Soft rocks, such as coal, are afected by sedimentary efects, and the surrounding rock mass of underground coal mines is generally soft and rich in joints and cracks. A clear and deep understanding of the relationship ...Soft rocks, such as coal, are afected by sedimentary efects, and the surrounding rock mass of underground coal mines is generally soft and rich in joints and cracks. A clear and deep understanding of the relationship between crack geometric parameters and rock mechanics properties in cracked rock is greatly important to the design of engineering rock mass struc‑tures. In this study, computed tomography (CT) scanning was used to extract the internal crack network of coal specimens. Based on the crack size and dominant crack number, the parameters of crack area, volume, length, width, and angle were statistically analyzed by diferent sampling thresholds. In addition, the Pearson correlation coefcients between the crack parameters and uniaxial compression rock mechanics properties (uniaxial compressive strength UCS, elasticity modulus E) were calculated to quantitatively analyze the impact of each parameter. Furthermore, a method based on Pearson coefcients was used to grade the correlation between crack geometric parameters and rock mechanical properties to determine threshold values. The results indicated that the UCS and E of the specimens changed with the varied internal crack structures of the specimens, the crack parameters of area, volume, length and width all showed negative correlations with UCS and E, and the dominant crack played an important role both in weakening strength and stifness. The crack parameters of the angle are all positively correlated with the UCS and E. More crack statistics can signifcantly improve the correlation between the parameters of the crack angle and the rock mechanics properties, and the statistics of the geometric parameters of at least 16 cracks or the area larger than 5 mm2 are suggested for the analysis of complex cracked rock masses or physical reproduction using 3D printing. The results are validated and further analyzed with triaxial tests. The fndings of this study have important reference value for future research regarding the accurate and efcient selection of a few cracks with a signifcant infuence on the rock mechanical properties of surrounding rock mass structures in coal engineering.展开更多
A new extrapolation approach was proposed to calculate the strain energy release rates of complex cracks. The point_by_point closed method was used to calculate the closed energy, thus the disadvantage of self_inconsi...A new extrapolation approach was proposed to calculate the strain energy release rates of complex cracks. The point_by_point closed method was used to calculate the closed energy, thus the disadvantage of self_inconsistency in some published papers can be avoided. The disadvantage is that the closed energy is repeatedly calculated: when closed nodal number along radial direction is more than two, the displacement of nodes behind the crack tip that is multiplied by nodal forces, the closed energy has been calculated and the crack surfaces have been closed, and that closed energy of middle point is calculated repeatedly. A DCB (double cantilever beam) specimen was calculated and compared with other theoretical results, it is shown that a better coincidence is obtained. In addition the same results are also obtained for compact tension specimen, three point bend specimen and single edge cracked specimen. In comparison with theoretical results,the error can be limited within 1 per cent. This method can be extended to analyze the fracture of composite laminates with various delamination cracks.展开更多
A three-node triangular element fitted to numerical manifold method with continuous nodal stress, called Trig_3-CNS(NMM)element, was recently proposed for linear elastic continuous problems and linear elastic simple c...A three-node triangular element fitted to numerical manifold method with continuous nodal stress, called Trig_3-CNS(NMM)element, was recently proposed for linear elastic continuous problems and linear elastic simple crack problems. The Trig_3-CNS(NMM) element can be considered as a development of both the Trig_3-CNS element and the numerical manifold method(NMM).Inheriting all the advantages of Trig_3-CNS element, calculations using Trig_3-CNS(NMM) element can obtain higher accuracy than Trig_3 element without extra degrees of freedom(DOFs) and yield continuous nodal stress without stress smoothing. Inheriting all the advantages of NMM, Trig_3-CNS(NMM) element can conveniently treat crack problems without deploying conforming mathematical mesh. In this paper,complex problems such as a crucifix crack and a star-shaped crack with many branches are studied to exhibit the advantageous features of the Trig_3-CNS(NMM) element. Numerical results show that the Trig_3-CNS(NMM) element is prominent in modeling complex crack problems.展开更多
Classical plate theory has been used to find out interfacial stress intensity factors in composite laminates. By using a well-known relation between the crack-tip energy release rate and the complex stress intensity f...Classical plate theory has been used to find out interfacial stress intensity factors in composite laminates. By using a well-known relation between the crack-tip energy release rate and the complex stress intensity factor. a closed-form solution for complex. Stress intensity in terms of external loading and a mode mix parameter for fairly. general composite laminates is given. Then a procedure for determining this mode mix. parameter is presented. followed by numerical results for some laminates. Small scale contact condition is expressed in terms of external loading In particular, a symmetric property of interfacial toughness curye is proven. Finally. the accuracy of failure load predicled by elininating oscllation index is discussed. and an example is presented to show the validity and limitation of β=0 approximation.展开更多
