Discontinuities constitute an integral part of rock mass and inherently affect its anisotropic deformation behavior.This work focuses on the equivalent elastic deformation of rock mass with multiple persistent joint s...Discontinuities constitute an integral part of rock mass and inherently affect its anisotropic deformation behavior.This work focuses on the equivalent elastic deformation of rock mass with multiple persistent joint sets.A new method based on the space geometric and mechanical properties of the modified crack tensor is proposed,providing an analytical solution for the equivalent elastic compliance tensor of rock mass.A series of experiments validate the capability of the compliance tensor to accurately represent the deformation of rock mass with multiple persistent joint sets,based on conditions set by the basic hypothesis.The spatially varying rules of the equivalent elastic parameters of rock mass with a single joint set are analyzed to reveal the universal law of the stratified rock mass.展开更多
A closed but approximate formula of Green’s function for an arbitrary aggregate of cubic crystallites is given to derive the e?ective elastic sti?ness tensor of the polycrystal. This formula, which includes thr...A closed but approximate formula of Green’s function for an arbitrary aggregate of cubic crystallites is given to derive the e?ective elastic sti?ness tensor of the polycrystal. This formula, which includes three elastic constants of single cubic crystal and ?ve texture coe?cients, accounts for the e?ects of the orientation distribution function (ODF) up to terms linear in the tex- ture coe?cients. Thus it is expected that our formula would be applicable to arbitrary aggregates with weak texture or to materials such as aluminum whose single crystal has weak anisotropy. Three examples are presented to compare predictions from our formula with those from Nishioka and Lothe’s formula and Synge’s contour integral through numerical integration. As an applica- tion of Green’s function, we brie?y describe the procedure of deriving the e?ective elastic sti?ness tensor for an orthorhombic aggregate of cubic crystallites. The comparison of the computational results given by the ?nite element method and our e?ective elastic sti?ness tensor is made by an example.展开更多
Different from the current measurement methods for Young’s modulus of metal materials,the Young’s modulus of intermetallic compounds(IMCs)was obtained by a non-destructive method based on Brillouin light scattering(...Different from the current measurement methods for Young’s modulus of metal materials,the Young’s modulus of intermetallic compounds(IMCs)was obtained by a non-destructive method based on Brillouin light scattering(BLS)in this paper.The single-phase regions of CoSn,CoSn_(2),Cu_(3)Sn and Cu_(6)Sn_(5) phases required for BLS test were obtained by applying long-term thermal stabilization through adjusting temperature gradient.The volume fractions of the corresponding phases near the solid-liquid interfaces of the samples were 98.3%,94.2%,99.6% and 95.9%,respectively.All the independent elastic coefficients and Young’s moduli of IMCs were obtained by Brillouin scatterometer.The Young’s moduli of CoSn,CoSn_(2) and Cu_(3)Sn and Cu_(6)Sn_(5) phases obtained through the present method are 115.0,101.7,129.9 and 125.6 GPa,respectively,which are in a good agreement with the previous experimental results.Thus,the effectiveness of BLS in measuring the Young’s moduli of IMCs in bulk alloys is confirmed.展开更多
In this paper. we obtain the rate-tvpe constitutive expressions of the nonlinearisotropic elastieity by using the Jaumann, Truesdell and Green-Naghdi stress rgterespectively,Through analysing the simple shear deformat...In this paper. we obtain the rate-tvpe constitutive expressions of the nonlinearisotropic elastieity by using the Jaumann, Truesdell and Green-Naghdi stress rgterespectively,Through analysing the simple shear deformation for Mooney-Rivlin material.three kinds of rate-type constitutive equations are verified to be equivalent to the original equation.Rate-type variational prineiples are also presented, and the Ritzmethod is used to obtain the numerical solution of a reetangular rubber membraneunder uniaxial streteh.展开更多
The properties of Cylindrical Internal-Surface Acoustic Waves (CISAW) propagating on the inside surface of a high purity fused quartz tubular fiber are derived from basic principles using a variational method. The CIS...The properties of Cylindrical Internal-Surface Acoustic Waves (CISAW) propagating on the inside surface of a high purity fused quartz tubular fiber are derived from basic principles using a variational method. The CISAW consist of Energy Momentum Packets (EMP) moving in a looping motion. The EMP have mass and are affected by gravity similar to a pendulum bob. The effect of gravity on CISAW is much larger than the effect of gravity in a light wave. Therefore, one can build much smaller CISAW Interferometer Gravity wave Observatories (CIGO) than the present km size Light Interferometer Gravity wave Observatories (LIGO). An array of CIGO can be used to detect gravity wave images. Since the wavelength of gravity waves is much larger than the expected spacing between CIGO array elements this would result in sub-wavelength images. It would be interesting to determine what new discoveries could be made using such an array.展开更多
