The main aim of this paper is to study the nonconforming linear triangular Crouzeix- Raviart type finite element approximation of planar linear elasticity problem with the pure displacement boundary value on anisotrop...The main aim of this paper is to study the nonconforming linear triangular Crouzeix- Raviart type finite element approximation of planar linear elasticity problem with the pure displacement boundary value on anisotropic general triangular meshes satisfying the maximal angle condition and coordinate system condition. The optimal order error estimates of energy norm and L2-norm are obtained, which are independent of lame parameter λ. Numerical results are given to demonstrate the validity of our theoretical analysis.Mathematics subject classification： 65N30, 65N15.展开更多
Negative thermal expansion(NTE)of materials is an intriguing phenomenon challenging the concept of traditional lattice dynamics and of importance for a variety of applications.Progresses in this field develop markedly...Negative thermal expansion(NTE)of materials is an intriguing phenomenon challenging the concept of traditional lattice dynamics and of importance for a variety of applications.Progresses in this field develop markedly and update continuously our knowledge on the NTE behavior of materials.In this article,we review the most recent understandings on the underlying mechanisms(anharmonic phonon vibration,magnetovolume effect,ferroelectrorestriction and charge transfer)of thermal shrinkage and the development of NTE materials under each mechanism from both the theoretical and experimental aspects.Besides the low frequency optical phonons which are usually accepted as the origins of NTE in framework structures,NTE driven by acoustic phonons and the interplay between anisotropic elasticity and phonons are stressed.Based on the data documented,some problems affecting applications of NTE materials are discussed and strategies for discovering and design novel framework structured NET materials are also presented.展开更多
The purpose of this research is to analyze and compare stress distribution patterns around dental implant made of pure titanium and yttrium-partial stabilized zirconia （YPSZ） in anisotropic versus isotropic finite e...The purpose of this research is to analyze and compare stress distribution patterns around dental implant made of pure titanium and yttrium-partial stabilized zirconia （YPSZ） in anisotropic versus isotropic finite element method under vertical and oblique loads. Although the properties of implant and crown were changed, similar stress distribution and close stress level were observed in two different implant finite element models. The stress values were a little lower in the YPSZ model. In the bone, anisotropy increased the stress values by 30%- 70% in the isotropic cases. The YPSZ implant could be more valuable choice for implant because of esthetic requirement. Anisotropy had subtle, yet significant effects on the stress level.展开更多
The orientation distribution of crystallites in a polycrystal can be described by the orientation distribution function(ODF) . The ODF can be expanded under the Wigner D-bases. The expanded coefficients in the ODF are...The orientation distribution of crystallites in a polycrystal can be described by the orientation distribution function(ODF) . The ODF can be expanded under the Wigner D-bases. The expanded coefficients in the ODF are called the texture coefficients. In this paper,we use the Clebsch-Gordan expression to derive an explicit expression of the elasticity tensor for an anisotropic cubic polycrystal. The elasticity tensor contains three material constants and nine texture coefficients. In order to measure the nine texture coefficients by ultrasonic wave,we give relations between the nine texture coefficients and ultrasonic propagation velocities. We also give a numerical example to check the relations.展开更多
The Stroh formalism is most elegant when the boundary conditions are simple, namely,they are prescribed in terms of traction or displacement.For mixed boundary conditions such as there for a slippery boundary,the conc...The Stroh formalism is most elegant when the boundary conditions are simple, namely,they are prescribed in terms of traction or displacement.For mixed boundary conditions such as there for a slippery boundary,the concise matrix expressions of the Stroh formalism are destroyed.We present a generalized Stroh formalism which is applicable to a class of general boundary conditions.The general boundary conditions in- clude the simple and slippery boundary conditions as special cases.For Green's functions for the half space, the general solution is applicable to the case when the surface of the half-space is a fixed,a free,a slippery, or other more general boundary.For the Griffith crack in the infinite space,the crack can be a slit-like crack with free surfaces,a rigid line inclusion(which is sometimes called an anticrack),or a rigid line with slippery surface or with other general surface conditions.It is worth mention that the modifications required on the Stroh formalism are minor.The generalized formalism and the final solutions look very similar to those of unmodified version.Yet the results are applicable to a rather wide range of boundary conditions.展开更多
