The paper presents constitutive theories for non-classical thermoviscoelastic fluids with dissipation and memory using a thermodynamic framework based on entirety of velocity gradient tensor. Thus, the conservation an...The paper presents constitutive theories for non-classical thermoviscoelastic fluids with dissipation and memory using a thermodynamic framework based on entirety of velocity gradient tensor. Thus, the conservation and the balance laws used in this work incorporate symmetric as well as antisymmetric part of the velocity gradient tensor. The constitutive theories derived here hold in coand contra-variant bases as well as in Jaumann rates and are derived using convected time derivatives of Green’s and Almansi strain tensors as well as the Cauchy stress tensor and its convected time derivatives in appropriate bases. The constitutive theories are presented in the absence as well as in the presence of the balance of moment of moments as balance law. It is shown that the dissipation mechanism and the fading memory in such fluids are due to stress rates as well as moment rates and their conjugates. The material coefficients are derived for the general forms of the constitutive theories based on integrity. Simplified linear (or quasi-linear) forms of the constitutive theories are also presented. Maxwell, Oldroyd-B and Giesekus constitutive models for non-classical thermoviscoelastic fluids are derived and are compared with those derived based on classical continuum mechanics. Both, compressible and incompressible thermoviscoelastic fluids are considered.展开更多
In recent papers, Surana et al. presented internal polar non-classical Continuum theory in which velocity gradient tensor in its entirety was incorporated in the conservation and balance laws. Thus, this theory incorp...In recent papers, Surana et al. presented internal polar non-classical Continuum theory in which velocity gradient tensor in its entirety was incorporated in the conservation and balance laws. Thus, this theory incorporated symmetric part of the velocity gradient tensor (as done in classical theories) as well as skew symmetric part representing varying internal rotation rates between material points which when resisted by deforming continua result in dissipation (and/or storage) of mechanical work. This physics referred as internal polar physics is neglected in classical continuum theories but can be quite significant for some materials. In another recent paper Surana et al. presented ordered rate constitutive theories for internal polar non-classical fluent continua without memory derived using deviatoric Cauchy stress tensor and conjugate strain rate tensors of up to orders n and Cauchy moment tensor and its conjugate symmetric part of the first convected derivative of the rotation gradient tensor. In this constitutive theory higher order convected derivatives of the symmetric part of the rotation gradient tensor are assumed not to contribute to dissipation. Secondly, the skew symmetric part of the velocity gradient tensor is used as rotation rates to determine rate of rotation gradient tensor. This is an approximation to true convected time derivatives of the rotation gradient tensor. The resulting constitutive theory: (1) is incomplete as it neglects the second and higher order convected time derivatives of the symmetric part of the rotation gradient tensor;(2) first convected derivative of the symmetric part of the rotation gradient tensor as used by Surana et al. is only approximate;(3) has inconsistent treatment of dissipation due to Cauchy moment tensor when compared with the dissipation mechanism due to deviatoric part of symmetric Cauchy stress tensor in which convected time derivatives of up to order n are considered in the theory. The purpose of this paper is to present ordered rate constitutive theories for deviatoric Cauchy strain tensor, moment tensor and heat vector for thermofluids without memory in which convected time derivatives of strain tensors up to order n are conjugate with the Cauchy stress tensor and the convected time derivatives of the symmetric part of the rotation gradient tensor up to orders 1n are conjugate with the moment tensor. Conservation and balance laws are used to determine the choice of dependent variables in the constitutive theories: Helmholtz free energy density Φ, entropy density η, Cauchy stress tensor, moment tensor and heat vector. Stress tensor is decomposed into symmetric and skew symmetric parts and the symmetric part of the stress tensor and the moment tensor are further decomposed into equilibrium and deviatoric tensors. It is established through conjugate pairs in entropy inequality that the constitutive theories only need to be derived for symmetric stress tensor, moment tensor and heat vector. Density in the current configuration, convected time derivatives of the strain tensor up to order n, convected time derivatives of the symmetric part of the rotation gradient tensor up to orders 1n, temperature gradient tensor and temperature are considered as argument tensors of all dependent variables in the constitutive theories based on entropy inequality and principle of equipresence. The constitutive theories are derived in contravariant and covariant bases as well as using Jaumann rates. The nth and 1nth order rate constitutive theories for internal polar non-classical thermofluids without memory are specialized for n = 1 and 1n = 1 to demonstrate fundamental differences in the constitutive theories presented here and those used presently for classical thermofluids without memory and those published by Surana et al. for internal polar non-classical incompressible thermofluids.展开更多
