A hierarchical multiscale modeling approach is used to investigate three-dimensional (3D) strain ... more A hierarchical multiscale modeling approach is used to investigate three-dimensional (3D) strain localization in granular media. Central to the multiscale approach is a hierarchical coupling of finite element method (FEM) and discrete element method (DEM), wherein the FEM is employed to treat a boundary value problem of a granular material and the required constitutive relation for FEM is derived directly from the DEM solution of a granular assembly embedded at each of the FEM Gauss integration points as the representative volume element (RVE). While being effective in reproducing the complex mechanical responses of granular media, the hierarchical approach helps to bypass the necessity of phenomenological constitutive models commonly needed by conventional FEM studies and meanwhile offers a viable way to link the macroscopic observations with their underlying microscopic mechanisms. To model the phenomenon of strain localization, key issues pertaining to the selection of proper RVE packings are first discussed. The multiscale approach is then applied to simulate the strain localization problem in a cubical specimen and a cylindrical specimen subjected to either conventional triaxial compression (CTC) or conventional triaxial extension (CTE) loading, which is further compared to a case under plane-strain biaxial compression (PBC) loading condition. Different failure patterns, including localized, bulging and diffuse failure modes, are observed and analyzed. Amongst all testing conditions, the PBC condition is found most favorable for the formation of localized failure. The CTC test on the cubical specimen leads to a 3D octopus-shaped localization zone, whereas the cylindrical specimen under CTC shows seemingly bulging failure from the outlook but rather more complex failure patterns within the specimen. The CTE test on a uniform specimen normally ends in a diffuse failure. Different micro mechanisms and controlling factors underlying the various interesting observations are examined and discussed.
This paper extends the hierarchical multiscale approach developed earlier by the authors to model... more This paper extends the hierarchical multiscale approach developed earlier by the authors to model the coupled hydro-mechanical behaviour for saturated granular soils. Based on a hierarchical coupling of the finite element method (FEM) and the discrete element method (DEM), the approach employs the FEM to solve a boundary value problem while using the DEM to derive the required nonlinear material responses at each FEM Gauss integration point. It helps to bypass the phenomenological constitutive model required in the conventional FEM simulations and offers a natural pathway for scale bridging. The current extension features further key consideration of the coupled hydro-mechanical behaviour in a saturated granular soil due to the presence of pore fluid and its flow. By invoking Terzaghi’s effective stress principle, a View the MathML source–p formulation is proposed for the multiscale framework to derive the effective stress from DEM solution of the representative volume element (RVE) embedded at each Gauss point which is then superimposed with the pore fluid pressure to obtain the total stress in solving the coupled governing equations for a fluid–solid mixture. This extension greatly enriches the predictive capacity of the multiscale approach for simulating saturated granular soils relevant to a wide variety of important civil/mining applications. The new approach is first benchmarked by closed-form solutions to classical 1D and 2D consolidation problems. It is then applied to simulate globally undrained biaxial compression tests on both dense and loose soils subjected to large deformation. We further discuss interesting fluid flow patterns and the failure modes (both localisation and diffuse liquefaction) observed from the simulations and provide detailed cross-scale analyses.
A novel hierarchical multiscale model has been applied to simulate the thick-walled hollow cylind... more A novel hierarchical multiscale model has been applied to simulate the thick-walled hollow cylinder tests in dry sand and to investigate the corresponding shear failures. The combined finite-element method and discrete-element method (FEM/DEM) model employs the FEM as a vehicle to advance the solution for a macroscopic non-linear boundary value problem incrementally. It is, meanwhile, free of conventional macroscopic phenomenological constitutive law, which is replaced by discrete-element simulations conducted with representative volume elements (RVEs) associated with the Gauss quadrature points of the FEM mesh. Numerical simulations proposed by the authors indicate that this multiscale approach is capable of replicating the evolution of cavity pressure during cavity expansion – before and after the onset of strain localisation – in qualitative agreement with laboratory tests. In particular, the curvilinear shear bands observed from experiments have been reproduced numerically. The information provided by the mesoscale DEM and the macroscale FEM reveals a close linkage between significant particle rotations taking place inside the dilative shear bands and the highly anisotropic microstructural attributes of the associated RVEs.
This paper presents a multiscale investigation on the interplay among inherent anisotropy, fabric... more This paper presents a multiscale investigation on the interplay among inherent anisotropy, fabric evolution and strain localisation in granular soils, based on a hierarchical multiscale framework with rigorous coupling of the finite-element method (FEM) and discrete-element method (DEM). DEM assemblies with elongated particles are generated to simulate inherent anisotropy and are embedded to the Gauss points of the FEM mesh to derive the required constitutive relation. Specimens prepared with different bedding plane angles are subjected to biaxial shear under either smooth or rough loading platens. Key factors and physical mechanisms contributing towards the occurrence and development of strain localisation are examined. The competing evolutions of two sources of anisotropy, one related to particle orientations and the other related to contact normals, are found to underpin the development of the shear band. A single band pattern is observed under smooth boundary conditions, and its orientation relative to the bedding plane depends critically on the relative dominance between the two anisotropies. Under rough boundary conditions, the non-coaxial material response and the boundary constraint jointly lead to cross-shaped double shear bands. The multiscale simulations indicate that the DEM assemblies inside the shear band(s) undergo extensive shearing, fabric evolution and particle rotation, and may reach the critical state, while those located outside the shear band(s) experience mild loading followed by unloading. The particle-orientation-based fabric anisotropy needs significantly larger shear and dilation for mobilisation than the contact-normal based one. The asynchrony in evolution of the two fabric anisotropies can cause non-coaxial responses for initially coaxial packings, which directly triggers strain localisation.
