A recent review publication presented an extensive and comprehensive assessment of the phenomenological relations of Poisson’s ratios (PRs) to the behavior and responses of contemporary materials under specific loadi...A recent review publication presented an extensive and comprehensive assessment of the phenomenological relations of Poisson’s ratios (PRs) to the behavior and responses of contemporary materials under specific loading conditions. The present review and analysis paper is intended as a theoretical mechanics complement covering mathematical and physical modeling of a single original elastic and of six time and process (i.e. path and stress) dependent viscoelastic PR definitions as well as a seventh special path independent one. The implications and consequences of such models on material characterization are analyzed and summarized. Indeed, PRs based on experimentally obtained 2-D strains under distinct creep and/or relaxation processes exhibit radically different time responses for identical material specimen. These results confirm the PR’s implicit path dependence in addition to their separate intrinsic time reliance. Such non-uniqueness of viscoelastic PRs renders them unsuitable as universal material descriptors. Analytical formulations and experimental measurements also examine the physical impossibility of instantaneously achieving time independent loads or strains or their rates thus making certain PR definitions based on constant state variables, while mathematically valid, physically unrealistic and unachievable. A newly developed theoretical/experimental protocol for the determination of the time when loading patterns reach stead-state conditions based on strain accelerations demonstrates the capability to measure this time from experimental data. Due to the process dependent PRs, i.e. stress and stress history paths, the non-existence of a unique viscoelastic PR and of a universal elastic-viscoelastic correspondence principle or analogy (EVCP) in terms of PRs is demonstrated. Additionally and independently, the required double convolution integral construction of linear viscoelastic constitutive relations with the inclusion of PRs is cumbersome analytically and computationally needlessly highly CPU intensive. Furthermore, there is no theoretical fundamental hint as to what loading path is required to produce a unique universal viscoelastic PR definition necessary for formulating a PR based constitutive relation or an EVCP protocol. The analysis associated with an additional Class VII viscoelastic PR establishes it as a universal representation which is loading path and strain independent while still remaining time dependent. This Class PR can be the one used if it is desired to express constitutive relations in terms of PRs, subject to the caveat applying to all PR Classes regarding the CPU intensiveness in the time space due to triple product and double convolution integral constitutive relations. However, the use PRs is unnecessary since any set of material behavior can be uniquely and completely defined in terms of only moduli and/or compliances. The mathematical model of instantaneous initial loading paths, based on Heavi-side functions, is examined in detail and shown to lead to infinite velocities and accelerations. Additionally, even if non-instantaneous gradual loading functions are employed the resulting PRs are still load and load history dependent. Consequently, they represent specialized PR responses applicable and limited to those particular load and history combinations. Although the analyses contained herein are generalized to non-homogeneous linear viscoelastic materials, the main focus is on PR time and process dependence. The non-homogeneous material results and conclusions presented herein apply equally to homogeneous viscoelasticity and per se do not influence the results or conclusions of the analytical development regarding viscoelastic PRs. In short, these PR analyses apply to all linear viscoelastic material characterization.展开更多
Based on the teleseismic waveform data recorded by 82 permanent broadband stations in Guangdong Province and its adjacent areas including Fujian, Jiangxi, Hunan, Guangxi, Hainan and Taiwan, we calculate body wave rece...Based on the teleseismic waveform data recorded by 82 permanent broadband stations in Guangdong Province and its adjacent areas including Fujian, Jiangxi, Hunan, Guangxi, Hainan and Taiwan, we calculate body wave receiver functions under all stations, and obtain the crustal thickness and average Poisson＇s ratio beneath all stations by the H-K stacking-search method of receiver function. The results show that the crustal thickness with an average thickness of 29. 5km in Guangdong Province and its adjacent areas ranges between 26. 8km and 33. 6kin and gradually thins from northwest to southeast. The crustal thickness in the Zhujiang Delta, western Guangdong, Nanning and Nan＇ao areas is relatively thinner and ranges between 25. 0km and 28. 0km. The minimum crustal thickness is about 26km beneath Wengtian, Hainan and the Zhanjiang zone and Shangchuan Island in Guangdong. The crustal thickness in the zones of Mingxi, Fujian and Yongzhou, Hunan is thicker and varies between 31.0km and 34.0km. The distribution of Poisson＇s ratio in our study region ranges between 0.20 and 0. 29. Poisson＇s ratios in Southeast Hainan, the coastal areas of East Guangdong and West Fujian and the South Jiangxi have distinctly higher values than in others. It suggests that the various geothermal fields located in these areas have high heat flow values. The distribution of crustal thickness and Poisson＇s ratio has an obvious block feature and may be related to the distribution of faults and historical earthquakes.展开更多