The linear analysis of the Rayleigh-Taylor instability in metal material is extended from the perfect plastic constitutive model to the Johnson-Cook and Steinberg-Guinan constitutive model, and from the constant loadi...The linear analysis of the Rayleigh-Taylor instability in metal material is extended from the perfect plastic constitutive model to the Johnson-Cook and Steinberg-Guinan constitutive model, and from the constant loading to a time-dependent loading. The analysis is applied to two Rayleigh-Taylor instability experiments in aluminum and vanadium with peak pressures of 20 GPa and 90 GPa, and strain rates of 6 × 106 s−1 and 3 × 107 s−1 respectively. When the time-dependent loading and the Steinberg-Guinan constitutive model are used in the linear analysis, the analytic results are in close agreement with experiments quantitatively, which indicates that the method in this paper is applicable to the Rayleigh-Taylor instability in aluminum and vanadium metal materials under high pressure and high strain rate. From these linear analyses, we find that the constitutive models and the loading process are of crucial importance in the linear analysis of the Rayleigh-Taylor instability in metal material, and a better understanding of the Rayleigh-Taylor instability in metals is gained. These results will serve as important references for evolving high-pressure, high-strain-rate experiments and numerical simulations.展开更多
Objective:To explore the effect of Guipi Decoction Combined with non steroidal anti-inflammatory drugs on sleep time of elderly patients with traumatic pain and Qi deficiency constitution during hospitalization.Method...Objective:To explore the effect of Guipi Decoction Combined with non steroidal anti-inflammatory drugs on sleep time of elderly patients with traumatic pain and Qi deficiency constitution during hospitalization.Methods:A total of 52 elderly patients hospitalized in the orthopedic(trauma)ward of the Second Affiliated Hospital of Zhejiang Chinese Medical University from November 2020 to may 2021 were randomly divided into control group and treatment group.Patients in the control group were treated with loxoprofen sodium tablets immediately after admission,and placebo was added to loxoprofen sodium tablets from the second day of admission;The patients in the treatment group were treated with loxoprofen sodium tablets after admission.Guipi Decoction was added on the basis of loxoprofen sodium tablets from the second day of admission.Before and after admission,all patients used the TCM constitution classification judgment table to evaluate the score of qi deficiency and VAS;From the first day to the fourth day after admission,the bracelet was worn to monitor the sleep time(total sleep time,deep sleep time,light sleep time and awakening times)every night.The patients were scored by VAS after taking drugs every morning.Results:Finally 25 patients in the control group and 24 patients in the treatment group completed the experiment.There was no significant difference in gender,age,fracture location,chronic medical history VAS score and TCM Qi deficiency constitution score,between two groups at admission(P>0.05).At the time of discharge,the score of qi deficiency constitution in the treatment group was 33.724±12.634;The TCM Qi deficiency constitution score of the control group was 42.25±15.912,and there was significant difference between the two groups(P<0.05);and there was significant difference in VAS score between the two groups at discharge(P<0.05).There were significant differences in total sleep time,light sleep time,deep sleep time and night awakening times between the two groups on the second,third and fourth day of admission(P<0.05).Conclusion:1.Guipi Decoction can significantly improve the sleep time of patients with Qi deficiency acute traumatic pain.2.Guipi Decoction can not only improve the constitution of patients with Qi deficiency bias,but also improve the VAS score at discharge.展开更多
Recent years have seen increasing academic interest in exploring the correlation between temperature and crime.However,it is uncertain whether similar long-term trends or seasonality(rather than causal effect)of tempe...Recent years have seen increasing academic interest in exploring the correlation between temperature and crime.However,it is uncertain whether similar long-term trends or seasonality(rather than causal effect)of temper-ature and crime is the major reason for the observed correlation between them.To explore whether there is still a correlation between temperature and crime when long-term trends and seasonal cycles are filtered out,we use the Kalman filter to decompose the time series of temperature and crimes,and then the fast Fourier transform is used to calculate the exact circle of their seasonality separately.Based on that,the box-plot method and linear regression are used to explore the correlation between temperature residuals and crime residuals.The results show that more than half of the crime types have similar seasonal cycles(approximately 1 year)to that of temperature.Moreover,the daily residual analyses show that temperature residuals have a positive correlation with assault and robbery residuals in all cities,whose average slopes are more than 0.1.The other four types of crimes vary greatly from case to case.The temperature residuals show a weak correlation with the residuals of some crime types.展开更多
