A mechanical model of the quasi-static interface of a mode I crack between a rigid and a pressure-sensitive viscoelastic material was established to investigate the mechanical characteristic of ship-building engineeri...A mechanical model of the quasi-static interface of a mode I crack between a rigid and a pressure-sensitive viscoelastic material was established to investigate the mechanical characteristic of ship-building engineering hi-materials. In the stable growth stage, stress and strain have the same singularity, ie （σ, ε） ∝ r^-1/（n-1）. The variable-separable asymptotic solutions of stress and strain at the crack tip were obtained by adopting Airy＇s stress function and the numerical results of stress and strain in the crack-tip field were obtained by the shooting method. The results showed that the near-tip fields are mainly governed by the power-hardening exponent n and the Poisson ratio v of the pressure-sensitive material. The fracture criterion of mode I quasi-static crack growth in pressure-sensitive materials, according to the asymptotic analyses of the crack-tip field, can be viewed from the perspective of strain.展开更多
We investigate the interface-guided mode of Lamb waves in a phononic crystal heterostructures plate, which is com- posed of two different semi-infinite phononic crystal （PC） plates. The interface-guided modes of the...We investigate the interface-guided mode of Lamb waves in a phononic crystal heterostructures plate, which is com- posed of two different semi-infinite phononic crystal （PC） plates. The interface-guided modes of the Lamb wave can be obtained by the lateral lattice slipping or by the interface longitudinal gliding. Significantly, it is observed that the condition to generate the interface-guided modes of the Lamb wave is more demanding than that of the studied fluid-fluid system. The interface-guided modes are strongly affected not only by the relative movement of the two semi-infinite PCs but also by the thickness of the PC plate.展开更多
By employing the dielectric continuum model and Loudon＇s uniaxial crystal model, the interface optical （IO） phonon modes in a freestanding quasi-one-dimensional （Q1D） wurtzite rectangular quantum wire are derived...By employing the dielectric continuum model and Loudon＇s uniaxial crystal model, the interface optical （IO） phonon modes in a freestanding quasi-one-dimensional （Q1D） wurtzite rectangular quantum wire are derived and analyzed. Numerical calculation on a freestanding wurtzite GaN quantum wire is performed. The resulte reveal that the dispersion frequencies of IO modes sensitively depend on the geometric structures of the Q1D wurtzite rectangular quantum wires, the free wave-number kz in z-direction and the dielectric constant of the nonpolar matrix. The degenerating behavior of the IO modes in Q1D wurtzite rectangular quantum wire has been clearly observed in the case of small wave-number kz and Iarge ratio of length to width of the rectangular crossing profile. The limited frequency behaviors of IO modes have been analyzed deeply, and detailed comparisons with those in wurtzite planar quantum wells and cylindrical quantum wires are also done. The present theories can be looked on as a generalization of that in isotropic rectangular quantum wires, and it can naturally reduce to the case of Q1D isotropic quantum wires once the anisotropy of the wurtzite material is ignored.展开更多
The fracture problems near the similar orthotropic composite materials are interface crack tip for mode Ⅱ of double disstudied. The mechanical models of interface crack for mode Ⅱ are given. By translating the gover...The fracture problems near the similar orthotropic composite materials are interface crack tip for mode Ⅱ of double disstudied. The mechanical models of interface crack for mode Ⅱ are given. By translating the governing equations into the generalized hi-harmonic equations, the stress functions containing two stress singularity exponents are derived with the help of a complex function method. Based on the boundary conditions, a system of non-homogeneous linear equations is found. Two real stress singularity exponents are determined be solving this system under appropriate conditions about bimaterial engineering parameters. According to the uniqueness theorem of limit, both the formulae of stress intensity factors and theoretical solutions of stress field near the interface crack tip are derived. When the two orthotropic materials are the same, the stress singularity exponents, stress intensity factors and stresses for mode II crack of the orthotropic single material are obtained.展开更多