An algorithm for integrating the constitutive equations in thermal framework is presented, in which the plastic deformation gradient is chosen as the integration variable. Compared with the classic algorithm, a key fe...An algorithm for integrating the constitutive equations in thermal framework is presented, in which the plastic deformation gradient is chosen as the integration variable. Compared with the classic algorithm, a key feature of this new approach is that it can describe the finite deformation of crystals under thermal conditions. The obtained plastic deformation gradient contains not only plastic defor- mation but also thermal effects. The governing equation for the plastic deformation gradient is obtained based on ther- mal multiplicative decomposition of the total deformation gradient. An implicit method is used to integrate this evo- lution equation to ensure stability. Single crystal 1 100 aluminum is investigated to demonstrate practical applications of the model. The effects of anisotropic properties, time step, strain rate and temperature are calculated using this integration model.展开更多
First-principles pseudopotential calculations are performed to investigate the phase transition and elastic properties of niobium nitrides （NbN）. The lattice parameters a0 and c0/a0, elastic constants Cu, bulk modul...First-principles pseudopotential calculations are performed to investigate the phase transition and elastic properties of niobium nitrides （NbN）. The lattice parameters a0 and c0/a0, elastic constants Cu, bulk modulus B0, and the pressure derivative of bulk modulus B0＇ are calculated. The results are in good agreement with numerous experimental and theoretical data. The enthalpy calculations predict that NbN undergoes phase transition from NaCl-type to NiAs-type structure at 13.4 GPa with a volume collapse of about 4.0% and from AsNi-type to CW-type structure at 26.5 GPa with a volume collapse of about 7.0%. Among the four types of structures, CW-type is the most stable structure. The elastic properties are analyzed on the basis of the calculated elastic constants. Isotropic wave velocities and anisotropic elasticity of NbN are studied in detail. The longitudinal and shear-wave velocities, Vr, Vs and V increase with increasing pressure, respectively. The Debye temperature OD increases monotonically with increasing pressure except for NiAs-type structure. Both the longitudinal velocity and the shear-wave velocity increase with pressure for wave vector along all the propagation directions, except for VTA（[100]） and VTA[001]（[110]） with NaCl structure and VTA[001]（[100]） with the other three types of structures.展开更多
Out-of-plane buckling of anisotropic elastic plate subjected to asimple shear is investigated. From exact 3-D equilibrium conditionsof anisotropic elastic body with a plane of elastic symmetry atcritical Configuration...Out-of-plane buckling of anisotropic elastic plate subjected to asimple shear is investigated. From exact 3-D equilibrium conditionsof anisotropic elastic body with a plane of elastic symmetry atcritical Configuration, the equation for buckling direction (bucklingwave direction) parameter is derived and the Shape functions ofpossible buckling modes are obtained. The traction free boundaryconditions which must Hold on the upper and lower surfaces of platelead to a linear eigenvalue problem whose nontrivial solutions Arejust the possible buckling modes for the plate.展开更多
In this paper,we establish a novel unique continuation property for two-dimensional anisotropic elasticity systems with partial information.More precisely,given a homogeneous elasticity system in a connected open boun...In this paper,we establish a novel unique continuation property for two-dimensional anisotropic elasticity systems with partial information.More precisely,given a homogeneous elasticity system in a connected open bounded domain,we investigate the unique continuation by assuming only the vanishing of one component of the solution in a subdomain.Using the corresponding Riemann function,we prove that the solution vanishes in the whole domain provided that the other component vanishes at one point up to its second derivatives.Further,we construct several examples showing the possibility of further reducing the additional information of the other component.This result possesses remarkable significance in both theoretical and practical aspects because the required data are almost halved for the unique determination of the whole solution.展开更多
The CAS phase is a major constituent phase for the continental crust and basaltic compositions at the P-T conditions of the Earth＇s mantle, and potentially plays an important role in the geodynamic processes related ...The CAS phase is a major constituent phase for the continental crust and basaltic compositions at the P-T conditions of the Earth＇s mantle, and potentially plays an important role in the geodynamic processes related to slab subduction. Its equation of state has been investigated here at ambient temperature up to about 25 GPa by using a diamond-anvil cell and synchrotron Xray radiation. Its P-V data, fitted to the third-order Birch-Murnaghan equation, yield an isothermal bulk modulus （KT） of 185 （9） GPa and first pressure derivative （ KT^t ） of 7.2 （12）. If KT^t is fixed at 4, file derived Kr is 212 （4） GPa. Additionally, the CAS phase is strongly elastically anisotropic, with its a-axis direction much less compressible than c-axis direction： Kr-a ： Kr-c = 2.19.展开更多
