Both the complex geometrical morphology of rough-walled rock fractures and the nonlinearity of fluid flow contribute to resistance in fluid flow through rock fractures.The interactions of the shear-flow process furthe...Both the complex geometrical morphology of rough-walled rock fractures and the nonlinearity of fluid flow contribute to resistance in fluid flow through rock fractures.The interactions of the shear-flow process further complicate the characterisation of flow behaviours in rock fractures.In this study,an improved friction factor model involving both the effects of viscous and inertial forces is presented based on the Forchheimer equation.The model incorporates two key variables,i.e.Reynolds number and relative roughness,which reflect the effects of flow regimes and fracture roughness,respectively.The changes in geometrical parameters induced by shearing are considered,with the peak asperity height predicted through a correlation with post-peak roughness degradation.The hydraulic aperture during shearing is estimated using a suggested equation that accounts for the mobilised contact area ratio and variable aperture distribution.The parametric sensitivity analysis reveals that shear-induced changes in fracture geometry enhance the flow nonlinearity in rock fractures.The model performs well in predicting the friction factor based on two validation criteria.Then,the proposed friction factor model is incorporated into the three-dimensional distinct element code(3DEC)in the form of the Darcy-Weisbach equation.Coupled with the numerically implemented mechanical model and hydraulic aperture prediction model,numerical simulations of coupled shear-flow processes in single rock fractures are conducted.The simulation outcomes are validated through comparison with the experimental results,showing acceptable agreement and demonstrating that the numerical model is capable of accurately evaluating the hydro-mechanical coupling behaviour during the shearing of rock fractures.展开更多
The authors make an endeavor to explain why a new hybrid wave model is here proposed when several such models have already been in operation and the so- called third generation wave modej is proving attractive. This p...The authors make an endeavor to explain why a new hybrid wave model is here proposed when several such models have already been in operation and the so- called third generation wave modej is proving attractive. This part of the paper is devoted to the wind wave model. Both deep and shallow water models have been developed, the former being actually a special case of the latter when water depth is great. The deep water model is exceptionally simple in form. Significant wave height is the only prognostic variable. In comparison with the usual methods to compute the energy input and dissipations empirically or by 'tuning', the proposed model has the merit that the effects of all source terms are combined into one term which is computed through empirical growth relations for significant waves, these relations being, relatively speaking, easier and more reliable to obtain than those for the source terms in the spectral energy balance equation. The discrete part of the model and the implementation of the model as a whole will be discussed in the second part of the present paper.展开更多
In the first part of the present paper we have explained why we manage to formulate another wave prediction model when so many of them, including the so-called third generation model, have already been in use. The win...In the first part of the present paper we have explained why we manage to formulate another wave prediction model when so many of them, including the so-called third generation model, have already been in use. The wind-wave part of the proposed model has also been given. Now we proceed to discuss the swell part,the implementation of the model as a prediction method,mumerical experiments done with ideal wind fields and hindcasts made in the Bohai Sea,in the neighboring seas adjacent to China and in the Northwest Pacific.展开更多
In the framework of elastoplastic theory,by introducing dissipative plastic energy(instead of cumulative plastic strain)and dissipative plastic energy rate(instead of cumulative plastic strain rate)into the ratchettin...In the framework of elastoplastic theory,by introducing dissipative plastic energy(instead of cumulative plastic strain)and dissipative plastic energy rate(instead of cumulative plastic strain rate)into the ratchetting parameter evolution equation and isotropic evolution rules respectively,a cyclic elastoplastic constitutive model based on dissipative plastic energy is established.This model,termed the WDP model,describes the physical meaning and evolution rule of the unclosed stress–strain hysteresis loop using an energy method.A comparison of numerical implementation results with experimental data demonstrates the capability of the WDP model to predict the cyclic deformation of EA4T steel,effectively capturing the cyclic softening characteristics and ratchetting behaviors of axle steel EA4T.展开更多
