李显方
从事新型材料的断裂分析及强度理论，智能材料与结构中的力学问题等研究
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 姓名：李显方
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固体力学
 研究兴趣：从事新型材料的断裂分析及强度理论，智能材料与结构中的力学问题等研究
李显方，男，1964年生。分别于1985年获学士学位（湖南师范大学），1987年获硕士学位（北京科技大学），1999年获博士学位（北京理工大学）；2004年从国防科技大学力学博士后流动站出站。现任中南大学教授、博士生导师，中国材料学会疲劳分会第三届理事会理事。2005年至今中南大学“升华学者”特聘教授。曾入选湖南省青年骨干教师。应对方邀请于2003年访问韩国Yonsei大学、2004－2005年访问美国Vanderbilt大学，并进行合作研究。先后主持或参加国家自然科学基金等课题近十项。在《J Mech Phys Solids》、《Philos Mag》、《J Appl Mech》及《中国科学》、《力学学报》等国内外著名刊物上已发表学术论文90余篇，其中SCI收录，EI收录分别超过50余篇，SCI他引次数100余次。曾获“湖南省自然科学优秀学术论文”一等奖和北京理工大学“优秀博士学位论文奖”的荣誉称号。现主要从事新型材料的断裂分析及强度理论，智能材料与结构中的力学问题等研究。

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【期刊论文】A decagonal quasicrystal with a Griffith crack
李显方， LiXianFang， FanTianYou and SunYingFei
A decagonal quasicrystal with a Grina th crack，0001，（）：
1年11月30日
The crack theory in conventional linear elasticity fracture mechanics is extended to quasicrystal linear elasticity fracture mechanics. A decagonal quasicrystal containinga Gri th crack penetrating through the solid along the period direction is considered. By means of a general solution, the analytical expressions for the entire stress field are obtained. The asymptotic behaviour of the stress around the crack tip indicates that the stress near the crack tip exhibits the square root singularity. The singularity in the phason stress field arises from that the phononandphason fields couplewitheach other. The crackstrain energy and energy release rate are also given.

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李显方， XianFang Lia， b， *， Kang Yong Leec
Journal of the Mechanics and Physics of Solids 52(2004)20792100，0001，（）：
1年11月30日
The assumptions of impermeable and permeable cracks give rise to signi'cant errors in determining electroelastic behavior of a cracked piezoelectric material. The former simply imposes that the permittivity or electric displacement of the crack interior vanishes, and the latter neglects also the e&ects of the dielectric of an opening crack interior. Considering the presence of the dielectric of an opening crack interior and the permeability of the crack surfaces for electric' eld, this paper analyzes electroelastic behavior induced by a pennyshaped dielectric crack in a piezoelectric ceramic layer. In the cases of prescribed displacement or prescribed stress at the layer surfaces, the Hankel transform technique is employed to reduce the problem to Fredholm integral equations with a parameter dependent nonlinearly on the unknown functions. For an in' nite piezoelectric space, a closedform solution can be derived explicitly, while for a piezoelectric layer, an iterative technique is suggested to solve the resulting nonlinear equations. Field intensity factors are obtained in terms of the solution of the equations. Numerical results of the crack opening displacement intensity factors are presented for a cracked PZT5H layer and the e&ect of applied electric 'eld on crack growth are examined for both cases. The results indicate that the fracture toughness of a piezoelectric ceramic is a&ected by the direction of applied electric' elds, dependent on the elastic boundary conditions.
Dielectric crack， COD intensity factor， Electroelastic behavior， Fracture toughness， Piezoelectric ceramic， Hankel transform