For a compression-shear mixed mode interface crack, it is difficult to solve the stress and strain fields considering the material viscosity, the crack-tip singularity, the frictional effect, and the mixed loading lev...For a compression-shear mixed mode interface crack, it is difficult to solve the stress and strain fields considering the material viscosity, the crack-tip singularity, the frictional effect, and the mixed loading level. In this paper, a mechanical model of the dynamic propagation interface crack for the compression-shear mixed mode is proposed using an elastic-viscoplastic constitutive model. The governing equations of propagation crack interface at the crack-tip are given. The numerical analysis is performed for the interface crack of the compression-shear mixed mode by introducing a displacement function and some boundary conditions. The distributed regularities of stress field of the interface crack-tip are discussed with several special parameters. The final results show that the viscosity effect and the frictional contact effect on the crack surface and the mixed-load parameter are important factors in studying the mixed mode interface crack- tip fields. These fields are controlled by the viscosity coefficient, the Mach number, and the singularity exponent.展开更多
By the application of the theory of complex functions, asymmetrical dynamic propagation problems on mode Ⅲ interface crack are studied. The universal representations of analytical solutions are obtained by the approa...By the application of the theory of complex functions, asymmetrical dynamic propagation problems on mode Ⅲ interface crack are studied. The universal representations of analytical solutions are obtained by the approaches of self-similar function. The problems researched can be facilely transformed into Riemann-Hilbert problems and analytical solution to an asymmetrical propagation crack under the condition of point loads and unit-step loads, respectively, is acquired. After those solutions were used by superposition theorem, the solutions of arbitrarily complex problems could be attained.展开更多
Two systems of non-homogeneous linear equations with 8 unknowns are obtained.This is done by introducing two stress functions containing 16 undetermined coefficients and two real stress singularity exponents with the ...Two systems of non-homogeneous linear equations with 8 unknowns are obtained.This is done by introducing two stress functions containing 16 undetermined coefficients and two real stress singularity exponents with the help of boundary conditions.By solving the above systems of non-homogeneous linear equations,the two real stress singularity exponents can be determined when the double material parameters meet certain conditions.The expression of the stress function and all coefficients are obtained based on the uniqueness theorem of limit.By substituting these parameters into the corresponding mechanics equations,theoretical solutions to the stress intensity factor,the stress field and the displacement field near the crack tip of each material can be obtained when both discriminants of the characteristic equations are less than zero.Stress and displacement near the crack tip show mixed crack characteristics without stress oscillation and crack surface overlapping.As an example,when the two orthotropic materials are the same,the stress singularity exponent,the stress intensity factor,and expressions for the stress and the displacement fields of the orthotropic single materials can be derived.展开更多
The mechanical behaviors near the interface crack tip for mode Ⅰ of orthotropic bimaterial are researched. With the help of the complex function method and the undetermined coefficient method, non-oscillatory field i...The mechanical behaviors near the interface crack tip for mode Ⅰ of orthotropic bimaterial are researched. With the help of the complex function method and the undetermined coefficient method, non-oscillatory field if the singularity exponent is a real number, and oscillatory field if the singularity exponent is a complex number are discussed, respectively. For each case, the stress functions are constructed which contain twelve undetermined coefficients and an unknown singularity exponent. Based on the boundary conditions, the system of non-homogeneous linear equations is obtained. According to the necessary and sufficient condition for the existence of solution for the system of non-homogeneous linear equations, the singularity exponent is determined under appropriate condition using bimaterial parameters. Both the theoretical formulae of stress intensity factors and analytic solutions of stress or displacement field near the interface crack tip are given. When the two orthotropic materials are the same, the classical results for orthotropic single material are deduced.展开更多
