The elastic stress distribution and the variation of the elastic energy with spacing between two inclusions of arbitrary sizes in an infinite isotropic cylindrical rod are obtained by an analytical approach and the ph...The elastic stress distribution and the variation of the elastic energy with spacing between two inclusions of arbitrary sizes in an infinite isotropic cylindrical rod are obtained by an analytical approach and the phase field microelasticity(PFM)simulation.The results show a near-attraction and far-repulsion elastic interaction between two inclusions with hydrostatic dilatation.The critical spacing,at which the interaction changes from attraction to repulsion,is on the order of the radius of the rod,dependent on the length and Poisson’s ratio of inclusions.Furthermore,the elastic energy calculations and PFM simulation results indicate that applying the local radial stress on the rod surface can modulate the elastic interaction between inclusions and adjust the periodicity of the superlattice nanowire structure.This can provide some guidelines for the tunable construction of superlattice nanowire structures.展开更多
Soliton theory plays an important role in nonlinear physics.The elastic interaction among solitons is oneof the most important properties for integrable systems.In this Letter, an elastic vortex interaction model is p...Soliton theory plays an important role in nonlinear physics.The elastic interaction among solitons is oneof the most important properties for integrable systems.In this Letter, an elastic vortex interaction model is proposed.It is found that the momenta, vortex momenta and the energies of every one vortex and the interaction energies of everytwo vortices are conserved.展开更多
Hirota＇s bilinear direct method is applied to constructing soliton solutions to a special coupled modified Korteweg- de Vries （mKdV） system. Some physical properties such as the spatiotemporal evolution, waveform s...Hirota＇s bilinear direct method is applied to constructing soliton solutions to a special coupled modified Korteweg- de Vries （mKdV） system. Some physical properties such as the spatiotemporal evolution, waveform structure, interactive phenomena of solitons are discussed, especially in the two-soliton case. It is found that different interactive behaviours of solitary waves take place under different parameter conditions of overtaking collision in this system. It is verified that the elastic interaction phenomena exist in this （1＋1）-dimensional integrable coupled model.展开更多
In order to improve the design level of partially embedded single piles under simultaneous axial and lateral loads, the differential solutions were deduced, in which the soil was treated as an ideal, elastic, homogene...In order to improve the design level of partially embedded single piles under simultaneous axial and lateral loads, the differential solutions were deduced, in which the soil was treated as an ideal, elastic, homogeneous, semi-infinite isotropic medium. A comparison was made between model test results and the obtained solutions to show their validity. The calculation results indicate that the horizontal displacement and bending moment of the pile increase with increases of the axial and lateral loads. The maximum horizontal displacement and bending moment decrease by 37.9% and 13.9%, respectively, when the elastic modulus of soil increases from 4 MPa to 20 MPa. The Poisson ratio of soil plays a marginal role in pile responses. There is a critical pile length under the ground, beyond which the pile behaves as though it was infinitely long. The presented solutions can make allowance for the continuous nature of soil, and if condition permits, they can approach exact ones.展开更多
Interface dislocations may dramatically change the electric properties, such as polarization, of the piezoelectric crystals. In this paper, we study the linear interactions of two interface dislocation loops with arbi...Interface dislocations may dramatically change the electric properties, such as polarization, of the piezoelectric crystals. In this paper, we study the linear interactions of two interface dislocation loops with arbitrary shape in generally anisotropic piezoelectric bi-crystals. A simple formula for calculating the interaction energy of the interface dislocation loops is derived and given by a double line integral along two closed dislocation curves. Particularly, interactions between two straight segments of the interface dislocations are solved analytically, which can be applied to approximate any curved loop so that an analytical solution can be also achieved. Numerical results show the influence of the bi-crystal interface as well as the material orientation on the interaction of interface dislocation loops.展开更多