Background: Wrinkles, pigmented spots, and roughness are representative parameters reflecting facial skin aging. Sulci cutis connecting to follicular orifices frequently form perifollicular cracks, which join together...Background: Wrinkles, pigmented spots, and roughness are representative parameters reflecting facial skin aging. Sulci cutis connecting to follicular orifices frequently form perifollicular cracks, which join together adjacent sulci. This follicle-sulcus-crack complex (FSCC) is exacerbated by dehydration. Purpose: Although dehydration is associated with facial skin aging, FSCC’s implications in facial skin aging remain unresolved. Method: We measured facial skin parameters in 1999 and 2010 in 108 Japanese women, and in 2006 and 2016 in 182 Chinese women. We addressed whether expansion of FSCC is associated with other skin aging parameters. We also examined whether skin moisturizer can reverse the expanded FSCC. Results: In both clinical studies, FSCC severity as well as wrinkles, spots, and roughness significantly deteriorated with age. Notably, FSCC significantly increased as early as in subjects in their 20s, whereas wrinkles, spots, and roughness became conspicuous in those in their 40s or older. Moreover, subjects with more severe FSCC in the initial measurement exhibited significantly worse wrinkles, spots, and roughness in the second measurement a decade later. Dehydration was significantly correlated with expanded FSCC. Furthermore, FSCC expansion was reversed after appropriate moisturization by daily application of Galactomyces ferment filtrate (GFF)-containing skincare product (SK-II Skin Power Cream) for 4 weeks in 37 women. Conclusion: The expanded FSCC is likely to be an early indicator of facial skin aging. Appropriate moisturization may reduce FSCC formation and decelerate facial skin aging.展开更多
Using the complex variable function method and the technique of the conformal mapping, the fracture problem of a semi-infinite crack in a piezoelectric strip is studied under the anti-plane shear stress and the in-pla...Using the complex variable function method and the technique of the conformal mapping, the fracture problem of a semi-infinite crack in a piezoelectric strip is studied under the anti-plane shear stress and the in-plane electric load. The analytic solutions of the field intensity factors and the mechanical strain energy release rate are presented under the assumption that the surface of the crack is electrically impermeable. When the height of the strip tends to infinity, the analytic solutions of an infinitely large piezoelectric solid with a semi-infinite crack are obtained. Moreover, the present results can be reduced to the well-known solutions for a purely elastic material in the absence of the electric loading. In addition, numerical examples are given to show the influences of the loaded crack length, the height of the strip, and the applied mechanical/electric loads on the mechanical strain energy release rate.展开更多
Using the complex variable function method and the conformal mapping technique, the fracture problem of two semi-infinite collinear cracks in a piezoelectric strip is studied under the anti-plane shear stress and the ...Using the complex variable function method and the conformal mapping technique, the fracture problem of two semi-infinite collinear cracks in a piezoelectric strip is studied under the anti-plane shear stress and the in-plane electric load on the partial crack surface. Analytic solutions of the field intensity factors and the mechanical strain energy release rate are derived under the assumption that the surfaces of the crack are electrically impermeable. The results can be reduced to the well-known solutions for a purely elastic material in the absence of an electric load. Moreover, when the distance between the two crack tips tends to infinity, analytic solutions of a semi-infinite crack in a piezoelectric strip can be obtained. Numerical examples are given to show the influence of the loaded crack length, the height of the strip, the distance between the two crack tips, and the applied mechanical/electric loads on the mechanical strain energy release rate. It is shown that the material is easier to fail when the distance between two crack tips becomes shorter, and the mechanical/electric loads have greater influence on the propagation of the left crack than those of the right one.展开更多
The existing analytical solutions are extended to obtain the stress fields and the stress intensity factors(SIFs) of two unequal aligned cracks emanating from an elliptical hole in an infinite isotropic plane. A confo...The existing analytical solutions are extended to obtain the stress fields and the stress intensity factors(SIFs) of two unequal aligned cracks emanating from an elliptical hole in an infinite isotropic plane. A conformal mapping is proposed and combined with the complex variable method. Due to some difficulties in the calculation of the stress function, the mapping function is approximated and simplified via the applications of the series expansion. To validate the obtained solution, several examples are analyzed with the proposed method, the finite element method, etc. In addition, the effects of the lengths of the cracks and the ratio of the semi-axes of the elliptical hole(a/b) on the SIFs are studied. The results show that the present analytical solution is applicable to the SIFs for small cracks.展开更多