Substrates provide the necessary support for scientific explorations of numerous promising features and exciting potential applications in two-dimensional (2D) transition metal dichalcogenides (TMDs). To utilize subst...Substrates provide the necessary support for scientific explorations of numerous promising features and exciting potential applications in two-dimensional (2D) transition metal dichalcogenides (TMDs). To utilize substrate engineering to alter the properties of 2D TMDs and avoid introducing unwanted adverse effects, various experimental techniques, such as high-frequency Raman spectroscopy, have been used to understand the interactions between 2D TMDs and substrates. However, sample-substrate interaction in 2D TMDs is not yet fully understood due to the lack of systematic studies by techniques that are sensitive to 2D TMD-substrate interaction. This work systematically investigates the interaction between tungsten disulfide (WS_(2)) monolayers and substrates by low-frequency Raman spectroscopy, which is very sensitive to WS_(2)-substrate interaction. Strong coupling with substrates is clearly revealed in chemical vapor deposition (CVD)-grown monolayer WS_(2) by its low-wavenumber interface mode. It is demonstrated that the enhanced sample-substrate interaction leads to tensile strain on monolayer WS_(2), which is induced during the cooling process of CVD growth and could be released for monolayer WS_(2) sample after transfer or fabricated by an annealing-free method such as mechanical exfoliation. These results not only suggest the effectiveness of low-frequency Raman spectroscopy for probing sample-substrate interactions in 2D TMDs, but also provide guidance for the design of high-performance devices with the desired sample-substrate coupling strength based on 2D TMDs.展开更多
The Richtmyer-Meshkov instability of interfaces separating elastic-plastic materials from vacuum is investigated by numerical simulation using a multi-material solid mechanics algorithm based on an Eulerian framework....The Richtmyer-Meshkov instability of interfaces separating elastic-plastic materials from vacuum is investigated by numerical simulation using a multi-material solid mechanics algorithm based on an Eulerian framework.The research efforts are directed to reveal the influence of the initial perturbation and material strength on the deformation of the perturbed interface impacted by an initial shock.By varying the initial amplitude(kx0)of the perturbed interface and the yield stress(sY),three typical modes of interface deformation have been identified as the broken mode,the stable mode and the oscillating mode.For the broken mode,the interface width(i.e.,the bubble position with respect to that of the spike)increases continuously resulting in a final separation of the spike from the perturbed interface.For the stable mode,the interface width grows to saturation and then maintains a nearly constant value in the long term.For the oscillating mode,the wavy-like interface moving forward obtains an aperiodic oscillation of small amplitude,namely,the interface width varies in time slightly around zero.The intriguing difference of the typical modes is interpreted qualitatively by comparing the early-stage wave motion and the commensurate pressure and effective stress.Further,the subsequent interface deformation is illustrated quantitatively via the time series of the interface positions and velocities of these three typical modes.展开更多
基金Supported by Heilongjiang Province Foundation under Grant No.LC08C02
文摘A mechanical model of the quasi-static interface of a mode I crack between a rigid and a pressure-sensitive viscoelastic material was established to investigate the mechanical characteristic of ship-building engineering hi-materials. In the stable growth stage, stress and strain have the same singularity, ie （σ, ε） ∝ r^-1/（n-1）. The variable-separable asymptotic solutions of stress and strain at the crack tip were obtained by adopting Airy＇s stress function and the numerical results of stress and strain in the crack-tip field were obtained by the shooting method. The results showed that the near-tip fields are mainly governed by the power-hardening exponent n and the Poisson ratio v of the pressure-sensitive material. The fracture criterion of mode I quasi-static crack growth in pressure-sensitive materials, according to the asymptotic analyses of the crack-tip field, can be viewed from the perspective of strain.
基金supported by the National Natural Science Foundation of China(Grant Nos.11374068 and 11374066)the Science&Technology Star of Zhujiang Foundation of Guangzhou,China(Grant No.2011J2200013)the Natural Science Foundation of Guangdong,China(Grant No.S2012020010885)
文摘We investigate the interface-guided mode of Lamb waves in a phononic crystal heterostructures plate, which is com- posed of two different semi-infinite phononic crystal （PC） plates. The interface-guided modes of the Lamb wave can be obtained by the lateral lattice slipping or by the interface longitudinal gliding. Significantly, it is observed that the condition to generate the interface-guided modes of the Lamb wave is more demanding than that of the studied fluid-fluid system. The interface-guided modes are strongly affected not only by the relative movement of the two semi-infinite PCs but also by the thickness of the PC plate.
基金The project supported by the Science and Technology Project of Advanced Academy of Guangzhou City under Grant No. 2060. The author acknowledges the detailed and valuable discussions with Prof. J.J. Shi.