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【期刊论文】Crack growth in a piezoelectric material with a Griﬃth crack perpendicular to the poling axis
李显方， XianFang Li‡zk and KangYong LEE§
Philosophical Magazine, 21 June 2004，0001，（）：
1年11月30日
Experimental results for cracked piezoelectric materials demonstrate that applied electric ﬁelds can enhance or inhibit crack growth, which cannot be explained via stress intensity factor K and energy release rate G, but may be predicted according to the fracture criterion of mechanical strain energy release rate Gm. However, the Gm criterion fails to predict the experimental observation that purely electric ﬁelds can drive crack growth in a poled ferroelectric ceramic. In this paper, using electric boundary conditions dependent on the crackopening displacement, the nonlinear relation between the electric displacement at the crack faces and applied loading is given explicitly. The Fourier transform technique is employed to reduce the problem to dualintegral equations. Solving the resulting equations, expressions for the electroelastic ﬁeld in the entire plane are obtained for a piezoelectric material weakened by a Griﬃth crack perpendicular to the poling axis. The distribution of asymptotic ﬁeld and the intensity factors of electroelastic ﬁeld as well as the elastic Tstress are determined. In particular, the strain intensity factor Ks is suggested as a fracture criterion for piezoelectric materials, which can explain successfully relevant experimental results. Results reveal that an applied electric ﬁeld tends to cause crack to open or close, depending on its positive or negative direction. A comparison of numerical results for PbðZr, TiÞO35H indicates that the Ks criterion is superior to other fracture criteria.

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【期刊论文】Electric and elastic behaviors of a piezoelectric ceramic with a charged surface electrode
李显方， XianFang Li， and Kang Yong Lee，
Smart Mater. Struct. 13(2004)424432，0001，（）：
1年11月30日
Previous studies on electric and elastic behaviors induced by internal or surface electrodes in a piezoelectric ceramic are mainly concentrated on a twodimensional analysis. However, most sensors and actuators are related to a threedimensional piezoelectric body with electrodes. This paper is concerned with the electroelastic analysis of a pennyshaped thin electrode coating on the surface of a hexagonal piezoelectric halfspace. The Hankel transform technique is employed to reduce the mixed boundary value problem to an Abel integral equation. Solving the resulting equation analytically, a solution is obtained in a closed form. Explicit expressions for the complete electric and elastic behaviors in any position in the entire piezoelectric halfspace are determined in terms of elementary functions. The results indicate that the vertical surface displacement reaches a maximum at the entire electrode region, while the radial surface displacement reaches a peak only at the electrode edge. Moreover, in addition to electric displacement and electric field, elastic stresses exhibit singular behavior near the electrode edge.

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【期刊论文】Spatial dispersion of short surface acoustic waves in piezoelectric ceramics
李显方， X.F. Li， J. S. Yang， Q. Jiang
Acta Mechanica (2005) DOI 10.1007/s0070700502676，0001，（）：
1年11月30日
This work explores the eﬀect of the electric ﬁeld gradient in the constitutive behavior of elastic dielectrics by analyzing the antiplane surface waves propagating over a halfspace of polarized ceramics. The obtained frequency equation shows that the gradienteﬀect makes the surface waves dispersive, although they are known to be nondispersive according to the classical theory of linear piezoelectricity that neglects the gradienteﬀect. This analysis further shows that there exists a microstructural characteristic length, comparing to which the dispersion is signiﬁcant for short waves while negligible for long waves. This suggests that the dispersion may have signiﬁcante ects for very small surface acoustic wave devices operating with highfrequency short waves.

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李显方， XIANFANG LI， and JIASHI YANG， *
International Journal of Fracture (2005) 132:4964，0001，（）：
1年11月30日
Based on the piezoelectromagnetism theory, the dynamic problem of a crack of ﬁnite length embedded in a polarized ceramic under the action of antiplane mechanical impact and inplane electric impact is considered. The basic equations are simpliﬁed to two decoupled wave equations. Integral transform techniques are employed to reduce the associated initialboundary value problem to integral equations. By using numerical methods, the resulting integral equations are solved and dynamic ﬁeld intensity factors are presented graphically. A comparison of the dynamic results and the quasistatic results for dynamic ﬁeld intensity factors near the crack tips is made, and the effect of mechanical impact on the dynamic magnetic ﬁeld intensity factor is examined.
Crack， dynamic behavior， electromagnetoelastic ﬁeld， piezoelectromagnetism，