The concept of elastic moment tensor occurs in several interesting contexts, in particular in imaging small elastic inclusions and in asymptotic models of dilute elastic composites. In this paper, we compute the elast...The concept of elastic moment tensor occurs in several interesting contexts, in particular in imaging small elastic inclusions and in asymptotic models of dilute elastic composites. In this paper, we compute the elastic moment tensors for ellipses and ellipsoids by using a systematic method based on layer potentials. Our computations reveal an underlying elegant relation between the elastic moment tensors and the single layer potential.展开更多
Multiple scattering of elastic waves in realistic media makes that averagefield intensities or energy densities follow diffusive processes. In such regime the successiveP to S energy conversions by distributed random ...Multiple scattering of elastic waves in realistic media makes that averagefield intensities or energy densities follow diffusive processes. In such regime the successiveP to S energy conversions by distributed random inhomogeneities give rise toequipartition which means that in the phase space the available elastic energy is distributedin averagewith equal amounts among the possible states of P and S waves. Insuch diffusive regime the P to S energy ratio equilibrates in an universal way independentof the particular details of the scattering. It has been demonstrated that averagingthe cross correlations at any two points of an elastic medium subjected to diffuse elasticwavefields leads to the emergence of the Green function, which is the wave fieldthat would be observed at one position if an impulsive load is applied at the other. Inthis work we study the problem of the retrieval of the 2D tensor elastodynamic Greenfunction in an infinite elastic space containing a circular cylinder inclusion. We illuminateisotropically the elastic spacewith plane waves. We assume the spectra for both Pand S waves uniform but such that the energy ratio ES/EP=(a/b)2, which is the onepredicted by equipartition theory in two-dimensions. We then show that the Fouriertransform of azimuthal average of the cross-correlation of motion between two pointswithin an elastic medium is proportional to the imaginary part of the exact Green tensorfunction between these points. The numerical results presented here point out thepossibility of detection and imaging of diffractors and resonant diffractors by crosscorrelation even in presence of attenuation exists.展开更多
In this paper, we establish the existence of traveling wave solutions to the nonlinear three-dimensional viscoelastic system exhibiting long range memory. Under certain hypotheses, if the speed of propagation is betwe...In this paper, we establish the existence of traveling wave solutions to the nonlinear three-dimensional viscoelastic system exhibiting long range memory. Under certain hypotheses, if the speed of propagation is between the speeds determined by the equilibrium and instantaneous elastic tensors, then the system has nontrivial trav- eling wave solutions. Moreover, the system has only trivial traveling wave solution in some cases.展开更多
基金Projects(41172284,51379202) supported by the National Natural Science Foundation of ChinaProject(2013CB036405) supported by the National Basic Research Program of ChinaProject(2013BAB02B01) supported by the National Key Technologies R&D Program of China
文摘Discontinuities constitute an integral part of rock mass and inherently affect its anisotropic deformation behavior.This work focuses on the equivalent elastic deformation of rock mass with multiple persistent joint sets.A new method based on the space geometric and mechanical properties of the modified crack tensor is proposed,providing an analytical solution for the equivalent elastic compliance tensor of rock mass.A series of experiments validate the capability of the compliance tensor to accurately represent the deformation of rock mass with multiple persistent joint sets,based on conditions set by the basic hypothesis.The spatially varying rules of the equivalent elastic parameters of rock mass with a single joint set are analyzed to reveal the universal law of the stratified rock mass.
基金Project supported by the Natural Science Foundation of Jiangxi Province (No. 0450035).
文摘A closed but approximate formula of Green’s function for an arbitrary aggregate of cubic crystallites is given to derive the e?ective elastic sti?ness tensor of the polycrystal. This formula, which includes three elastic constants of single cubic crystal and ?ve texture coe?cients, accounts for the e?ects of the orientation distribution function (ODF) up to terms linear in the tex- ture coe?cients. Thus it is expected that our formula would be applicable to arbitrary aggregates with weak texture or to materials such as aluminum whose single crystal has weak anisotropy. Three examples are presented to compare predictions from our formula with those from Nishioka and Lothe’s formula and Synge’s contour integral through numerical integration. As an applica- tion of Green’s function, we brie?y describe the procedure of deriving the e?ective elastic sti?ness tensor for an orthorhombic aggregate of cubic crystallites. The comparison of the computational results given by the ?nite element method and our e?ective elastic sti?ness tensor is made by an example.
基金supported by the Gansu Key Research and Development Project,China(No.23YFGA0003)the Key Science and Technology Projects of Gansu Province,China(No.22ZD6GB019)+2 种基金Gansu Provincial Joint Research Fund,China(No.23JRRC0004)the Industry Support Plan of Gansu Universities,China(No.2024CYZC-01)the Fundamental Research Funds for the Central Universities,China(No.lzujbky-2022-ey15).
