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Nano Research 2022年第6期15卷 4873-4879页

作者： changjun cheng Xiaofu Zhang Michel J.R.Haché Yu Zou Department of Materials Science and Engineering University of TorontoTorontoOntario M5S 3E4Canada State Key Laboratory of Functional Materials for Informatics Shanghai Institute of Microsystem and Information Technology and Center for Excellence in Superconducting ElectronicsChinese Academy of Sciences(CAS)Shanghai 200050China

Refractory high-entropy alloys(HEAs)possess many useful properties such as high strength and high-temperature stability.So far,most studies on refractory HEAs have been limited to a few well-known compositions and on their coarse-grain bulk forms.Here we fabricate nanocrystalline(TiZrHf)_(x)(NbTa)_(1−x)HEA thin films with a large range of compositions(x=0.07–0.90)by the direct current(DC)magnetron co-sputtering technique and measure their mechanical properties using the nanoindentation method.All the as-deposited HEA thin films show a solid-solution body-centered cubic(bcc)structure.As the compositional ratio(x)increases,the elastic modulus decreases from 153 to 123 GPa,following the trend of the rule of mixture.As x increases,the hardness first decreases from 6.5 GPa(x=0.07)to the lowest value(4.6 GPa,x=0.48)and then increases to the highest value(7.1 GPa,x=0.90),showing a concave trend.The change in hardness might be attributed to the combinational influence caused by the atomic size and modulus effects,as well as the texture effect.The authors also propose a few open questions for future studies on this and related HEA systems.

关键词： high-entropy alloys nanocrystalline alloys refractory metals thin films magnetron co-sputtering nanoindentation

COUPLING EFFECTS OF VOID SHAPE AND VOID SIZE ON THE GROWTH OF AN ELLIPTIC VOID IN A FIBER-REINFORCED HYPER-ELASTIC THIN PLATE

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Acta Mechanica Solida Sinica 2012年第3期25卷 312-320页

作者： Jiusheng Ren Hanhai Li changjun cheng Xuegang Yuan Department of Mechanics Shanghai UniversityShanghai 200444China Shanghai Key Laboratory of Mechanics in Energy and Environment Engineering Shanghai 200444China College of Science Dalian Nationalities UniversityDalian 116600China

The growth of a prolate or oblate elliptic micro-void in a fiber reinforced anisotropic incompressible hyper-elastic rectangular thin plate subjected to uniaxial extensions is studied within the framework of finite elasticity. Coupling effects of void shape and void size on the growth of the void are paid special attention to. The deformation function of the plate with an isolated elliptic void is given, which is expressed by two parameters to solve the differential equation. The solution is approximately obtained from the minimum potential energy principle. Deformation curves for the void with a wide range of void aspect ratios and the stress distributions on the surface of the void have been obtained by numerical computation. The growth behavior of the void and the characteristics of stress distributions on the surface of the void are captured. The combined effects of void size and void shape on the growth of the void in the thin plate are discussed. The maximum stresses for the void with different sizes and different void aspect ratios are compared.

关键词： fiber reinforced hyper-elastic material rectangular thin plate with void void shapeand void size potential energy principle growth of void

DYNAMIC CHARACTERISTICS IN INCOMPRESSIBLE HYPERELASTIC CYLINDRICAL MEMBRANES

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Acta Mechanica Solida Sinica 2010年第5期23卷 420-427页

作者： Datian Niu Xuegang Yuan changjun cheng Jiusheng Ren School of Science Dalian Nationalities University Dalian 116600 China Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200072 China

In this paper, the dynamic characteristics are examined for a cylindrical membrane composed of a transversely isotropic incompressible hyperelastic material under an applied uniform radial constant pressure at its inner surface. A second-order nonlinear ordinary differential equation that approximately describes the radial oscillation of the inner surface of the membrane with respect to time is obtained. Some interesting conclusions are proposed for different materials, such as the neo-Hookean material, the Mooney-Rivlin material and the Rivlin-Saunders material. Firstly, the bifurcation conditions depending on the material parameters and the pressure loads are determined. Secondly, the conditions of periodic motion are presented in detail for membranes composed of different materials. Meanwhile, numerical simulations are also provided.