The dynamic scaling behaviour of late-stage phase separation and coarsening mechanisms of L12 and D022 in Ni75AlxV25-x （3 ≤ x ≤ 10, at.%） alloys are studied using the microscopic phase-field dynamic model. The mic...The dynamic scaling behaviour of late-stage phase separation and coarsening mechanisms of L12 and D022 in Ni75AlxV25-x （3 ≤ x ≤ 10, at.%） alloys are studied using the microscopic phase-field dynamic model. The microelaso ticity field is incorporated into the diffusion dynamic model. The results show the morphology and coarsening dynamics being greatly changed by the elastic interactions among different precipitates, the particles aligning along the dominant directions, the average domain size （ADS） of L12 and D022 deviating from the exponent of temporal power-law, and the growth slowing down due to the increasing of elastic interactions. The dynamic scaling regime of late-stage coarsening of the precipitates is attained. Thus the scaling behaviour of structure function is also applicable for elastic interaction systems. It is also found that the variations of ADS and scaling function depend on the volume fraction of precipitates.展开更多
We study instability of a Newtonian Couette flow past a gel-like film in the limit of vanishing Reynolds number. Three models are explored including one hyperelastic（neo-Hookean） solid, and two viscoelastic（Kelvin...We study instability of a Newtonian Couette flow past a gel-like film in the limit of vanishing Reynolds number. Three models are explored including one hyperelastic（neo-Hookean） solid, and two viscoelastic（Kelvin–Voigt and Zener） solids. Instead of using the conventional Lagrangian description in the solid phase for solving the displacement field, we construct equivalent ‘‘differential＇＇ models in an Eulerian reference frame, and solve for the velocity, pressure, and stress in both fluid and solid phases simultaneously. We find the interfacial instability is driven by the first-normal stress difference in the basestate solution in both hyperelastic and viscoelastic models. For the neo-Hookean solid, when subjected to a shear flow, the interface exhibits a short-wave（finite-wavelength） instability when the film is thin（thick）. In the Kelvin–Voigt and Zener solids where viscous effects are incorporated, instability growth is enhanced at small wavenumber but suppressed at large wavenumber, leading to a dominant finitewavelength instability. In addition, adding surface tension effectively stabilizes the interface to sustain fluid shear.展开更多
A numerical–analytical approach is described to investigate the process of impact interaction between a long smooth rigid body and the surface of a circular cylindrical cavity in elastic space. A non-stationary mixed...A numerical–analytical approach is described to investigate the process of impact interaction between a long smooth rigid body and the surface of a circular cylindrical cavity in elastic space. A non-stationary mixed initial boundary value problem is formulated with a priori unknown boundaries moving with variable velocity. The problem is solved using the methods of the theory of integral transforms, expansion of desired variables into a Fourier series, and the quadrature method to reduce the problem to solving a system of linear algebraic equations at each time step. Some concrete numerical computations are presented.The cylindrical body mass and radius impact on the proile of the transient process of contact interaction has been analysed.展开更多
Self-accommodation microstructure,a typical crystallographic texture developed from phase transformation,is often observed in various alloys.In this work,a molecular dynamics simulation was conducted to reveal the fin...Self-accommodation microstructure,a typical crystallographic texture developed from phase transformation,is often observed in various alloys.In this work,a molecular dynamics simulation was conducted to reveal the fine details of self-accommodation microstructure evolution during the phase transformation from austenite to ferrite in pure iron.The growth and shrinkage of ferrite grains with different orientation relationships(ORs)are interpreted based on the analysis combining the elastic interaction energy and the interfacial energy.It was found that the strain energy determines the priority of potential ORs,while the interfacial energy selects the specific preferred ORs to form.The present atomistic process and energetic interpretation of the self-accommodation microstructure provide helpful insight into phase transformation textures observed in various alloys.展开更多
For a one(2+1)-dimensional combined Kadomtsev-Petviashvili with its hierarchy equation, the missing D’Alembert type solution is derived first through the traveling wave transformation which contains several special k...For a one(2+1)-dimensional combined Kadomtsev-Petviashvili with its hierarchy equation, the missing D’Alembert type solution is derived first through the traveling wave transformation which contains several special kink molecule structures. Further, after introducing the B?cklund transformation and an auxiliary variable, the N-soliton solution which contains some soliton molecules for this equation, is presented through its Hirota bilinear form. The concrete molecules including line solitons, breathers and a lump as well as several interactions of their hybrid are shown with the aid of special conditions and parameters. All these dynamical features are demonstrated through the different figures.展开更多