文摘Different from the current measurement methods for Young’s modulus of metal materials,the Young’s modulus of intermetallic compounds(IMCs)was obtained by a non-destructive method based on Brillouin light scattering(BLS)in this paper.The single-phase regions of CoSn,CoSn_(2),Cu_(3)Sn and Cu_(6)Sn_(5) phases required for BLS test were obtained by applying long-term thermal stabilization through adjusting temperature gradient.The volume fractions of the corresponding phases near the solid-liquid interfaces of the samples were 98.3%,94.2%,99.6% and 95.9%,respectively.All the independent elastic coefficients and Young’s moduli of IMCs were obtained by Brillouin scatterometer.The Young’s moduli of CoSn,CoSn_(2) and Cu_(3)Sn and Cu_(6)Sn_(5) phases obtained through the present method are 115.0,101.7,129.9 and 125.6 GPa,respectively,which are in a good agreement with the previous experimental results.Thus,the effectiveness of BLS in measuring the Young’s moduli of IMCs in bulk alloys is confirmed.
文摘In this paper. we obtain the rate-tvpe constitutive expressions of the nonlinearisotropic elastieity by using the Jaumann, Truesdell and Green-Naghdi stress rgterespectively,Through analysing the simple shear deformation for Mooney-Rivlin material.three kinds of rate-type constitutive equations are verified to be equivalent to the original equation.Rate-type variational prineiples are also presented, and the Ritzmethod is used to obtain the numerical solution of a reetangular rubber membraneunder uniaxial streteh.
文摘The properties of Cylindrical Internal-Surface Acoustic Waves (CISAW) propagating on the inside surface of a high purity fused quartz tubular fiber are derived from basic principles using a variational method. The CISAW consist of Energy Momentum Packets (EMP) moving in a looping motion. The EMP have mass and are affected by gravity similar to a pendulum bob. The effect of gravity on CISAW is much larger than the effect of gravity in a light wave. Therefore, one can build much smaller CISAW Interferometer Gravity wave Observatories (CIGO) than the present km size Light Interferometer Gravity wave Observatories (LIGO). An array of CIGO can be used to detect gravity wave images. Since the wavelength of gravity waves is much larger than the expected spacing between CIGO array elements this would result in sub-wavelength images. It would be interesting to determine what new discoveries could be made using such an array.
基金Partly supported by Korea Science and Engineering Foundation grant R02-2003-000-10012-0.
文摘The concept of elastic moment tensor occurs in several interesting contexts, in particular in imaging small elastic inclusions and in asymptotic models of dilute elastic composites. In this paper, we compute the elastic moment tensors for ellipses and ellipsoids by using a systematic method based on layer potentials. Our computations reveal an underlying elegant relation between the elastic moment tensors and the single layer potential.
基金from project CGL2005-05500-C02-02/BTE from CICYT,Spainfrom the EU with FEDER+2 种基金the Research Team RNM-194 of Junta de Andaluc´ıa,Spainfrom CONACYT,Mexico,under grant NC-204from DGAPA-UNAM,Mexico,under grant IN114706,are gratefully acknowledged.
文摘Multiple scattering of elastic waves in realistic media makes that averagefield intensities or energy densities follow diffusive processes. In such regime the successiveP to S energy conversions by distributed random inhomogeneities give rise toequipartition which means that in the phase space the available elastic energy is distributedin averagewith equal amounts among the possible states of P and S waves. Insuch diffusive regime the P to S energy ratio equilibrates in an universal way independentof the particular details of the scattering. It has been demonstrated that averagingthe cross correlations at any two points of an elastic medium subjected to diffuse elasticwavefields leads to the emergence of the Green function, which is the wave fieldthat would be observed at one position if an impulsive load is applied at the other. Inthis work we study the problem of the retrieval of the 2D tensor elastodynamic Greenfunction in an infinite elastic space containing a circular cylinder inclusion. We illuminateisotropically the elastic spacewith plane waves. We assume the spectra for both Pand S waves uniform but such that the energy ratio ES/EP=(a/b)2, which is the onepredicted by equipartition theory in two-dimensions. We then show that the Fouriertransform of azimuthal average of the cross-correlation of motion between two pointswithin an elastic medium is proportional to the imaginary part of the exact Green tensorfunction between these points. The numerical results presented here point out thepossibility of detection and imaging of diffractors and resonant diffractors by crosscorrelation even in presence of attenuation exists.
文摘In this paper, we establish the existence of traveling wave solutions to the nonlinear three-dimensional viscoelastic system exhibiting long range memory. Under certain hypotheses, if the speed of propagation is between the speeds determined by the equilibrium and instantaneous elastic tensors, then the system has nontrivial trav- eling wave solutions. Moreover, the system has only trivial traveling wave solution in some cases.
