Compatibility conditions of a deformation field in continuum mechanics have been revisited via two different routes. One is to use the deformation gradient, and the other is a pure geometric one. Variations of the dis...Compatibility conditions of a deformation field in continuum mechanics have been revisited via two different routes. One is to use the deformation gradient, and the other is a pure geometric one. Variations of the displacement vector and the displacement density tensor are obtained explicitly in terms of the Riemannian curvature tensor. The explicit relations reconfirm that the compatibility condition is equivalent to the vanishing of the Riemann curvature tensor and reveals the non-Euclidean nature of the space in which the dislocated continuum is imbedded. Comparisons with the theory of Kr¨oner and Le-Stumpf are provided.展开更多
Anisotropic metamaterial with only one component of the mass density tensor near zero （ADNZ） is proposed to control the sound wave propagation. We find that such an anisotropic metamaterial can be used to realize pe...Anisotropic metamaterial with only one component of the mass density tensor near zero （ADNZ） is proposed to control the sound wave propagation. We find that such an anisotropic metamaterial can be used to realize perfect bending waveguides. According to a coordinate transformation, the surface waves on the input and output interfaces of the ADNZ metamaterial induces the sound energy flow to be redistributed and match smoothly with the propagating modes inside the metamaterial waveguide. According to the theory of bending waveguide, we realize the ＂T＂-type sound shunting and convergence, as well as acoustic channel selection by embedding small-sized defects. Numerical calculations are performed to confirm the above effects.展开更多
The dislocation density tensor computed as the cud of plastic distortion is regarded as a new constitutive variable in crystal plasticity. The dependence of the free energy function on the dislocation density tensor i...The dislocation density tensor computed as the cud of plastic distortion is regarded as a new constitutive variable in crystal plasticity. The dependence of the free energy function on the dislocation density tensor is explored starting from a quadratic ansatz. Rank one and logarithmic dependencies are then envisaged based on considerations from the statistical theory of dislocations. The rele- vance of the presented free energy potentials is evaluated from the corresponding analytical solutions of the periodic two-phase laminate problem under shear where one layer is a single crystal material undergoing single slip and the second one remains purely elastic.展开更多
Shale reservoirs are typically very tight, and crack are only a small part of the reservoir. The directional arrangement of cracks leads to the anisotropic characteristics of shale, and the type of fluid filled in cra...Shale reservoirs are typically very tight, and crack are only a small part of the reservoir. The directional arrangement of cracks leads to the anisotropic characteristics of shale, and the type of fluid filled in cracks affects the shale reservoir evaluation and late development. Many rock physics theories and methods typically use second-and fourthorder crack density tensors to characterize the elastic anisotropy induced by cracks as well as the normal-to-tangential crack compliance ratio to distinguish between dry and saturated cracks. This study def ines an anisotropic crack f luid indicator for vertical transversely isotropy(VTI) media with vertical symmetry axis which is the integration of the normal-to-tangential crack compliance ratio in three directions. A new dimensionless fourth-order tensor, including crack f luid type, azimuth distribution, and geometric shape, is constructed by substituting the normal and tangential compliance into the fourth-order crack density tensor, which can also be used to identify the type of crack fluid in the VTI media. Using the Callovo–Oxfordian shale experimental data, the variation of the elastic properties of dry and saturated shale samples with axial stress is analyzed. The results demonstrate that the anisotropic crack f luid indicator of water-bearing shale samples is less than that of the dry shale samples and that the dimensionless fourth-order tensor of water-bearing shale samples is nearly one order of magnitude greater than that of the dry shale samples. Therefore, the anisotropic crack f luid indicator and dimensionless fourth-order tensor can ref lect the crack f luid type in shale samples and can be used for shale reservoir prediction and f luid identif ication.展开更多
The paper shows how a generalization of the elasticity theory to four dimensions and to space-time allows for a consistent description of the homogeneous and isotropic universe,including the accelerated expansion.The ...The paper shows how a generalization of the elasticity theory to four dimensions and to space-time allows for a consistent description of the homogeneous and isotropic universe,including the accelerated expansion.The analogy is manifested by the inclusion in the traditional Lagrangian of general relativity of an additional term accounting for the strain induced in the manifold(i.e.in space-time)by the curvature,be it induced by the presence of a texture defect or by a matter/energy distribution.The additional term is su?cient to account for various observed features of the universe and to give a simple interpretation for the so called dark energy.Then,we show how the same approach can be adopted back in three dimensions to obtain the equilibrium configuration of a given solid subject to strain induced by defects or applied forces.Finally,it is shown how concepts coming from the familiar elasticity theory can inspire new approaches to cosmology and in return how methods appropriated to General Relativity can be applied back to classical problems of elastic deformations in three dimensions.展开更多
基金Project supported by the National Research Foundation of South Africa(NRF)(No.93918)
文摘Compatibility conditions of a deformation field in continuum mechanics have been revisited via two different routes. One is to use the deformation gradient, and the other is a pure geometric one. Variations of the displacement vector and the displacement density tensor are obtained explicitly in terms of the Riemannian curvature tensor. The explicit relations reconfirm that the compatibility condition is equivalent to the vanishing of the Riemann curvature tensor and reveals the non-Euclidean nature of the space in which the dislocated continuum is imbedded. Comparisons with the theory of Kr¨oner and Le-Stumpf are provided.