In engineering practice,analysis of interfacial thermal stresses in composites is a crucial task for assuring structural integrity when sever environmental temperature changes under operations.In this article,the dire...In engineering practice,analysis of interfacial thermal stresses in composites is a crucial task for assuring structural integrity when sever environmental temperature changes under operations.In this article,the directly transformed boundary integrals presented previously for treating generally anisotropic thermoelasticity in two-dimension are fully regularized by a semi-analytical approach for modeling thin multi-layers of anisotropic/isotropic composites,subjected to general thermal loads with boundary conditions prescribed.In this process,an additional difficulty,not reported in the literature,arises due to rapid fluctuation of an integrand in the directly transformed boundary integral equation.In conventional analysis,thin adhesives are usually neglected due to modeling difficulties.A major concern arises regarding the modeling error caused by such negligence of the thin adhesives.For investigating the effect of the thin adhesives considered,the regularized integral equation is applied for analyzing interfacial stresses in multiply bonded composites when thin adhesives are considered.Since all integrals are completely regularized,very accurate integration values can be still obtained no matter how the source point is close to the integration element.Comparisons are made for some examples when the thin adhesives are considered or neglected.Truly,this regularization task has laid sound fundamentals for the boundary element method to efficiently analyze the interfacial thermal stresses in 2D thin multiply bonded anisotropic composites.展开更多
The method of fundamental solutions(MFS)is a boundary-type and truly meshfree method,which is recognized as an efficient numerical tool for solving boundary value problems.The geometrical shape,boundary conditions,and...The method of fundamental solutions(MFS)is a boundary-type and truly meshfree method,which is recognized as an efficient numerical tool for solving boundary value problems.The geometrical shape,boundary conditions,and applied loads can be easily modeled in the MFS.This capability makes the MFS particularly suitable for shape optimization,moving load,and inverse problems.However,it is observed that the standard MFS lead to inaccurate solutions for some elastostatic problems with stress concentration and/or highly anisotropic materials.In thiswork,by a numerical study,the important parameters,which have significant influence on the accuracy of the MFS for the analysis of two-dimensional anisotropic elastostatic problems,are investigated.The studied parameters are the degree of anisotropy of the problem,the ratio of the number of collocation points to the number of source points,and the distance between main and pseudo boundaries.It is observed that as the anisotropy of the material increases,there will be more errors in the results.It is also observed that for simple problems,increasing the distance between main and pseudo boundaries enhances the accuracy of the results;however,it is not the case for complicated problems.Moreover,it is concluded that more collocation points than source points can significantly improve the accuracy of the results.展开更多
基金Acknowledgments. This work was supported by National Natural Science Foundation of China （No. 10971203）, Specialized Research Fund for the Doctoral Program of Higher Education （No. 20094101110006）, the Educational Department Foundation of Henan Province of China （No.2009B110013）.
文摘The main aim of this paper is to study the nonconforming linear triangular Crouzeix- Raviart type finite element approximation of planar linear elasticity problem with the pure displacement boundary value on anisotropic general triangular meshes satisfying the maximal angle condition and coordinate system condition. The optimal order error estimates of energy norm and L2-norm are obtained, which are independent of lame parameter λ. Numerical results are given to demonstrate the validity of our theoretical analysis.Mathematics subject classification： 65N30, 65N15.
基金This work was supported by the National Natural Science Foundation of China(Nos.11874328,11774078,and 21905252)China Postdoctoral Science Foundation(No.2019M652558).
文摘Negative thermal expansion(NTE)of materials is an intriguing phenomenon challenging the concept of traditional lattice dynamics and of importance for a variety of applications.Progresses in this field develop markedly and update continuously our knowledge on the NTE behavior of materials.In this article,we review the most recent understandings on the underlying mechanisms(anharmonic phonon vibration,magnetovolume effect,ferroelectrorestriction and charge transfer)of thermal shrinkage and the development of NTE materials under each mechanism from both the theoretical and experimental aspects.Besides the low frequency optical phonons which are usually accepted as the origins of NTE in framework structures,NTE driven by acoustic phonons and the interplay between anisotropic elasticity and phonons are stressed.Based on the data documented,some problems affecting applications of NTE materials are discussed and strategies for discovering and design novel framework structured NET materials are also presented.
文摘The purpose of this research is to analyze and compare stress distribution patterns around dental implant made of pure titanium and yttrium-partial stabilized zirconia （YPSZ） in anisotropic versus isotropic finite element method under vertical and oblique loads. Although the properties of implant and crown were changed, similar stress distribution and close stress level were observed in two different implant finite element models. The stress values were a little lower in the YPSZ model. In the bone, anisotropy increased the stress values by 30%- 70% in the isotropic cases. The YPSZ implant could be more valuable choice for implant because of esthetic requirement. Anisotropy had subtle, yet significant effects on the stress level.