文摘The paper presents constitutive theories for non-classical thermoviscoelastic fluids with dissipation and memory using a thermodynamic framework based on entirety of velocity gradient tensor. Thus, the conservation and the balance laws used in this work incorporate symmetric as well as antisymmetric part of the velocity gradient tensor. The constitutive theories derived here hold in coand contra-variant bases as well as in Jaumann rates and are derived using convected time derivatives of Green’s and Almansi strain tensors as well as the Cauchy stress tensor and its convected time derivatives in appropriate bases. The constitutive theories are presented in the absence as well as in the presence of the balance of moment of moments as balance law. It is shown that the dissipation mechanism and the fading memory in such fluids are due to stress rates as well as moment rates and their conjugates. The material coefficients are derived for the general forms of the constitutive theories based on integrity. Simplified linear (or quasi-linear) forms of the constitutive theories are also presented. Maxwell, Oldroyd-B and Giesekus constitutive models for non-classical thermoviscoelastic fluids are derived and are compared with those derived based on classical continuum mechanics. Both, compressible and incompressible thermoviscoelastic fluids are considered.
文摘In recent papers, Surana et al. presented internal polar non-classical Continuum theory in which velocity gradient tensor in its entirety was incorporated in the conservation and balance laws. Thus, this theory incorporated symmetric part of the velocity gradient tensor (as done in classical theories) as well as skew symmetric part representing varying internal rotation rates between material points which when resisted by deforming continua result in dissipation (and/or storage) of mechanical work. This physics referred as internal polar physics is neglected in classical continuum theories but can be quite significant for some materials. In another recent paper Surana et al. presented ordered rate constitutive theories for internal polar non-classical fluent continua without memory derived using deviatoric Cauchy stress tensor and conjugate strain rate tensors of up to orders n and Cauchy moment tensor and its conjugate symmetric part of the first convected derivative of the rotation gradient tensor. In this constitutive theory higher order convected derivatives of the symmetric part of the rotation gradient tensor are assumed not to contribute to dissipation. Secondly, the skew symmetric part of the velocity gradient tensor is used as rotation rates to determine rate of rotation gradient tensor. This is an approximation to true convected time derivatives of the rotation gradient tensor. The resulting constitutive theory: (1) is incomplete as it neglects the second and higher order convected time derivatives of the symmetric part of the rotation gradient tensor;(2) first convected derivative of the symmetric part of the rotation gradient tensor as used by Surana et al. is only approximate;(3) has inconsistent treatment of dissipation due to Cauchy moment tensor when compared with the dissipation mechanism due to deviatoric part of symmetric Cauchy stress tensor in which convected time derivatives of up to order n are considered in the theory. The purpose of this paper is to present ordered rate constitutive theories for deviatoric Cauchy strain tensor, moment tensor and heat vector for thermofluids without memory in which convected time derivatives of strain tensors up to order n are conjugate with the Cauchy stress tensor and the convected time derivatives of the symmetric part of the rotation gradient tensor up to orders 1n are conjugate with the moment tensor. Conservation and balance laws are used to determine the choice of dependent variables in the constitutive theories: Helmholtz free energy density Φ, entropy density η, Cauchy stress tensor, moment tensor and heat vector. Stress tensor is decomposed into symmetric and skew symmetric parts and the symmetric part of the stress tensor and the moment tensor are further decomposed into equilibrium and deviatoric tensors. It is established through conjugate pairs in entropy inequality that the constitutive theories only need to be derived for symmetric stress tensor, moment tensor and heat vector. Density in the current configuration, convected time derivatives of the strain tensor up to order n, convected time derivatives of the symmetric part of the rotation gradient tensor up to orders 1n, temperature gradient tensor and temperature are considered as argument tensors of all dependent variables in the constitutive theories based on entropy inequality and principle of equipresence. The constitutive theories are derived in contravariant and covariant bases as well as using Jaumann rates. The nth and 1nth order rate constitutive theories for internal polar non-classical thermofluids without memory are specialized for n = 1 and 1n = 1 to demonstrate fundamental differences in the constitutive theories presented here and those used presently for classical thermofluids without memory and those published by Surana et al. for internal polar non-classical incompressible thermofluids.