This paper presents the changes of crust thickness and Poisson＇s ratios distribution in the Binchuan region, where the first air-gun transmitting station and it＇s a small dense array were deployed. From September 20...This paper presents the changes of crust thickness and Poisson＇s ratios distribution in the Binchuan region, where the first air-gun transmitting station and it＇s a small dense array were deployed. From September 2011 to January 2014, more than 239 teleseismic events of M≥ 6.0 were recorded in 16 stations in the Binchuan region. Their P-wave receiver functions were analyzed respectively. The high spatial resolution result shows that the average crust thickness of Binchuan region is 45.3km, it follows the rule of ＂deeper in the north and east part, shallower in the south and west part. ＂ The deepest region is in Xiaoyindian Station; the crust thickness is 47.9km; the shallowest region is in Paiying Station, it has the thickness of 42. lkm. It shows that the deeper Moho surface nearby the Chenghai fault and shallower nearby the Honghe fault; the isoline distribution of thickness changes greatly nearby the Chenghai fault and slowly nearby the Honghe fault. From the distribution of Poisson＇s ratios, it is unevenly in the study area with a great difference from the north part to the south part, which shows a characteristic of ＂lower in the north, higher in the south＂. The Poisson＇s ratio nearby the Honghe fault is medium too high （ 0. 26 ≤ σ≤0. 29 ） ; lower nearby the Chenghai fault （ ≤0. 26）. This paper concludes the possible reason of different characteristic between Poisson＇s ratio and crust thickness is thicker in the upper crust in the Binchuan region.展开更多
The anisotropic continuum stored energy density (ACSED) functional is applied for accurate constitutive modeling of biological tissues and finite element implementation without the isochoric—volumetric split, the ani...The anisotropic continuum stored energy density (ACSED) functional is applied for accurate constitutive modeling of biological tissues and finite element implementation without the isochoric—volumetric split, the anisotropic—isotropic split, or the anisotropic invariant split. Related stress and elasticity tensors in the reference and current configurations are worked out. A new kinematic model is derived based on the tangent Poisson’s ratio as a cubic polynomial function of stretch. The ACSED model, along with the kinematic model, accurately fits uniaxial extension test data for compressible human skin, bovine articular cartilage, and human aorta samples.展开更多
A total of 1939 receiver functions were obtained from 732 teleseismic events （M〉5.0） recorded at 21 broadband portable seis- mic stations on the Tengchong, Baoshan and Simao blocks and Yangtze platform. These stati...A total of 1939 receiver functions were obtained from 732 teleseismic events （M〉5.0） recorded at 21 broadband portable seis- mic stations on the Tengchong, Baoshan and Simao blocks and Yangtze platform. These stations were installed by the Institute of Crustal Dynamics, China Earthquake Administration during 2010 and 2011. Using the H-x stacking and searching method, crustal thickness and velocity ratio beneath the stations are obtained. Results show that crustal thickness and Poisson＇s ratio in- ferred from the velocity ratio clearly vary, and they illustrate block features in deep structures. Except for the Tengchong block crustal thickness increases from south to north along the same block and from west to east across different blocks. In the Yangtze platform, Poisson＇s ratio and crustal thickness show a consistent and significant increasing trend from south to north, possibly indicating that crustal thickening is caused mainly by lower crustal variations. In contrast, Poisson＇s ratio has no sig- nificant change within the Baoshan and Simao blocks. Such differences demonstrate that the Jinshajiang-Red River fault is a southern boundary of the South China block. The H-κ results inferred from three portable stations on the Tengchong block show high Poisson＇s ratios, but they vary clearly with back-azimuth, implying the existence of strong anisotropy in the crustal medium beneath the stations.展开更多
