional hinders further development of density-functional theory （DFT）, and the formula of exchange-correlation functional given in this study might provide a new perspective to help DFT out of this awkward situation.

关键词： Density-functional theory exchange-correlation functional bulk modulus band structure aluminum silicon

Interactions of penny-shaped cracks in three-dimensional solids

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Acta Mechanica Sinica 2006年第4期22卷 341-353页

作者： Shige Zhan tzuchiang wang Department of Mathematical and Physical Sciences NSFC Beijing 100085 China LNM Institute of Mechanics Chinese Academy of Sciences Beijing 100080 China

The interaction of arbitrarily distributed penny-shaped cracks in three-dimensional solids is analyzed in this paper. Using oblate spheroidal coordinates and displacement functions, an analytic method is devel- oped in which the opening and the sliding displacements on each crack surface are taken as the basic unknown functions. The basic unknown functions can be expanded in series of Legendre polynomials with unknown coefficients. Based on superposition technique, a set of governing equations for the unknown coefficients are formulated from the traction free conditions on each crack surface. The boundary collocation procedure and the average method for crack-surface tractions are used for solving the governing equations. The solution can be obtained for quite closely located cracks. Numerical examples are given for several crack problems. By comparing the present results with other existing results, one can conclude that the present method provides a direct and efficient approach to deal with three-dimensional solids containing multiple cracks.

关键词： Three-dimensional problem Penny-shaped cracks Interaction

CRACK PROBLEMS OF PIEZOELECTRIC MATERIALS

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Acta Mechanica Solida Sinica 1999年第2期12卷 95-105页

作者： wang tzuchiang LNM Institute of MechanicsChinese Academy o f Science.Beijing 100080China

This paper presents an analysis of crack problems in homogeneouspiezoelectrics or on the interfaces between two dissimilarpiezoelectric materials based on the continuity of normal electricdisplacement and electric potential across the crack faces. Theexplicit analytic solutions are obtained for a single crack inpiezoelectrics or on the interfaces of piezoelectric bimaterials. Aclass of boundary problems involving many cracks is also solved.

关键词： piezoelectric materials crack interface

A new thermo-elasto-plasticity constitutive theory for polycrystalline metals

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Acta Mechanica Sinica 2015年第3期31卷 338-348页

作者： Cen Chen Qiheng Tang tzuchiang wang State Key Laboratory of Nonlinear Mechanics Institute of Mechanics Chinese Academy of Sciences

In this study, the behavior of polycrystalline metals at different temperatures is investigated by a new thermo-elasto-plasticity constitutive theory. Based on solid mechanical and interatomic potential, the constitutive equa- tion is established using a new decomposition of the deformation gradient. For polycrystalline copper and magnesium, the stress-strain curves from 77 to 764 K （copper）, and 77 to 870 K （magnesium） under quasi-static uniaxial loading are calculated, and then the calculated results are compared with the experiment results. Also, it is determined that the present model has the capacity to describe the decrease of the elastic modulus and yield stress with the increasing temperature, as well as the change of hardening behaviors of the polycrystalline metals. The calculation process is simple and explicit, which makes it easy to implement into the applications.

关键词： Thermo-elasto-plasticity constitutive theory Yield stress Hardening behaviors Finite temperature

A new thermo-elasto-plasticity constitutive equation for crystals

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Science China(Physics,Mechanics & Astronomy) 2015年第5期58卷 99-108页

作者： CHEN Cen TANG QiHeng wang tzuchiang State Key Laboratory of Nonlinear Mechanics Institute of Mechanics Chinese Academy of Sciences

Based on the crystal plasticity theory and interatomic potential, in this paper a new thermo-elasto-plasticity constitutive model is proposed to study the behavior of metal crystals at finite temperature. By applying the present constitutive model, the stress-strain curves under uniaxial tension at different temperatures are calculated for the typical crystal A1, and the calculated results are compared with the experimental results. From the comparisons, it can be seen that the present theory has the capability to describe the thermo-elasto-plastic behavior of metal crystals at finite temperature through a concise and explicit calculation process.