文摘The linear analysis of the Rayleigh-Taylor instability in metal material is extended from the perfect plastic constitutive model to the Johnson-Cook and Steinberg-Guinan constitutive model, and from the constant loading to a time-dependent loading. The analysis is applied to two Rayleigh-Taylor instability experiments in aluminum and vanadium with peak pressures of 20 GPa and 90 GPa, and strain rates of 6 × 106 s−1 and 3 × 107 s−1 respectively. When the time-dependent loading and the Steinberg-Guinan constitutive model are used in the linear analysis, the analytic results are in close agreement with experiments quantitatively, which indicates that the method in this paper is applicable to the Rayleigh-Taylor instability in aluminum and vanadium metal materials under high pressure and high strain rate. From these linear analyses, we find that the constitutive models and the loading process are of crucial importance in the linear analysis of the Rayleigh-Taylor instability in metal material, and a better understanding of the Rayleigh-Taylor instability in metals is gained. These results will serve as important references for evolving high-pressure, high-strain-rate experiments and numerical simulations.
基金general scientific research project of Zhejiang Provincial Department of education in 2020,Project No.:Y202044448。
文摘Objective:To explore the effect of Guipi Decoction Combined with non steroidal anti-inflammatory drugs on sleep time of elderly patients with traumatic pain and Qi deficiency constitution during hospitalization.Methods:A total of 52 elderly patients hospitalized in the orthopedic(trauma)ward of the Second Affiliated Hospital of Zhejiang Chinese Medical University from November 2020 to may 2021 were randomly divided into control group and treatment group.Patients in the control group were treated with loxoprofen sodium tablets immediately after admission,and placebo was added to loxoprofen sodium tablets from the second day of admission;The patients in the treatment group were treated with loxoprofen sodium tablets after admission.Guipi Decoction was added on the basis of loxoprofen sodium tablets from the second day of admission.Before and after admission,all patients used the TCM constitution classification judgment table to evaluate the score of qi deficiency and VAS;From the first day to the fourth day after admission,the bracelet was worn to monitor the sleep time(total sleep time,deep sleep time,light sleep time and awakening times)every night.The patients were scored by VAS after taking drugs every morning.Results:Finally 25 patients in the control group and 24 patients in the treatment group completed the experiment.There was no significant difference in gender,age,fracture location,chronic medical history VAS score and TCM Qi deficiency constitution score,between two groups at admission(P>0.05).At the time of discharge,the score of qi deficiency constitution in the treatment group was 33.724±12.634;The TCM Qi deficiency constitution score of the control group was 42.25±15.912,and there was significant difference between the two groups(P<0.05);and there was significant difference in VAS score between the two groups at discharge(P<0.05).There were significant differences in total sleep time,light sleep time,deep sleep time and night awakening times between the two groups on the second,third and fourth day of admission(P<0.05).Conclusion:1.Guipi Decoction can significantly improve the sleep time of patients with Qi deficiency acute traumatic pain.2.Guipi Decoction can not only improve the constitution of patients with Qi deficiency bias,but also improve the VAS score at discharge.
基金support for this study by the National Natural Science Foundation of China(Grant No.72174203,No.41971367).
文摘Recent years have seen increasing academic interest in exploring the correlation between temperature and crime.However,it is uncertain whether similar long-term trends or seasonality(rather than causal effect)of temper-ature and crime is the major reason for the observed correlation between them.To explore whether there is still a correlation between temperature and crime when long-term trends and seasonal cycles are filtered out,we use the Kalman filter to decompose the time series of temperature and crimes,and then the fast Fourier transform is used to calculate the exact circle of their seasonality separately.Based on that,the box-plot method and linear regression are used to explore the correlation between temperature residuals and crime residuals.The results show that more than half of the crime types have similar seasonal cycles(approximately 1 year)to that of temperature.Moreover,the daily residual analyses show that temperature residuals have a positive correlation with assault and robbery residuals in all cities,whose average slopes are more than 0.1.The other four types of crimes vary greatly from case to case.The temperature residuals show a weak correlation with the residuals of some crime types.