文摘A recent review publication presented an extensive and comprehensive assessment of the phenomenological relations of Poisson’s ratios (PRs) to the behavior and responses of contemporary materials under specific loading conditions. The present review and analysis paper is intended as a theoretical mechanics complement covering mathematical and physical modeling of a single original elastic and of six time and process (i.e. path and stress) dependent viscoelastic PR definitions as well as a seventh special path independent one. The implications and consequences of such models on material characterization are analyzed and summarized. Indeed, PRs based on experimentally obtained 2-D strains under distinct creep and/or relaxation processes exhibit radically different time responses for identical material specimen. These results confirm the PR’s implicit path dependence in addition to their separate intrinsic time reliance. Such non-uniqueness of viscoelastic PRs renders them unsuitable as universal material descriptors. Analytical formulations and experimental measurements also examine the physical impossibility of instantaneously achieving time independent loads or strains or their rates thus making certain PR definitions based on constant state variables, while mathematically valid, physically unrealistic and unachievable. A newly developed theoretical/experimental protocol for the determination of the time when loading patterns reach stead-state conditions based on strain accelerations demonstrates the capability to measure this time from experimental data. Due to the process dependent PRs, i.e. stress and stress history paths, the non-existence of a unique viscoelastic PR and of a universal elastic-viscoelastic correspondence principle or analogy (EVCP) in terms of PRs is demonstrated. Additionally and independently, the required double convolution integral construction of linear viscoelastic constitutive relations with the inclusion of PRs is cumbersome analytically and computationally needlessly highly CPU intensive. Furthermore, there is no theoretical fundamental hint as to what loading path is required to produce a unique universal viscoelastic PR definition necessary for formulating a PR based constitutive relation or an EVCP protocol. The analysis associated with an additional Class VII viscoelastic PR establishes it as a universal representation which is loading path and strain independent while still remaining time dependent. This Class PR can be the one used if it is desired to express constitutive relations in terms of PRs, subject to the caveat applying to all PR Classes regarding the CPU intensiveness in the time space due to triple product and double convolution integral constitutive relations. However, the use PRs is unnecessary since any set of material behavior can be uniquely and completely defined in terms of only moduli and/or compliances. The mathematical model of instantaneous initial loading paths, based on Heavi-side functions, is examined in detail and shown to lead to infinite velocities and accelerations. Additionally, even if non-instantaneous gradual loading functions are employed the resulting PRs are still load and load history dependent. Consequently, they represent specialized PR responses applicable and limited to those particular load and history combinations. Although the analyses contained herein are generalized to non-homogeneous linear viscoelastic materials, the main focus is on PR time and process dependence. The non-homogeneous material results and conclusions presented herein apply equally to homogeneous viscoelasticity and per se do not influence the results or conclusions of the analytical development regarding viscoelastic PRs. In short, these PR analyses apply to all linear viscoelastic material characterization.
基金sponsored by the Science and Technology Program of Guangdong Province(20090308)
文摘Based on the teleseismic waveform data recorded by 82 permanent broadband stations in Guangdong Province and its adjacent areas including Fujian, Jiangxi, Hunan, Guangxi, Hainan and Taiwan, we calculate body wave receiver functions under all stations, and obtain the crustal thickness and average Poisson＇s ratio beneath all stations by the H-K stacking-search method of receiver function. The results show that the crustal thickness with an average thickness of 29. 5km in Guangdong Province and its adjacent areas ranges between 26. 8km and 33. 6kin and gradually thins from northwest to southeast. The crustal thickness in the Zhujiang Delta, western Guangdong, Nanning and Nan＇ao areas is relatively thinner and ranges between 25. 0km and 28. 0km. The minimum crustal thickness is about 26km beneath Wengtian, Hainan and the Zhanjiang zone and Shangchuan Island in Guangdong. The crustal thickness in the zones of Mingxi, Fujian and Yongzhou, Hunan is thicker and varies between 31.0km and 34.0km. The distribution of Poisson＇s ratio in our study region ranges between 0.20 and 0. 29. Poisson＇s ratios in Southeast Hainan, the coastal areas of East Guangdong and West Fujian and the South Jiangxi have distinctly higher values than in others. It suggests that the various geothermal fields located in these areas have high heat flow values. The distribution of crustal thickness and Poisson＇s ratio has an obvious block feature and may be related to the distribution of faults and historical earthquakes.