关键词： incompressible hyperelastic material cylindrical membrane dynamical character- istic nonlinear periodic oscillation

Finite elastic torsional instability of incompressible thermo-hyperelastic cylinder

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Acta Mechanica Sinica 2006年第2期22卷 156-161页

作者： Jiusheng Ren changjun cheng Department Of Mechanics.Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200444 China

Torsional instability of an incompressible thermo-hyperelastic cylindrical rod, subjected to axial stretching and large torsions, is examined within the framework of finite elasticity. When the cylinder is stretched and twisted by a sufficiently large degree, a knot may form suddenly at one point. This inherent elastic instability is analyzed with the minimum potential energy principle and the critical values of torsion are obtained. The distribution of stresses as well as the tensile force and the torque are studied. Effect of tem- perature change is specifically discussed.

关键词： Incompressible thermo-hyperelastic material Torsional instability Effect of temperature Finite elastic

CAVITATED BIFURCATION FOR COMPOSED COMPRESSIBLE HYPER-ELASTIC MATERIALS

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Acta Mechanica Solida Sinica 2002年第3期15卷 208-213页

作者： Ren Jiusheng cheng changjun Shanghai Univ Shanghai Inst Appl Math & Mech Dept Mech Shanghai 200072 Peoples R China

The cavitated bifurcation problem in a solid sphere composed oftwo compressible hyper-elas- tic materials is examined. Thebifurcation solution for the composed sphere under a uniform radialtensile boundary dead-load is obtained. The bifurcation curves andthe stress contributions subsequent to the cavita- tion are given.The right and left bifurcation as well as the catastrophe andconcentration of stresses are ana- lyzed. The stability of solutionsis discussed through an energy comparison.

关键词： composed compressible hyper-elastic material void bifurcation catastropheand concentra- tion of stress energy comparion

A METHOD FOR CALCULATING THE LYAPUNOV EXPONENT SPECTRUM OF A PERIODICALLY EXCITED NON-AUTONOMOUS DYNAMICAL SYSTEM

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Acta Mechanica Solida Sinica 2000年第3期13卷 254-261页

作者： cheng changjun Fan Xiaojun Shanghai Institute of Applied Mathematics and Mechanics Department of MechanicsShanghai UniversityShanghai 200072China School of Civil Engineering and Mechanics Xi’an Jiaotong UniversityXi’an 710049China

The relation between the Lyapunov exponent spectrum of a periodically excited non-autonomous dynamical system and the Lyapunov exponent spectrum of the corresponding autonomous system is given and the validity of the relation is verified theoretically and computationally. A direct method for calculating the Lyapunov exponent spectrum of non-autonomous dynamical systems is suggested in this paper, which makes it more convenient to calculate the Lyapunov exponent spectrum of the dynamical system periodically excited. Following the definition of the Lyapunov dimension D-L((A)) of the autonomous system, the definition of the Lyapunov dimension D-L of the non-autonomous dynamical system is also given, and the difference between them is the integer 1, namely, D-L((A)) - D-L = 1. For a quasi-periodically excited dynamical system, similar conclusions are formed.

关键词： periodically excited dynamical system Lyapunov exponent spectrum Lyapunov dimension Duffing equation van der Pol equation

A VARIATIONAL PRINCIPLE OF PERTURBED MOTION ON VISCOELASTIC THIN PLATES WITH APPLICATIONS

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Acta Mechanica Solida Sinica 1999年第2期12卷 121-128页

作者： Zhang Nenghui cheng changjun Shanghai Univ Shanghai Inst Appl Math & Mech Shanghai 200072 Peoples R China Shanghai Univ Dept Mech Shanghai 200072 Peoples R China

In this paper, in the light of the Boltzmann superpositionprinciple in linear viscoelastic- ity, a mathematical model ofperturbed motion on viscoelastic thin place is established. Thecorre- sponding variational principle is obtained in a convolutionbilinear form. For application the problems of free vibration, forcedvibration and stability of a viscoelastic simply-supportedrectangular thin plate are considered. The results show thatnumerical solutions agree well with analytical solutions.