Non-linear numerical modeling, widely used in research and development to understand many complex processes such as forming or machining, does not guarantee the success of a study to be performed. Indeed, the numerica...Non-linear numerical modeling, widely used in research and development to understand many complex processes such as forming or machining, does not guarantee the success of a study to be performed. Indeed, the numerical simulation uses finite element codes where the models already integrated are not based on shapes adjustable to any type of study. In this study, a new form of non-linear constitutive flow law based on the Modified Zerilli-Armstrong model, which can answer the above problem, has been developed to apply it to the numerical simulation of two different tests (a quasi-static compression test, the necking of a circular bar). This flow law is based on the modified Zerilli-Armstrong model, which, together with the new modified Johnson-Cook model, has been compared to appreciate the relevance of the proposal. For that, an implementation of this new law via the VUHARD subroutine into the Abaqus/Explicit finite element code was made to model the two tests. The comparison of the results obtained (from identification) by our proposed law with those obtained using the NMJC shows that this new law better approaches the experiments than the other one. This is also shown through the numerical results using the Abaqus software. It can be said that this way of formulating a flow law allows highlighting the great performance of the proposed approach. Although this law has been only used for quasi-static tests, we can say that it can also be used in dynamic tests.展开更多
A dynamic free energy hysteresis model in magnetostrictive actuators is presented. It is the free energy hysteresis model coupled to an ordinary different equation in an unusual way. According to its special structure...A dynamic free energy hysteresis model in magnetostrictive actuators is presented. It is the free energy hysteresis model coupled to an ordinary different equation in an unusual way. According to its special structure, numerical implementation method of the dynamic model is provided. The resistor parameter in the dynamic model changes according to different frequency ranges. This makes numerical implementation results reasonable in the discussed operating frequency range. The validity of the dynamic free energy model is illustrated by comparison with experimental data.展开更多
Damage and fracture are the most extensive failure modes of rock materials,which may easily induce disaster and instability of engineering structures.This study developed a nonlocal damage fracture phase field model f...Damage and fracture are the most extensive failure modes of rock materials,which may easily induce disaster and instability of engineering structures.This study developed a nonlocal damage fracture phase field model for rocks considering the heterogeneity of rocks.The modified phase field model introduced the heterogeneity of fracture parameters and modified the governing equations.Meanwhile,the free energy was constructed by the elastic strain energy sphere‐bias decomposition and the plastic strain energy.As for the numerical implementation,the three layers finite elements method structure was used in the frame of the finite element method.The ability of the modified phase field model has been illustrated by reproducing the experiment results of rock samples with pre‐existing cracks under compression.展开更多
Earth medium is not completely elastic, with its viscosity resulting in attenuation and dispersion of seismic waves. Most viscoelastic numerical simulations are based on the finite-difference and finite-element method...Earth medium is not completely elastic, with its viscosity resulting in attenuation and dispersion of seismic waves. Most viscoelastic numerical simulations are based on the finite-difference and finite-element methods. Targeted at viscoelastic numerical modeling for multilayered media, the constant-Q acoustic wave equation is transformed into the corresponding wave integral representation with its Green＇s function accounting for viscoelastic coefficients. An efficient alternative for full-waveform solution to the integral equation is proposed in this article by extending conventional frequency-domain boundary element methods to viscoelastic media. The viscoelastic boundary element method enjoys a distinct characteristic of the explicit use of boundary continuity conditions of displacement and traction, leading to a semi-analytical solution with sufficient accuracy for simulating the viscoelastic effect across irregular interfaces. Numerical experiments to study the viscoelastic absorption of different Q values demonstrate the accuracy and applicability of the method.展开更多
This paper analyzes and values an American barrier option with continuous payment plan written on a dividend paying asset under the classical Black-Scholes model.The integral representation of the initial premium alon...This paper analyzes and values an American barrier option with continuous payment plan written on a dividend paying asset under the classical Black-Scholes model.The integral representation of the initial premium along with the delta hedge parameter for an American continuous-installment down-and-out call option are obtained by using the decomposition technique.This offers a system of nonlinear integral equations for determining the optimal exercise and stopping boundaries,which can be utilized to approximate the option price and delta hedge parameter.The implementation is based on discretizing the quadrature formula in the system of equations and using the Newton-Raphson method to compute the two optimal boundaries at each time points.Numerical results are provided to illustrate the computational accuracy and the effects on the initial premium and optimal boundaries with respect to barrier.展开更多
基金supported by the China Scholarship Council(CSC)(Grant No.202006060033).