Quantification of complicated surface morphology of soil crack is a prerequisite and key to soil crack study. This paper takes soil crack quads in Yuanmou arid-hot valley region as examples, selecting several morpholo...Quantification of complicated surface morphology of soil crack is a prerequisite and key to soil crack study. This paper takes soil crack quads in Yuanmou arid-hot valley region as examples, selecting several morphological indicators, and analyzes the soil crack＇s morphological features under various development degrees. By statistic analysis, three quantitative indicators for surface morphology are selected, namely soil crack area density, area weighted mean fractal dimension and connectivity index R, which can not only express the development intensity of soil cracks, but also effectively describe its morphological complexity and connectivity. The research results set a good base for the establishment of soil crack assessment system in Yuanmou arid-hot valley region.展开更多
Based on the natural characters of stratum, complicated geological mining conditions and the essence of mining rock mass destruction, the complexity of rock mass destruction caused by miningw as analyzed. The inner li...Based on the natural characters of stratum, complicated geological mining conditions and the essence of mining rock mass destruction, the complexity of rock mass destruction caused by miningw as analyzed. The inner link between rock mass destruction phenomena caused by mining and nonlinear science was revealed. There are numerous cracks in natural rock mass. The cracks’ distribution is irregular and is of statistical fractal structure. Self-organizational nonlinear evolution of the inner structure flaws leads to the rock mass destruction with external force. The evolution includes single fault’s fractal development, formation and evolution of fractal crack network and coordination of fractal crack network, etc. The law of fractal crack network’s evolution was introduced, at the same time, the coordination of fractal crack network was analyzed. Finally, based on coordination the principal equation of mining-caused subsidence of structural rock mass was established and its steady-state solution and unsteady-state solution were found.展开更多
The system of a wedge disclination dipole interacting with an internal crack was investigated. By using the complex variable method, the closed form solutions of complex potentials to this problem were presented. The ...The system of a wedge disclination dipole interacting with an internal crack was investigated. By using the complex variable method, the closed form solutions of complex potentials to this problem were presented. The analytic formulae of the physics variables, such as stress intensity factors at the tips of the crack produced by the wedge disclination dipole and the image force acting on disclination dipole center were obtained. The influence of the orientation, the dipole arm and the location of the disclination dipole on the stress intensity factors was discussed in detail. Furthermore, the equilibrium position of the wedge disclination dipole was also examined. It is shown that the shielding or antishielding effect of the wedge disclination to the stress intensity factors is significant when the disclination dipole moves to the crack tips.展开更多
The electroelastic interaction of a screw dislocation inside a circular inclusion with inteffacial cracks in piezoelectric composite materials under anti-plane shear and in-plane electric loads at infinity is investig...The electroelastic interaction of a screw dislocation inside a circular inclusion with inteffacial cracks in piezoelectric composite materials under anti-plane shear and in-plane electric loads at infinity is investigated. The general solution to this problem was obtained by means of Riemann-Schwarz＇ s symmetry principle integrated with analysis of singularities of corresponding complex potentials. As a typical example, closed form expressions of the complex potentials and electroelastic field components in the matrix and inhomogeneity regions were derived explicitly when the interface contains a single crack. The image force acting on the screw dislocation was calculated by using the generalized Peach-Koehler formula. The influence of interfacial crack geometry and piezoelectric material property combinations upon the image force was discussed in detail. The results show that interfacial crack has a significant perturbation effect on the image force and the equilibrium position of the screw dislocation. The presence of the interfacial crack can change the direction of the image force when the length of the crack goes up to a critical value. The obtained explicit solutions can be used as Green＇s functions to study the problem on the interaction between interfacial cracks and arbitrary shape crack inside the inclusion. The present solutions can lead to previously known results as the special case.展开更多
基金supported by the Young Scientist Project of National Key Research and Development Program of China(2021YFC2900600)National Natural Science Foundation of China(52074166)Shandong Province(ZR2021YQ38).