基金sponsored by the Special Science and Technology Program of Earthquake Administration of Yunnan Province (KJZX02)Academician Chen Yong Workstation Project of Earthquake Administration of Yunnan Province
文摘This paper presents the changes of crust thickness and Poisson＇s ratios distribution in the Binchuan region, where the first air-gun transmitting station and it＇s a small dense array were deployed. From September 2011 to January 2014, more than 239 teleseismic events of M≥ 6.0 were recorded in 16 stations in the Binchuan region. Their P-wave receiver functions were analyzed respectively. The high spatial resolution result shows that the average crust thickness of Binchuan region is 45.3km, it follows the rule of ＂deeper in the north and east part, shallower in the south and west part. ＂ The deepest region is in Xiaoyindian Station; the crust thickness is 47.9km; the shallowest region is in Paiying Station, it has the thickness of 42. lkm. It shows that the deeper Moho surface nearby the Chenghai fault and shallower nearby the Honghe fault; the isoline distribution of thickness changes greatly nearby the Chenghai fault and slowly nearby the Honghe fault. From the distribution of Poisson＇s ratios, it is unevenly in the study area with a great difference from the north part to the south part, which shows a characteristic of ＂lower in the north, higher in the south＂. The Poisson＇s ratio nearby the Honghe fault is medium too high （ 0. 26 ≤ σ≤0. 29 ） ; lower nearby the Chenghai fault （ ≤0. 26）. This paper concludes the possible reason of different characteristic between Poisson＇s ratio and crust thickness is thicker in the upper crust in the Binchuan region.
文摘The anisotropic continuum stored energy density (ACSED) functional is applied for accurate constitutive modeling of biological tissues and finite element implementation without the isochoric—volumetric split, the anisotropic—isotropic split, or the anisotropic invariant split. Related stress and elasticity tensors in the reference and current configurations are worked out. A new kinematic model is derived based on the tangent Poisson’s ratio as a cubic polynomial function of stretch. The ACSED model, along with the kinematic model, accurately fits uniaxial extension test data for compressible human skin, bovine articular cartilage, and human aorta samples.
基金supported by the National Natural Science Foundation of China(Grant No. 40974021)Basic Science and Research Special Project(Grant No. ZDJ2012-19)
文摘A total of 1939 receiver functions were obtained from 732 teleseismic events （M〉5.0） recorded at 21 broadband portable seis- mic stations on the Tengchong, Baoshan and Simao blocks and Yangtze platform. These stations were installed by the Institute of Crustal Dynamics, China Earthquake Administration during 2010 and 2011. Using the H-x stacking and searching method, crustal thickness and velocity ratio beneath the stations are obtained. Results show that crustal thickness and Poisson＇s ratio in- ferred from the velocity ratio clearly vary, and they illustrate block features in deep structures. Except for the Tengchong block crustal thickness increases from south to north along the same block and from west to east across different blocks. In the Yangtze platform, Poisson＇s ratio and crustal thickness show a consistent and significant increasing trend from south to north, possibly indicating that crustal thickening is caused mainly by lower crustal variations. In contrast, Poisson＇s ratio has no sig- nificant change within the Baoshan and Simao blocks. Such differences demonstrate that the Jinshajiang-Red River fault is a southern boundary of the South China block. The H-κ results inferred from three portable stations on the Tengchong block show high Poisson＇s ratios, but they vary clearly with back-azimuth, implying the existence of strong anisotropy in the crustal medium beneath the stations.