基金the National Natural Science Foundation of China (Grant Nos. 10562004 and 10662004)the Jiangxi Project to Nature Academic and Technical Leaders in Targeted Areas, and Research Fund for the Doctoral Program of Higher Education (Grant No. 20070403003)
文摘The orientation distribution of crystallites in a polycrystal can be described by the orientation distribution function(ODF) . The ODF can be expanded under the Wigner D-bases. The expanded coefficients in the ODF are called the texture coefficients. In this paper,we use the Clebsch-Gordan expression to derive an explicit expression of the elasticity tensor for an anisotropic cubic polycrystal. The elasticity tensor contains three material constants and nine texture coefficients. In order to measure the nine texture coefficients by ultrasonic wave,we give relations between the nine texture coefficients and ultrasonic propagation velocities. We also give a numerical example to check the relations.
文摘The Stroh formalism is most elegant when the boundary conditions are simple, namely,they are prescribed in terms of traction or displacement.For mixed boundary conditions such as there for a slippery boundary,the concise matrix expressions of the Stroh formalism are destroyed.We present a generalized Stroh formalism which is applicable to a class of general boundary conditions.The general boundary conditions in- clude the simple and slippery boundary conditions as special cases.For Green's functions for the half space, the general solution is applicable to the case when the surface of the half-space is a fixed,a free,a slippery, or other more general boundary.For the Griffith crack in the infinite space,the crack can be a slit-like crack with free surfaces,a rigid line inclusion(which is sometimes called an anticrack),or a rigid line with slippery surface or with other general surface conditions.It is worth mention that the modifications required on the Stroh formalism are minor.The generalized formalism and the final solutions look very similar to those of unmodified version.Yet the results are applicable to a rather wide range of boundary conditions.
基金supported by the Key Project of the National Natural Science Foundation of China(10932003)Project of Chinese National Programs for Fundamental Research and Development(2012CB619603 and 2010CB832700)"04" Great Project of Ministry of Industrialization and Information of China (2011ZX04001-21)
文摘An algorithm for integrating the constitutive equations in thermal framework is presented, in which the plastic deformation gradient is chosen as the integration variable. Compared with the classic algorithm, a key feature of this new approach is that it can describe the finite deformation of crystals under thermal conditions. The obtained plastic deformation gradient contains not only plastic defor- mation but also thermal effects. The governing equation for the plastic deformation gradient is obtained based on ther- mal multiplicative decomposition of the total deformation gradient. An implicit method is used to integrate this evo- lution equation to ensure stability. Single crystal 1 100 aluminum is investigated to demonstrate practical applications of the model. The effects of anisotropic properties, time step, strain rate and temperature are calculated using this integration model.
文摘First-principles pseudopotential calculations are performed to investigate the phase transition and elastic properties of niobium nitrides （NbN）. The lattice parameters a0 and c0/a0, elastic constants Cu, bulk modulus B0, and the pressure derivative of bulk modulus B0＇ are calculated. The results are in good agreement with numerous experimental and theoretical data. The enthalpy calculations predict that NbN undergoes phase transition from NaCl-type to NiAs-type structure at 13.4 GPa with a volume collapse of about 4.0% and from AsNi-type to CW-type structure at 26.5 GPa with a volume collapse of about 7.0%. Among the four types of structures, CW-type is the most stable structure. The elastic properties are analyzed on the basis of the calculated elastic constants. Isotropic wave velocities and anisotropic elasticity of NbN are studied in detail. The longitudinal and shear-wave velocities, Vr, Vs and V increase with increasing pressure, respectively. The Debye temperature OD increases monotonically with increasing pressure except for NiAs-type structure. Both the longitudinal velocity and the shear-wave velocity increase with pressure for wave vector along all the propagation directions, except for VTA（[100]） and VTA[001]（[110]） with NaCl structure and VTA[001]（[100]） with the other three types of structures.
基金the National Natural Science Foundation of China(No.19772032)
文摘Out-of-plane buckling of anisotropic elastic plate subjected to asimple shear is investigated. From exact 3-D equilibrium conditionsof anisotropic elastic body with a plane of elastic symmetry atcritical Configuration, the equation for buckling direction (bucklingwave direction) parameter is derived and the Shape functions ofpossible buckling modes are obtained. The traction free boundaryconditions which must Hold on the upper and lower surfaces of platelead to a linear eigenvalue problem whose nontrivial solutions Arejust the possible buckling modes for the plate.