基金Project supported by the Strategic Priority Research Program of the Chinese Academy of Sciences(No.XDB22040502)the National Natural Science Foundation of China(No.11672285)and the Fundamental Research Funds for the Central Universities of China(No.WK2090050043)。
文摘The elastic stress distribution and the variation of the elastic energy with spacing between two inclusions of arbitrary sizes in an infinite isotropic cylindrical rod are obtained by an analytical approach and the phase field microelasticity(PFM)simulation.The results show a near-attraction and far-repulsion elastic interaction between two inclusions with hydrostatic dilatation.The critical spacing,at which the interaction changes from attraction to repulsion,is on the order of the radius of the rod,dependent on the length and Poisson’s ratio of inclusions.Furthermore,the elastic energy calculations and PFM simulation results indicate that applying the local radial stress on the rod surface can modulate the elastic interaction between inclusions and adjust the periodicity of the superlattice nanowire structure.This can provide some guidelines for the tunable construction of superlattice nanowire structures.
基金Supported by the National Natural Science Foundation of China under Grant No.10735030 the National Basic Research Programs of China (973 Programs) under Grant Nos.2007CB814800 and 2005CB422301the PCSIRT (IRT0734)
文摘Soliton theory plays an important role in nonlinear physics.The elastic interaction among solitons is oneof the most important properties for integrable systems.In this Letter, an elastic vortex interaction model is proposed.It is found that the momenta, vortex momenta and the energies of every one vortex and the interaction energies of everytwo vortices are conserved.
文摘Hirota＇s bilinear direct method is applied to constructing soliton solutions to a special coupled modified Korteweg- de Vries （mKdV） system. Some physical properties such as the spatiotemporal evolution, waveform structure, interactive phenomena of solitons are discussed, especially in the two-soliton case. It is found that different interactive behaviours of solitary waves take place under different parameter conditions of overtaking collision in this system. It is verified that the elastic interaction phenomena exist in this （1＋1）-dimensional integrable coupled model.
基金Projects(50708093,51208409)supported by the National Natural Science Foundation of ChinaProject(DB01129)supported by the Talent Foundation of Xi’an University of Architecture and Technology,China
文摘In order to improve the design level of partially embedded single piles under simultaneous axial and lateral loads, the differential solutions were deduced, in which the soil was treated as an ideal, elastic, homogeneous, semi-infinite isotropic medium. A comparison was made between model test results and the obtained solutions to show their validity. The calculation results indicate that the horizontal displacement and bending moment of the pile increase with increases of the axial and lateral loads. The maximum horizontal displacement and bending moment decrease by 37.9% and 13.9%, respectively, when the elastic modulus of soil increases from 4 MPa to 20 MPa. The Poisson ratio of soil plays a marginal role in pile responses. There is a critical pile length under the ground, beyond which the pile behaves as though it was infinitely long. The presented solutions can make allowance for the continuous nature of soil, and if condition permits, they can approach exact ones.
基金supports from the National Natural Science Foundation of China(11402133 and 11502128)
文摘Interface dislocations may dramatically change the electric properties, such as polarization, of the piezoelectric crystals. In this paper, we study the linear interactions of two interface dislocation loops with arbitrary shape in generally anisotropic piezoelectric bi-crystals. A simple formula for calculating the interaction energy of the interface dislocation loops is derived and given by a double line integral along two closed dislocation curves. Particularly, interactions between two straight segments of the interface dislocations are solved analytically, which can be applied to approximate any curved loop so that an analytical solution can be also achieved. Numerical results show the influence of the bi-crystal interface as well as the material orientation on the interaction of interface dislocation loops.
基金Project supported by the National Natural Science Foundation of China （Grant No 50071046） and the National High Technology and Development Program of China （Grant No 2002AA331050）, and the Doctorate Foundation of Northwestern Polytechnical University of China （Grant No CX200507）.