文摘Soft rocks, such as coal, are afected by sedimentary efects, and the surrounding rock mass of underground coal mines is generally soft and rich in joints and cracks. A clear and deep understanding of the relationship between crack geometric parameters and rock mechanics properties in cracked rock is greatly important to the design of engineering rock mass struc‑tures. In this study, computed tomography (CT) scanning was used to extract the internal crack network of coal specimens. Based on the crack size and dominant crack number, the parameters of crack area, volume, length, width, and angle were statistically analyzed by diferent sampling thresholds. In addition, the Pearson correlation coefcients between the crack parameters and uniaxial compression rock mechanics properties (uniaxial compressive strength UCS, elasticity modulus E) were calculated to quantitatively analyze the impact of each parameter. Furthermore, a method based on Pearson coefcients was used to grade the correlation between crack geometric parameters and rock mechanical properties to determine threshold values. The results indicated that the UCS and E of the specimens changed with the varied internal crack structures of the specimens, the crack parameters of area, volume, length and width all showed negative correlations with UCS and E, and the dominant crack played an important role both in weakening strength and stifness. The crack parameters of the angle are all positively correlated with the UCS and E. More crack statistics can signifcantly improve the correlation between the parameters of the crack angle and the rock mechanics properties, and the statistics of the geometric parameters of at least 16 cracks or the area larger than 5 mm2 are suggested for the analysis of complex cracked rock masses or physical reproduction using 3D printing. The results are validated and further analyzed with triaxial tests. The fndings of this study have important reference value for future research regarding the accurate and efcient selection of a few cracks with a signifcant infuence on the rock mechanical properties of surrounding rock mass structures in coal engineering.
文摘A new extrapolation approach was proposed to calculate the strain energy release rates of complex cracks. The point_by_point closed method was used to calculate the closed energy, thus the disadvantage of self_inconsistency in some published papers can be avoided. The disadvantage is that the closed energy is repeatedly calculated: when closed nodal number along radial direction is more than two, the displacement of nodes behind the crack tip that is multiplied by nodal forces, the closed energy has been calculated and the crack surfaces have been closed, and that closed energy of middle point is calculated repeatedly. A DCB (double cantilever beam) specimen was calculated and compared with other theoretical results, it is shown that a better coincidence is obtained. In addition the same results are also obtained for compact tension specimen, three point bend specimen and single edge cracked specimen. In comparison with theoretical results,the error can be limited within 1 per cent. This method can be extended to analyze the fracture of composite laminates with various delamination cracks.
基金the National Natural Science Foundation of China(Grant Nos 51609240,11572009&51538001)and the National Basic Research Program of China(Grant No 2014CB047100)
文摘A three-node triangular element fitted to numerical manifold method with continuous nodal stress, called Trig_3-CNS(NMM)element, was recently proposed for linear elastic continuous problems and linear elastic simple crack problems. The Trig_3-CNS(NMM) element can be considered as a development of both the Trig_3-CNS element and the numerical manifold method(NMM).Inheriting all the advantages of Trig_3-CNS element, calculations using Trig_3-CNS(NMM) element can obtain higher accuracy than Trig_3 element without extra degrees of freedom(DOFs) and yield continuous nodal stress without stress smoothing. Inheriting all the advantages of NMM, Trig_3-CNS(NMM) element can conveniently treat crack problems without deploying conforming mathematical mesh. In this paper,complex problems such as a crucifix crack and a star-shaped crack with many branches are studied to exhibit the advantageous features of the Trig_3-CNS(NMM) element. Numerical results show that the Trig_3-CNS(NMM) element is prominent in modeling complex crack problems.