关键词： viscoelastic thin plate perturbed motion variational principle

CAVITATION IN HOOKEAN ELASTIC MEMBRANES

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Acta Mechanica Solida Sinica 2002年第1期15卷 89-94页

作者： Shang Xinchun cheng changjun Department of Mathematics and Mechanics University of Science and Technology BeijingBeijing 100083China Department of Mechanics Shanghai UniversityShanghai 200072China Shanghai Institute of Applied Mathematics and Mechanics Shanghai 200072China

An exact solution to cavitation is found tension of ac lass ofCauchy elastic membranes. The constitutive relationship of materialsis based on Hookean elastic law and finite logarithmic strain mea-Sure. A variable transformation is used in solving the two-pointboundary-value problem of nonlinear ordinary Different equation. Asimple formula to calculate the critical stretch for cavitation isderived. As the nu- Merical results, the bifurcation curvesdescribing void nucleation and suddenly rapidly growth of the cavityAre obtained. The boundary layers of displacements and stresses nearthe cavity wall are observed.

关键词： cavitaion bifurcation boundary layer elastic membrane

Dynamical cavitation and oscillation of an anisotropic incompressible hyper-elastic sphere

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Science China(Physics,Mechanics & Astronomy) 2012年第5期55卷 822-827页

作者： REN JiuSheng LI HanHai YUAN XueGang cheng changjun Department of Mechanics Shanghai Key Laboratory of Mechanics in Energy and Environment EngineeringShanghai UniversityShanghai 200444China College of Science Dalian Nationalities UniversityDalian 116600China

Dynamical cavitation and oscillation of an anisotropic two-family fiber-reinforced incompressible hyper-elastic sphere subjected to a suddenly applied constant boundary dead load are examined within the framework of finite elasto-dynamics.An exact differential equation between the radius of the cavity and the applied load is obtained.The curves for the variation of the maximum radius of the cavity with the load and the phase diagrams are obtained by vibration theories and numerical computation.It is shown that there exists a critical value for the applied load.When the applied load is larger than the critical value,a spherical cavity will suddenly form at the center of the sphere.It is proved that the evolution of the cavity radius with time follows that of nonlinear periodic oscillation,and oscillation of the anisotropic sphere is not the same as that of the isotropic sphere.

关键词：周期振荡各向异性不可压缩超弹性球体最大半径塑性动力学纤维增强

GENERAL MATHEMATICAL THEORY OF LARGE DEFLECTIONS OF THIN PLATES WITH SOME HOLES

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Acta Mechanica Sinica 1986年第3期2卷 278-288+265页

作者： Zhu Zhengyou cheng changjun(Lanzhou University,Lanzhou) Lanzhou University Lanzhou

The theoretical analysis and the numerical computations for the problem of a thin platewith large deflection and some holes become much more difficult due to the multi-valued propertiesof the stress function F and the single-valued demands on the displacements.The necessary andsufficient conditions which can assure F to be single-valued are obtained in this paper.At the sametime,we prove that the single-valued demands on the displacements are equivalent to 3m functionalconstraint equations DC(w,F)=0,where m is the number of holes.From these conclusions,thesingle-valued governing equations of the problem of plates with large deflection and some holes arederived.It is a system of fourth order partial differential equations with 3m unknown constants andconstrained equations.A numerical method for solving this problem is presented.The problem ofthe critical load is considered and an iterative scheme for computing the buckled states is given whena critical load λ is ‘single’.

关键词： large defiection orthogenally anisotropic plates with holes multiply connected region eigenvalue and eigenfunction bifurcation theory