文摘The dynamic scaling behaviour of late-stage phase separation and coarsening mechanisms of L12 and D022 in Ni75AlxV25-x （3 ≤ x ≤ 10, at.%） alloys are studied using the microscopic phase-field dynamic model. The microelaso ticity field is incorporated into the diffusion dynamic model. The results show the morphology and coarsening dynamics being greatly changed by the elastic interactions among different precipitates, the particles aligning along the dominant directions, the average domain size （ADS） of L12 and D022 deviating from the exponent of temporal power-law, and the growth slowing down due to the increasing of elastic interactions. The dynamic scaling regime of late-stage coarsening of the precipitates is attained. Thus the scaling behaviour of structure function is also applicable for elastic interaction systems. It is also found that the variations of ADS and scaling function depend on the volume fraction of precipitates.
基金the National Science Foundation(NSF)(DMS-1619960 and CBET1702987)NSF(CMMI-1538137)
文摘We study instability of a Newtonian Couette flow past a gel-like film in the limit of vanishing Reynolds number. Three models are explored including one hyperelastic（neo-Hookean） solid, and two viscoelastic（Kelvin–Voigt and Zener） solids. Instead of using the conventional Lagrangian description in the solid phase for solving the displacement field, we construct equivalent ‘‘differential＇＇ models in an Eulerian reference frame, and solve for the velocity, pressure, and stress in both fluid and solid phases simultaneously. We find the interfacial instability is driven by the first-normal stress difference in the basestate solution in both hyperelastic and viscoelastic models. For the neo-Hookean solid, when subjected to a shear flow, the interface exhibits a short-wave（finite-wavelength） instability when the film is thin（thick）. In the Kelvin–Voigt and Zener solids where viscous effects are incorporated, instability growth is enhanced at small wavenumber but suppressed at large wavenumber, leading to a dominant finitewavelength instability. In addition, adding surface tension effectively stabilizes the interface to sustain fluid shear.
文摘A numerical–analytical approach is described to investigate the process of impact interaction between a long smooth rigid body and the surface of a circular cylindrical cavity in elastic space. A non-stationary mixed initial boundary value problem is formulated with a priori unknown boundaries moving with variable velocity. The problem is solved using the methods of the theory of integral transforms, expansion of desired variables into a Fourier series, and the quadrature method to reduce the problem to solving a system of linear algebraic equations at each time step. Some concrete numerical computations are presented.The cylindrical body mass and radius impact on the proile of the transient process of contact interaction has been analysed.
基金financially supported by the National Natural Science Foundation of China (Nos.51471097 and 51671111)the National Key Research and Development Program of China (No. 2016YFB0701304)
文摘Self-accommodation microstructure,a typical crystallographic texture developed from phase transformation,is often observed in various alloys.In this work,a molecular dynamics simulation was conducted to reveal the fine details of self-accommodation microstructure evolution during the phase transformation from austenite to ferrite in pure iron.The growth and shrinkage of ferrite grains with different orientation relationships(ORs)are interpreted based on the analysis combining the elastic interaction energy and the interfacial energy.It was found that the strain energy determines the priority of potential ORs,while the interfacial energy selects the specific preferred ORs to form.The present atomistic process and energetic interpretation of the self-accommodation microstructure provide helpful insight into phase transformation textures observed in various alloys.
基金supported by the National Natural Science Foundation of China(Nos.11705077,11775104 and 11447017)。
文摘For a one(2+1)-dimensional combined Kadomtsev-Petviashvili with its hierarchy equation, the missing D’Alembert type solution is derived first through the traveling wave transformation which contains several special kink molecule structures. Further, after introducing the B?cklund transformation and an auxiliary variable, the N-soliton solution which contains some soliton molecules for this equation, is presented through its Hirota bilinear form. The concrete molecules including line solitons, breathers and a lump as well as several interactions of their hybrid are shown with the aid of special conditions and parameters. All these dynamical features are demonstrated through the different figures.