文摘Both the complex geometrical morphology of rough-walled rock fractures and the nonlinearity of fluid flow contribute to resistance in fluid flow through rock fractures.The interactions of the shear-flow process further complicate the characterisation of flow behaviours in rock fractures.In this study,an improved friction factor model involving both the effects of viscous and inertial forces is presented based on the Forchheimer equation.The model incorporates two key variables,i.e.Reynolds number and relative roughness,which reflect the effects of flow regimes and fracture roughness,respectively.The changes in geometrical parameters induced by shearing are considered,with the peak asperity height predicted through a correlation with post-peak roughness degradation.The hydraulic aperture during shearing is estimated using a suggested equation that accounts for the mobilised contact area ratio and variable aperture distribution.The parametric sensitivity analysis reveals that shear-induced changes in fracture geometry enhance the flow nonlinearity in rock fractures.The model performs well in predicting the friction factor based on two validation criteria.Then,the proposed friction factor model is incorporated into the three-dimensional distinct element code(3DEC)in the form of the Darcy-Weisbach equation.Coupled with the numerically implemented mechanical model and hydraulic aperture prediction model,numerical simulations of coupled shear-flow processes in single rock fractures are conducted.The simulation outcomes are validated through comparison with the experimental results,showing acceptable agreement and demonstrating that the numerical model is capable of accurately evaluating the hydro-mechanical coupling behaviour during the shearing of rock fractures.
文摘The authors make an endeavor to explain why a new hybrid wave model is here proposed when several such models have already been in operation and the so- called third generation wave modej is proving attractive. This part of the paper is devoted to the wind wave model. Both deep and shallow water models have been developed, the former being actually a special case of the latter when water depth is great. The deep water model is exceptionally simple in form. Significant wave height is the only prognostic variable. In comparison with the usual methods to compute the energy input and dissipations empirically or by 'tuning', the proposed model has the merit that the effects of all source terms are combined into one term which is computed through empirical growth relations for significant waves, these relations being, relatively speaking, easier and more reliable to obtain than those for the source terms in the spectral energy balance equation. The discrete part of the model and the implementation of the model as a whole will be discussed in the second part of the present paper.
文摘In the first part of the present paper we have explained why we manage to formulate another wave prediction model when so many of them, including the so-called third generation model, have already been in use. The wind-wave part of the proposed model has also been given. Now we proceed to discuss the swell part,the implementation of the model as a prediction method,mumerical experiments done with ideal wind fields and hindcasts made in the Bohai Sea,in the neighboring seas adjacent to China and in the Northwest Pacific.
基金supported by the Science&Technology Development Fund of Tianjin Education Commission for Higher Education(No.2023KJ250).
文摘In the framework of elastoplastic theory,by introducing dissipative plastic energy(instead of cumulative plastic strain)and dissipative plastic energy rate(instead of cumulative plastic strain rate)into the ratchetting parameter evolution equation and isotropic evolution rules respectively,a cyclic elastoplastic constitutive model based on dissipative plastic energy is established.This model,termed the WDP model,describes the physical meaning and evolution rule of the unclosed stress–strain hysteresis loop using an energy method.A comparison of numerical implementation results with experimental data demonstrates the capability of the WDP model to predict the cyclic deformation of EA4T steel,effectively capturing the cyclic softening characteristics and ratchetting behaviors of axle steel EA4T.