基金Project supported by the National Basic Research Program of China(Grant No.2012CB921504)the National Natural Science Foundation of China(Grant No.11474160)+2 种基金the Fundamental Research Funds for the Central Universities,China(Grant No.020414380001)the State Key Laboratory of Acoustics,Chinese Academy of Sciences(Grant No.SKLA201609)the Priority Academic Program Development of Jiangsu Higher Education Institution,China
文摘Anisotropic metamaterial with only one component of the mass density tensor near zero （ADNZ） is proposed to control the sound wave propagation. We find that such an anisotropic metamaterial can be used to realize perfect bending waveguides. According to a coordinate transformation, the surface waves on the input and output interfaces of the ADNZ metamaterial induces the sound energy flow to be redistributed and match smoothly with the propagating modes inside the metamaterial waveguide. According to the theory of bending waveguide, we realize the ＂T＂-type sound shunting and convergence, as well as acoustic channel selection by embedding small-sized defects. Numerical calculations are performed to confirm the above effects.
基金Dr. F.Latourte (EDF Research and Development Division,Les Renardières,Moret-sur-Loing,France) and Dr. J.M.Proix (EDF Research and Development Division,Clamart,France),and the MAI-SN (EDF,Les Renardières,Moret-sur-Loing,France) for stimulating discussions and financial support for part of this study
文摘The dislocation density tensor computed as the cud of plastic distortion is regarded as a new constitutive variable in crystal plasticity. The dependence of the free energy function on the dislocation density tensor is explored starting from a quadratic ansatz. Rank one and logarithmic dependencies are then envisaged based on considerations from the statistical theory of dislocations. The rele- vance of the presented free energy potentials is evaluated from the corresponding analytical solutions of the periodic two-phase laminate problem under shear where one layer is a single crystal material undergoing single slip and the second one remains purely elastic.
基金supported by the National Natural Science Foundation of China(Nos.41874146,41674130)National Key S&T Special Project of China(No.2017ZX05049-002,2016ZX05027-004-001)+2 种基金the Fundamental Research Funds for the Central University(No.18CX02061A)the Innovative Fund Project of China National Petroleum Corporation(No.2016D-5007-0301)the Scientific Research&Technology Development Project of China National Petroleum Corporation(No.2017D-3504)
文摘Shale reservoirs are typically very tight, and crack are only a small part of the reservoir. The directional arrangement of cracks leads to the anisotropic characteristics of shale, and the type of fluid filled in cracks affects the shale reservoir evaluation and late development. Many rock physics theories and methods typically use second-and fourthorder crack density tensors to characterize the elastic anisotropy induced by cracks as well as the normal-to-tangential crack compliance ratio to distinguish between dry and saturated cracks. This study def ines an anisotropic crack f luid indicator for vertical transversely isotropy(VTI) media with vertical symmetry axis which is the integration of the normal-to-tangential crack compliance ratio in three directions. A new dimensionless fourth-order tensor, including crack f luid type, azimuth distribution, and geometric shape, is constructed by substituting the normal and tangential compliance into the fourth-order crack density tensor, which can also be used to identify the type of crack fluid in the VTI media. Using the Callovo–Oxfordian shale experimental data, the variation of the elastic properties of dry and saturated shale samples with axial stress is analyzed. The results demonstrate that the anisotropic crack f luid indicator of water-bearing shale samples is less than that of the dry shale samples and that the dimensionless fourth-order tensor of water-bearing shale samples is nearly one order of magnitude greater than that of the dry shale samples. Therefore, the anisotropic crack f luid indicator and dimensionless fourth-order tensor can ref lect the crack f luid type in shale samples and can be used for shale reservoir prediction and f luid identif ication.
文摘The paper shows how a generalization of the elasticity theory to four dimensions and to space-time allows for a consistent description of the homogeneous and isotropic universe,including the accelerated expansion.The analogy is manifested by the inclusion in the traditional Lagrangian of general relativity of an additional term accounting for the strain induced in the manifold(i.e.in space-time)by the curvature,be it induced by the presence of a texture defect or by a matter/energy distribution.The additional term is su?cient to account for various observed features of the universe and to give a simple interpretation for the so called dark energy.Then,we show how the same approach can be adopted back in three dimensions to obtain the equilibrium configuration of a given solid subject to strain induced by defects or applied forces.Finally,it is shown how concepts coming from the familiar elasticity theory can inspire new approaches to cosmology and in return how methods appropriated to General Relativity can be applied back to classical problems of elastic deformations in three dimensions.