文摘Classical plate theory has been used to find out interfacial stress intensity factors in composite laminates. By using a well-known relation between the crack-tip energy release rate and the complex stress intensity factor. a closed-form solution for complex. Stress intensity in terms of external loading and a mode mix parameter for fairly. general composite laminates is given. Then a procedure for determining this mode mix. parameter is presented. followed by numerical results for some laminates. Small scale contact condition is expressed in terms of external loading In particular, a symmetric property of interfacial toughness curye is proven. Finally. the accuracy of failure load predicled by elininating oscllation index is discussed. and an example is presented to show the validity and limitation of β=0 approximation.
文摘Background: Wrinkles, pigmented spots, and roughness are representative parameters reflecting facial skin aging. Sulci cutis connecting to follicular orifices frequently form perifollicular cracks, which join together adjacent sulci. This follicle-sulcus-crack complex (FSCC) is exacerbated by dehydration. Purpose: Although dehydration is associated with facial skin aging, FSCC’s implications in facial skin aging remain unresolved. Method: We measured facial skin parameters in 1999 and 2010 in 108 Japanese women, and in 2006 and 2016 in 182 Chinese women. We addressed whether expansion of FSCC is associated with other skin aging parameters. We also examined whether skin moisturizer can reverse the expanded FSCC. Results: In both clinical studies, FSCC severity as well as wrinkles, spots, and roughness significantly deteriorated with age. Notably, FSCC significantly increased as early as in subjects in their 20s, whereas wrinkles, spots, and roughness became conspicuous in those in their 40s or older. Moreover, subjects with more severe FSCC in the initial measurement exhibited significantly worse wrinkles, spots, and roughness in the second measurement a decade later. Dehydration was significantly correlated with expanded FSCC. Furthermore, FSCC expansion was reversed after appropriate moisturization by daily application of Galactomyces ferment filtrate (GFF)-containing skincare product (SK-II Skin Power Cream) for 4 weeks in 37 women. Conclusion: The expanded FSCC is likely to be an early indicator of facial skin aging. Appropriate moisturization may reduce FSCC formation and decelerate facial skin aging.
基金Project supported by the National Natural Science Foundation of China(Nos.10932001 and 11072015)the Scientific Research Key Program of Beijing Municipal Commission of Education (No.KZ201010005003)the Ph.D.Innovation Foundation of Beijing University of Aeronautics and Astronautics(No.300351)
文摘Using the complex variable function method and the technique of the conformal mapping, the fracture problem of a semi-infinite crack in a piezoelectric strip is studied under the anti-plane shear stress and the in-plane electric load. The analytic solutions of the field intensity factors and the mechanical strain energy release rate are presented under the assumption that the surface of the crack is electrically impermeable. When the height of the strip tends to infinity, the analytic solutions of an infinitely large piezoelectric solid with a semi-infinite crack are obtained. Moreover, the present results can be reduced to the well-known solutions for a purely elastic material in the absence of the electric loading. In addition, numerical examples are given to show the influences of the loaded crack length, the height of the strip, and the applied mechanical/electric loads on the mechanical strain energy release rate.
基金Project supported by the National Natural Science Foundation of China(Nos.10932001 and 11072015)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20101102110016)
文摘Using the complex variable function method and the conformal mapping technique, the fracture problem of two semi-infinite collinear cracks in a piezoelectric strip is studied under the anti-plane shear stress and the in-plane electric load on the partial crack surface. Analytic solutions of the field intensity factors and the mechanical strain energy release rate are derived under the assumption that the surfaces of the crack are electrically impermeable. The results can be reduced to the well-known solutions for a purely elastic material in the absence of an electric load. Moreover, when the distance between the two crack tips tends to infinity, analytic solutions of a semi-infinite crack in a piezoelectric strip can be obtained. Numerical examples are given to show the influence of the loaded crack length, the height of the strip, the distance between the two crack tips, and the applied mechanical/electric loads on the mechanical strain energy release rate. It is shown that the material is easier to fail when the distance between two crack tips becomes shorter, and the mechanical/electric loads have greater influence on the propagation of the left crack than those of the right one.