文摘By employing the dielectric continuum model and Loudon＇s uniaxial crystal model, the interface optical （IO） phonon modes in a freestanding quasi-one-dimensional （Q1D） wurtzite rectangular quantum wire are derived and analyzed. Numerical calculation on a freestanding wurtzite GaN quantum wire is performed. The resulte reveal that the dispersion frequencies of IO modes sensitively depend on the geometric structures of the Q1D wurtzite rectangular quantum wires, the free wave-number kz in z-direction and the dielectric constant of the nonpolar matrix. The degenerating behavior of the IO modes in Q1D wurtzite rectangular quantum wire has been clearly observed in the case of small wave-number kz and Iarge ratio of length to width of the rectangular crossing profile. The limited frequency behaviors of IO modes have been analyzed deeply, and detailed comparisons with those in wurtzite planar quantum wells and cylindrical quantum wires are also done. The present theories can be looked on as a generalization of that in isotropic rectangular quantum wires, and it can naturally reduce to the case of Q1D isotropic quantum wires once the anisotropy of the wurtzite material is ignored.
基金supported by the Natural Science Foundation of Shaanxi Province (No.2007011008)
文摘The fracture problems near the similar orthotropic composite materials are interface crack tip for mode Ⅱ of double disstudied. The mechanical models of interface crack for mode Ⅱ are given. By translating the governing equations into the generalized hi-harmonic equations, the stress functions containing two stress singularity exponents are derived with the help of a complex function method. Based on the boundary conditions, a system of non-homogeneous linear equations is found. Two real stress singularity exponents are determined be solving this system under appropriate conditions about bimaterial engineering parameters. According to the uniqueness theorem of limit, both the formulae of stress intensity factors and theoretical solutions of stress field near the interface crack tip are derived. When the two orthotropic materials are the same, the stress singularity exponents, stress intensity factors and stresses for mode II crack of the orthotropic single material are obtained.
基金Project supported by the National Natural Science Foundation of China(No.11302054)the Fundamental Research Funds for the Central Universities(No.HEUCF130216)
文摘For a compression-shear mixed mode interface crack, it is difficult to solve the stress and strain fields considering the material viscosity, the crack-tip singularity, the frictional effect, and the mixed loading level. In this paper, a mechanical model of the dynamic propagation interface crack for the compression-shear mixed mode is proposed using an elastic-viscoplastic constitutive model. The governing equations of propagation crack interface at the crack-tip are given. The numerical analysis is performed for the interface crack of the compression-shear mixed mode by introducing a displacement function and some boundary conditions. The distributed regularities of stress field of the interface crack-tip are discussed with several special parameters. The final results show that the viscosity effect and the frictional contact effect on the crack surface and the mixed-load parameter are important factors in studying the mixed mode interface crack- tip fields. These fields are controlled by the viscosity coefficient, the Mach number, and the singularity exponent.
基金Project supported by the Postdoctoral Science Foundation of China (No.2005038199)the Natural Science Foundation of Heilongjiang Province of China (No.ZJG04-08)
文摘By the application of the theory of complex functions, asymmetrical dynamic propagation problems on mode Ⅲ interface crack are studied. The universal representations of analytical solutions are obtained by the approaches of self-similar function. The problems researched can be facilely transformed into Riemann-Hilbert problems and analytical solution to an asymmetrical propagation crack under the condition of point loads and unit-step loads, respectively, is acquired. After those solutions were used by superposition theorem, the solutions of arbitrarily complex problems could be attained.
基金Project supported by the Major Project of Science and Technology of Ministry of Education of China(No.208022)the Natural Science Foundation of Shanxi Province(No.2007011008)
文摘Two systems of non-homogeneous linear equations with 8 unknowns are obtained.This is done by introducing two stress functions containing 16 undetermined coefficients and two real stress singularity exponents with the help of boundary conditions.By solving the above systems of non-homogeneous linear equations,the two real stress singularity exponents can be determined when the double material parameters meet certain conditions.The expression of the stress function and all coefficients are obtained based on the uniqueness theorem of limit.By substituting these parameters into the corresponding mechanics equations,theoretical solutions to the stress intensity factor,the stress field and the displacement field near the crack tip of each material can be obtained when both discriminants of the characteristic equations are less than zero.Stress and displacement near the crack tip show mixed crack characteristics without stress oscillation and crack surface overlapping.As an example,when the two orthotropic materials are the same,the stress singularity exponent,the stress intensity factor,and expressions for the stress and the displacement fields of the orthotropic single materials can be derived.