文摘Non-linear numerical modeling, widely used in research and development to understand many complex processes such as forming or machining, does not guarantee the success of a study to be performed. Indeed, the numerical simulation uses finite element codes where the models already integrated are not based on shapes adjustable to any type of study. In this study, a new form of non-linear constitutive flow law based on the Modified Zerilli-Armstrong model, which can answer the above problem, has been developed to apply it to the numerical simulation of two different tests (a quasi-static compression test, the necking of a circular bar). This flow law is based on the modified Zerilli-Armstrong model, which, together with the new modified Johnson-Cook model, has been compared to appreciate the relevance of the proposal. For that, an implementation of this new law via the VUHARD subroutine into the Abaqus/Explicit finite element code was made to model the two tests. The comparison of the results obtained (from identification) by our proposed law with those obtained using the NMJC shows that this new law better approaches the experiments than the other one. This is also shown through the numerical results using the Abaqus software. It can be said that this way of formulating a flow law allows highlighting the great performance of the proposed approach. Although this law has been only used for quasi-static tests, we can say that it can also be used in dynamic tests.
文摘A dynamic free energy hysteresis model in magnetostrictive actuators is presented. It is the free energy hysteresis model coupled to an ordinary different equation in an unusual way. According to its special structure, numerical implementation method of the dynamic model is provided. The resistor parameter in the dynamic model changes according to different frequency ranges. This makes numerical implementation results reasonable in the discussed operating frequency range. The validity of the dynamic free energy model is illustrated by comparison with experimental data.
基金Key Laboratory of Geological Safety of Coastal Urban Underground Space,Ministry of Natural Resources,Grant/Award Number:BHKF2022Y03。
文摘Damage and fracture are the most extensive failure modes of rock materials,which may easily induce disaster and instability of engineering structures.This study developed a nonlocal damage fracture phase field model for rocks considering the heterogeneity of rocks.The modified phase field model introduced the heterogeneity of fracture parameters and modified the governing equations.Meanwhile,the free energy was constructed by the elastic strain energy sphere‐bias decomposition and the plastic strain energy.As for the numerical implementation,the three layers finite elements method structure was used in the frame of the finite element method.The ability of the modified phase field model has been illustrated by reproducing the experiment results of rock samples with pre‐existing cracks under compression.
基金supported by the National Natural Science Foundation of China (No. 41130418)the Strategic Leading Science and Technology Programme (Class B) of the Chinese Academy of Sciences (No. XDB10010400)
文摘Earth medium is not completely elastic, with its viscosity resulting in attenuation and dispersion of seismic waves. Most viscoelastic numerical simulations are based on the finite-difference and finite-element methods. Targeted at viscoelastic numerical modeling for multilayered media, the constant-Q acoustic wave equation is transformed into the corresponding wave integral representation with its Green＇s function accounting for viscoelastic coefficients. An efficient alternative for full-waveform solution to the integral equation is proposed in this article by extending conventional frequency-domain boundary element methods to viscoelastic media. The viscoelastic boundary element method enjoys a distinct characteristic of the explicit use of boundary continuity conditions of displacement and traction, leading to a semi-analytical solution with sufficient accuracy for simulating the viscoelastic effect across irregular interfaces. Numerical experiments to study the viscoelastic absorption of different Q values demonstrate the accuracy and applicability of the method.
基金supported by the National Natural Science Foundation of China under Grant No.40675023Guangxi Natural Science Foundation under Grant No.0991091
文摘This paper analyzes and values an American barrier option with continuous payment plan written on a dividend paying asset under the classical Black-Scholes model.The integral representation of the initial premium along with the delta hedge parameter for an American continuous-installment down-and-out call option are obtained by using the decomposition technique.This offers a system of nonlinear integral equations for determining the optimal exercise and stopping boundaries,which can be utilized to approximate the option price and delta hedge parameter.The implementation is based on discretizing the quadrature formula in the system of equations and using the Newton-Raphson method to compute the two optimal boundaries at each time points.Numerical results are provided to illustrate the computational accuracy and the effects on the initial premium and optimal boundaries with respect to barrier.