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李显方， XianFang Li*
International Journal of Solids and Structures 42(2005)31853205，0001，（）：
1年11月30日
The transient analysis of a magnetoelectroelastic medium containing a crack is made under antiplane mechanical and inplane electric and magnetic impacts. The crack is assumed to penetrate through the solid along the poling direction. By using the Fourier and Laplace transforms, the associated mixed boundary value problem is reduced to a Fredholm integral equation of the second kind, which is solved numerically. By means of a numerical inversion of the Laplace transform, dynamic ﬁeld intensity actors are obtained in the time domain. Numerical results are presented graphically to show the e ects of the material properties and applied electric and magnetic impacts on the dynamic intensity factors of COD and stress, and dynamic energy density factors. The results indicate that except for the intensity factors of electric displacement and magnetic induction, other ﬁeld intensity factors exhibit apparent transient feature. Moreover, they depend strongly on mechanical input as well as electric and magnetic impacts.
Magnetoelectroelastic medium， Crack， Transient response， Dynamic ﬁeld intensity factors， Energy density factor

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【期刊论文】Tstress near the tips of a cruciform crack with unequal arms
李显方， XianFang Li
Engineering Fracture Mechanics 73(2006)671683，0001，（）：
1年11月30日
The Tstress near the tips of a crack of cross shape embedded in an isotropic elastic solid is analyzed. The integral transform technique is employed to convert the associated boundary value problem to a system of singular integral equations. According to the stress diﬀerence method, Tstresses can be expressed as a sum of an integral involving crack opening displacement (COD) and applied loading at inﬁnity. Obtained results indicate that, in addition to applied loading, Tstresses at the horizontal (vertical) crack tips depend on the COD of the vertical (horizontal) crack surface. COD plays a leading role in determining Tstresses, in particular for a cruciform crack of two crackarm lengths of the same order. Moreover, Tstresses for a singlecrack limiting case can be recovered from the present results as the length of one arm approaches zero. For a biaxial tension of the same magnitude, Tstresses are present for a cruciform crack, but absent for a single crack. Finally, for several cases of interest, Tstresses for a cruciform crack are evaluated and compared with those for a single crack, and the inﬂuence of the ratio of two crackarm lengths b/a and the COD on the Tstress of a cruciform crack is examined.
Cruciform crack， Tstress， COD

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李显方， XianFang LiL. Roy Xu
，0001，（）：
1年11月30日
The transient response of a finite bimaterial plate with a crack perpendicular to and terminating at the interface is analyzed for two types of boundaries (freefree and clampedclamped). The crack surface is loaded by arbitrary timedependent antiplane shear impact. The mixed initialboundary value problem is reduced to a singular integral equation of a generalized Cauchy kernel for the crack tearing displacement density or screw dislocation density. The GaussJacobi quadrature technique is employed to numerically solve the singular integral equation, and then the dynamic stress intensity factors are determined by implementing a numerical inversion of the Laplace transform. As an example, numerical calculations are carried out for a cracked bimaterial plate composed of aluminum (material I) and epoxy or steel (material II). The effects of material properties, geometry, and boundary types on the variations of dynamic stress intensity factors are discussed in detail. Results indicate that an overshoot of the normalized stress intensity factor of the crack tip at the interface decreases for a cracked bimaterial plate, and the occurrence of which is delayed for a cracked aluminum/epoxy plate compared to a pure aluminum plate with the same crack.

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【期刊论文】Elastic field for a straight dislocation in a decagonal quasicrystal
李显方， XianFang Li†， XiangYang Duan‡， TianYou Fan† and YingFei Sun†
J. Phys.: Condens. Matter 11(1999)703711. Printed in the UK，0001，（）：
1年11月30日
A straight dislocation line in a decagonal quasicrystal is considered. For a decagonal quasicrystal of point groups 10, 10 and 10/m with a straight dislocation parallel to the periodic direction, the basic governing equations are solved by decoupling this problem into a plane elasticity problem and an ntiplane elasticity problem. For the latter, the solution is known; for the former, it is reduced to a single equation, △4F(x, y)= 0, △ being the harmonic operator, by introducing a displacement function F. A general solution is formulated. Using a general solution and the Fourier transform, the explicit expressions for the dislocationinduced elastic field in a decagonal quasicrystal are obtained and the energy per unit length on the dislocation is given.

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