文摘The existing analytical solutions are extended to obtain the stress fields and the stress intensity factors(SIFs) of two unequal aligned cracks emanating from an elliptical hole in an infinite isotropic plane. A conformal mapping is proposed and combined with the complex variable method. Due to some difficulties in the calculation of the stress function, the mapping function is approximated and simplified via the applications of the series expansion. To validate the obtained solution, several examples are analyzed with the proposed method, the finite element method, etc. In addition, the effects of the lengths of the cracks and the ratio of the semi-axes of the elliptical hole(a/b) on the SIFs are studied. The results show that the present analytical solution is applicable to the SIFs for small cracks.
基金the National Natural Science Foundation of China (30470297)the National Key Technologies Research and Development Program in the Eleventh Five-Year Plan of China (2006BAC01A11)the Youth Foundation of Institute of Mountain Hazards and Environment of Chinese Academy of Sciences
文摘Quantification of complicated surface morphology of soil crack is a prerequisite and key to soil crack study. This paper takes soil crack quads in Yuanmou arid-hot valley region as examples, selecting several morphological indicators, and analyzes the soil crack＇s morphological features under various development degrees. By statistic analysis, three quantitative indicators for surface morphology are selected, namely soil crack area density, area weighted mean fractal dimension and connectivity index R, which can not only express the development intensity of soil cracks, but also effectively describe its morphological complexity and connectivity. The research results set a good base for the establishment of soil crack assessment system in Yuanmou arid-hot valley region.
基金Foundatinitem Project(50274044) supported by the National Natural Science Foundation of China .
文摘Based on the natural characters of stratum, complicated geological mining conditions and the essence of mining rock mass destruction, the complexity of rock mass destruction caused by miningw as analyzed. The inner link between rock mass destruction phenomena caused by mining and nonlinear science was revealed. There are numerous cracks in natural rock mass. The cracks’ distribution is irregular and is of statistical fractal structure. Self-organizational nonlinear evolution of the inner structure flaws leads to the rock mass destruction with external force. The evolution includes single fault’s fractal development, formation and evolution of fractal crack network and coordination of fractal crack network, etc. The law of fractal crack network’s evolution was introduced, at the same time, the coordination of fractal crack network was analyzed. Finally, based on coordination the principal equation of mining-caused subsidence of structural rock mass was established and its steady-state solution and unsteady-state solution were found.
基金Project supported by the National Natural Science Foundation of China (No. 10472030)
文摘The system of a wedge disclination dipole interacting with an internal crack was investigated. By using the complex variable method, the closed form solutions of complex potentials to this problem were presented. The analytic formulae of the physics variables, such as stress intensity factors at the tips of the crack produced by the wedge disclination dipole and the image force acting on disclination dipole center were obtained. The influence of the orientation, the dipole arm and the location of the disclination dipole on the stress intensity factors was discussed in detail. Furthermore, the equilibrium position of the wedge disclination dipole was also examined. It is shown that the shielding or antishielding effect of the wedge disclination to the stress intensity factors is significant when the disclination dipole moves to the crack tips.
文摘The electroelastic interaction of a screw dislocation inside a circular inclusion with inteffacial cracks in piezoelectric composite materials under anti-plane shear and in-plane electric loads at infinity is investigated. The general solution to this problem was obtained by means of Riemann-Schwarz＇ s symmetry principle integrated with analysis of singularities of corresponding complex potentials. As a typical example, closed form expressions of the complex potentials and electroelastic field components in the matrix and inhomogeneity regions were derived explicitly when the interface contains a single crack. The image force acting on the screw dislocation was calculated by using the generalized Peach-Koehler formula. The influence of interfacial crack geometry and piezoelectric material property combinations upon the image force was discussed in detail. The results show that interfacial crack has a significant perturbation effect on the image force and the equilibrium position of the screw dislocation. The presence of the interfacial crack can change the direction of the image force when the length of the crack goes up to a critical value. The obtained explicit solutions can be used as Green＇s functions to study the problem on the interaction between interfacial cracks and arbitrary shape crack inside the inclusion. The present solutions can lead to previously known results as the special case.