基金supported by the A3 Foresight Program“Modeling and Computation of Applied Inverse Problems”Japan Society for the Promotion of Science(JSPS)+5 种基金National Natural Science Foundation of China(NSFC)supported by NSFC(No.11971121)partially supported by JSPS KAKENHI Grant Number JP15H05740supported by NSFC(No.11771270)partly supported by NSFC(No.91730303)RUDN University Program5-100。
文摘In this paper,we establish a novel unique continuation property for two-dimensional anisotropic elasticity systems with partial information.More precisely,given a homogeneous elasticity system in a connected open bounded domain,we investigate the unique continuation by assuming only the vanishing of one component of the solution in a subdomain.Using the corresponding Riemann function,we prove that the solution vanishes in the whole domain provided that the other component vanishes at one point up to its second derivatives.Further,we construct several examples showing the possibility of further reducing the additional information of the other component.This result possesses remarkable significance in both theoretical and practical aspects because the required data are almost halved for the unique determination of the whole solution.
基金supported by National Natural Science Founda-tion of China (Grant Nos. 40872033, 40821002)Fundamental Research Funds for the Central Universities to Liu Xi
文摘The CAS phase is a major constituent phase for the continental crust and basaltic compositions at the P-T conditions of the Earth＇s mantle, and potentially plays an important role in the geodynamic processes related to slab subduction. Its equation of state has been investigated here at ambient temperature up to about 25 GPa by using a diamond-anvil cell and synchrotron Xray radiation. Its P-V data, fitted to the third-order Birch-Murnaghan equation, yield an isothermal bulk modulus （KT） of 185 （9） GPa and first pressure derivative （ KT^t ） of 7.2 （12）. If KT^t is fixed at 4, file derived Kr is 212 （4） GPa. Additionally, the CAS phase is strongly elastically anisotropic, with its a-axis direction much less compressible than c-axis direction： Kr-a ： Kr-c = 2.19.
基金The financial support provided from the Ministry of Science and Technology of Taiwan is greatly appreciated by the authors(MOST 108-2221-E-006-186).
文摘In engineering practice,analysis of interfacial thermal stresses in composites is a crucial task for assuring structural integrity when sever environmental temperature changes under operations.In this article,the directly transformed boundary integrals presented previously for treating generally anisotropic thermoelasticity in two-dimension are fully regularized by a semi-analytical approach for modeling thin multi-layers of anisotropic/isotropic composites,subjected to general thermal loads with boundary conditions prescribed.In this process,an additional difficulty,not reported in the literature,arises due to rapid fluctuation of an integrand in the directly transformed boundary integral equation.In conventional analysis,thin adhesives are usually neglected due to modeling difficulties.A major concern arises regarding the modeling error caused by such negligence of the thin adhesives.For investigating the effect of the thin adhesives considered,the regularized integral equation is applied for analyzing interfacial stresses in multiply bonded composites when thin adhesives are considered.Since all integrals are completely regularized,very accurate integration values can be still obtained no matter how the source point is close to the integration element.Comparisons are made for some examples when the thin adhesives are considered or neglected.Truly,this regularization task has laid sound fundamentals for the boundary element method to efficiently analyze the interfacial thermal stresses in 2D thin multiply bonded anisotropic composites.
基金The first author would like to acknowledge the support received from the Vice Chancellor of Research at Shiraz University under Grant No.99GRC1M1820.
文摘The method of fundamental solutions(MFS)is a boundary-type and truly meshfree method,which is recognized as an efficient numerical tool for solving boundary value problems.The geometrical shape,boundary conditions,and applied loads can be easily modeled in the MFS.This capability makes the MFS particularly suitable for shape optimization,moving load,and inverse problems.However,it is observed that the standard MFS lead to inaccurate solutions for some elastostatic problems with stress concentration and/or highly anisotropic materials.In thiswork,by a numerical study,the important parameters,which have significant influence on the accuracy of the MFS for the analysis of two-dimensional anisotropic elastostatic problems,are investigated.The studied parameters are the degree of anisotropy of the problem,the ratio of the number of collocation points to the number of source points,and the distance between main and pseudo boundaries.It is observed that as the anisotropy of the material increases,there will be more errors in the results.It is also observed that for simple problems,increasing the distance between main and pseudo boundaries enhances the accuracy of the results;however,it is not the case for complicated problems.Moreover,it is concluded that more collocation points than source points can significantly improve the accuracy of the results.