基金supported by the Natural Science Foundation of Shanxi Province (Grant No. 2011011021-3)
文摘The mechanical behaviors near the interface crack tip for mode Ⅰ of orthotropic bimaterial are researched. With the help of the complex function method and the undetermined coefficient method, non-oscillatory field if the singularity exponent is a real number, and oscillatory field if the singularity exponent is a complex number are discussed, respectively. For each case, the stress functions are constructed which contain twelve undetermined coefficients and an unknown singularity exponent. Based on the boundary conditions, the system of non-homogeneous linear equations is obtained. According to the necessary and sufficient condition for the existence of solution for the system of non-homogeneous linear equations, the singularity exponent is determined under appropriate condition using bimaterial parameters. Both the theoretical formulae of stress intensity factors and analytic solutions of stress or displacement field near the interface crack tip are given. When the two orthotropic materials are the same, the classical results for orthotropic single material are deduced.
基金This work is supported by the National Natural Science Foundation of China(Nos.62004197 and 61774040)the Ministry of Education of Singapore(No.MOE2019-T2-1-004)+5 种基金the Singapore National Research Foundation under the Competitive Research Programs(No.NRF-CRP-21-2018-0007)the National Key R&D Program of China(No.2018YFA0703700)the National Young 1000 Talent Plan of China,the Shanghai Municipal Natural Science Foundation(No.20ZR1403200)the Shanghai Municipal Science and Technology Commission(No.18JC1410300)the Fudan University-CIOMP Joint Fund(No.FC2018-002)the Natural Science Foundation of Liaoning Province,China(Nos.2019-BS-243 and 2019-MS-320).
文摘Substrates provide the necessary support for scientific explorations of numerous promising features and exciting potential applications in two-dimensional (2D) transition metal dichalcogenides (TMDs). To utilize substrate engineering to alter the properties of 2D TMDs and avoid introducing unwanted adverse effects, various experimental techniques, such as high-frequency Raman spectroscopy, have been used to understand the interactions between 2D TMDs and substrates. However, sample-substrate interaction in 2D TMDs is not yet fully understood due to the lack of systematic studies by techniques that are sensitive to 2D TMD-substrate interaction. This work systematically investigates the interaction between tungsten disulfide (WS_(2)) monolayers and substrates by low-frequency Raman spectroscopy, which is very sensitive to WS_(2)-substrate interaction. Strong coupling with substrates is clearly revealed in chemical vapor deposition (CVD)-grown monolayer WS_(2) by its low-wavenumber interface mode. It is demonstrated that the enhanced sample-substrate interaction leads to tensile strain on monolayer WS_(2), which is induced during the cooling process of CVD growth and could be released for monolayer WS_(2) sample after transfer or fabricated by an annealing-free method such as mechanical exfoliation. These results not only suggest the effectiveness of low-frequency Raman spectroscopy for probing sample-substrate interactions in 2D TMDs, but also provide guidance for the design of high-performance devices with the desired sample-substrate coupling strength based on 2D TMDs.
基金supported by the National Natural Science Foundation of China(Nos.12172353,92052301,11621202 and 12202436)the Science Challenge Project(No.TZ2016001)the National Science Foundation(No.CBET0755269).
文摘The Richtmyer-Meshkov instability of interfaces separating elastic-plastic materials from vacuum is investigated by numerical simulation using a multi-material solid mechanics algorithm based on an Eulerian framework.The research efforts are directed to reveal the influence of the initial perturbation and material strength on the deformation of the perturbed interface impacted by an initial shock.By varying the initial amplitude(kx0)of the perturbed interface and the yield stress(sY),three typical modes of interface deformation have been identified as the broken mode,the stable mode and the oscillating mode.For the broken mode,the interface width(i.e.,the bubble position with respect to that of the spike)increases continuously resulting in a final separation of the spike from the perturbed interface.For the stable mode,the interface width grows to saturation and then maintains a nearly constant value in the long term.For the oscillating mode,the wavy-like interface moving forward obtains an aperiodic oscillation of small amplitude,namely,the interface width varies in time slightly around zero.The intriguing difference of the typical modes is interpreted qualitatively by comparing the early-stage wave motion and the commensurate pressure and effective stress.Further,the subsequent interface deformation is illustrated quantitatively via the time series of the interface positions and velocities of these three typical modes.