关键词： thermo-elasto.plasticity theory constitutive equation interatomic potential critical resolved shear stress hardening

EFFECT OF TEMPERATURE ON DISLOCATION EMISSION FROM CRACK TIP FOR BCC METAL MO

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Acta Mechanica Solida Sinica 1998年第3期11卷 189-198页

作者： Tang Qiheng wang tzuchiang Chinese Acad Sci Inst Mech LNM Beijing 100080 Peoples R China

The effect of thermally activated energy on the dislocationemission from a crack tip in BCC metal Mo is simulated in this *** on the correlative reference model on which the flexi- bledisplacement boundary scheme is introduced naturally, the simulationshows that as temperature in creases the critical stress intensityfactor for the first dislocation emission will decrease and the totalnumber of emitted dislocations increase for the same external *** dislocation velocity and exten- sive distance among partialdislocations are not sensitive to temperature.

关键词： correlative reference model flexible displacement boundary moleculardynamics

A continuum thermal stress theory for crystals based on interatomic potentials

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Science China(Physics,Mechanics & Astronomy) 2014年第2期57卷 208-217页

作者： LIU XiaoLei TANG QiHeng wang tzuchiang State Key Laboratory of Nonlinear Mechanics Institute of MechanicsChinese Academy of Sciences

This paper presents a new continuum thermal stress theory for crystals based on interatomic *** effect of finite temperature is taken into account via a harmonic *** EAM potential for copper is adopted in this paper and verified by computing the effect of the temperature on the specific heat,coefficient of thermal expansion and lattice *** we calculate the elastic constants of copper at finite *** calculation results are in good agreement with experimental *** thermal stress theory is applied to an anisotropic crystal graphite,in which the Brenner potential is *** dependence of the thermodynamic properties,lattice constants and thermal strains for graphite is *** calculation results are also in good agreement with experimental data.

关键词： thermal stress theory interatomic potential thermal strain finite temperature

Nonlinear constitutive behavior of ferroelectric materials

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Science China(Physics,Mechanics & Astronomy) 2008年第9期51卷 1339-1356页

作者： LI HaiJun LIU Feng wang tzuchiang LNM Institute of MechanicsChinese Academy of SciencesBeijing 100190China

The ferroelectric specimen is considered as an aggregation of many randomly oriented domains. According to this mechanism,a multi-domain mechanical model is developed in this paper. Each domain is represented by one element. The applied stress and electric field are taken to be the stress and electric field in the formula of the driving force of domain switching for each element in the specimen. It means that the macroscopic switching criterion is used for calculating the volume fraction of domain switching for each element. By using the hardening relation between the driving force of domain switching and the volume fraction of domain switching calibrated,the volume fraction of domain switching for each element is calculated. Substituting the stress and electric field and the volume fraction of domain switching into the constitutive equation of ferroelectric material,one can easily get the strain and electric displacement for each element. The macroscopic behavior of the ferroelectric specimen is then directly calculated by volume averaging. Mean-while,the nonlinear finite element analysis for the ferroelectric specimen is carried out. In the finite element simulation,the volume fraction of domain switching for each element is calculated by using the same method mentioned above. The in-teraction between different elements is taken into account in the finite element simulation and the local stress and electric field for each element is obtained. The macroscopic behavior of the specimen is then calculated by volume averaging. The computation results involve the electric butterfly shaped curves of axial strain versus the axial electric field and the hysteresis loops of electric displacement versus the electric field for ferroelectric specimens under the uniaxial coupled stress and electric field loading. The present theoretical prediction agrees reasonably with the experimental results.

关键词： volume fraction of domain switching multi-domain mechanical model finite element method (FEM) domain switching

Thermodynamic properties and constitutive relations of crystals at finite temperature

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Science China(Physics,Mechanics & Astronomy) 2012年第6期55卷 918-926页

作者： TANG QiHeng wang tzuchiang SHANG BaoShuang LIU Feng State Key Laboratory of Nonlinear Mechanics Institute of MechanicsChinese Academy of SciencesBeifing 100190China

The dynamics equation for each individual atom is established directly around the equilibrium state of the system of N atoms based on the inter-atomic potential energy of EAM *** the theory of lattice dynamics and periodical boundary condition,the 3N×3N stiffness matrix in eigen equations of vibration frequencies for a parallelepiped crystal is reduced to a 3n×3n matrix of eigen equations of vibration frequencies for a unit *** constitutive relation of the crystal at finite temperature is extracted based on the quantum-mechanical *** thermodynamic properties and the stress-strain relationships of crystal Cu with large plastic deformation at different temperatures are calculated,the calculation results agree well with experimental data.

关键词： lattice wave theory molecular dynamics thermodynamic properties constitutive model interatomic potential