International Journal for Numerical and Analytical Methods in Geomechanics
We pay a revisit to some classical geomechanics problems using a novel computational multiscale m... more We pay a revisit to some classical geomechanics problems using a novel computational multiscale modelling approach. The multiscale approach employs a hierarchical coupling of the finite element method (FEM) and the discrete element method. It solves a boundary value problem at the continuum scale by FEM and derives the material point response from the discrete element method simulation attached to each Gauss point of the FEM mesh. The multiscale modelling framework not only helps successfully bypass phenomenological constitutive assumptions as required in conventional modelling approaches but also facilitates effective cross-scale interpretation and understanding of soil behaviour. We examine the classical retaining wall and footing problems by this method and demonstrate that the simulating results can be well validated and verified by their analytical solutions. Furthermore, the study sheds novel multiscale insights into these classical problems and offers a new tool for geotechnical engineers to design and analyse geotechnical applications based directly upon particle-level information of soils.
International Journal for Numerical Methods in Engineering
A hierarchical multiscale framework is proposed to model the mechanical behaviour of granular med... more A hierarchical multiscale framework is proposed to model the mechanical behaviour of granular media. The framework employs a rigorous hierarchical coupling between the FEM and the discrete element method (DEM). To solve a BVP, the FEM is used to discretise the macroscopic geometric domain into an FEM mesh. A DEM assembly with memory of its loading history is embedded at each Gauss integration point of the mesh to serve as the representative volume element (RVE). The DEM assembly receives the global deformation at its Gauss point from the FEM as input boundary conditions and is solved to derive the required constitutive relation at the specific material point to advance the FEM computation. The DEM computation employs simple physically based contact laws in conjunction with Coulomb's friction for interparticle contacts to capture the loading-history dependence and highly nonlinear dissipative response of a granular material. The hierarchical scheme helps to avoid the phenomenological assumptions on constitutive relation in conventional continuum modelling and retains the computational efficiency of FEM in solving large-scale BVPs. The hierarchical structure also makes it ideal for distributed parallel computing to fully unleash its predictive power. Importantly, the framework offers rich information on the particle level with direct link to the macroscopic material response, which helps to shed lights on cross-scale understanding of granular media. The developed framework is first benchmarked by a simulation of single-element drained test and is then applied to the predictions of strain localisation for sand subject to monotonic biaxial compression, as well as the liquefaction and cyclic mobility of sand in cyclic simple shear tests. It is demonstrated that the proposed method may reproduce interesting experimental observations that are otherwise difficult to be captured by conventional FEM or pure DEM simulations, such as the inception of shear band under smooth symmetric boundary conditions, non-coaxial granular response, large dilation and rotation at the edges of shear band and critical state reached within the shear band.
We investigate the local fluctuations in dense granular media subjected to athermal, quasistatic ... more We investigate the local fluctuations in dense granular media subjected to athermal, quasistatic shearing, based on three-dimensional discrete element method simulations. By shearing granular assemblies of different polydispersities under constant-volume constraint, we quantify the characteristics of local structures (in terms of local volume and local anisotropy) and local deformation (using local shear strain and nonaffine displacement). The distribution of the local volume in a granular medium is found unchanged during the entire shearing process, which indicates a constant temperaturelike compactivity for the material. The compactivity is not, however, equilibrated among different particle groups in a polydisperse assembly. The local structures of a disordered granular assembly are inherently anisotropic. The fluctuations in local anisotropy can be well captured by a gamma or mixed-gamma distribution function, which is also unchanged during the shear. The local anisotropic orientation evolves towards the coaxial direction of the stress anisotropy with shear. The deformation characteristics of a jammed granular medium have their origins in the structural amorphousness. The local shear strain field depicts clear shear transformation zones which act as plasticity carriers. The spatial correlation of the local shear strains exhibits a fourfold pattern which is stronger in the stress deviatoric planes than in the stress isotropic plane. The fluctuations of nonaffine displacement suggest an isotropic granular temperature and an isotropic spatial correlation independent of the stress state. Both the local strain and the nonaffine displacement exhibit a power-law decayed distribution with a long-range correlation. We further modify the shear-transformation-zone theory to predict the pressure-dependent constitutive behavior of a sheared granular material and compare its prediction with our simulation data.
This paper presents a micromechanical study on the behavior of granular materials under confined ... more This paper presents a micromechanical study on the behavior of granular materials under confined shear using a three-dimensional Discrete Element Method (DEM). We consider rotational resistance among spherical particles in the DEM code as an approximate way to account for the effect of particle shape. Under undrained shear, it is found rotational resistance may help to increase the shear strength of a granular system and to enhance its resistance to liquefaction. The evolution of internal structure and anisotropy in granular systems with different initial conditions depict a clear bimodal character which distinguishes two contact subnetworks. In the presence of rotational resistance, a good correlation is found between an analytical stress-force-fabric relation and the DEM results, in which the normal force anisotropy plays a dominant role. The unique properties of critical state and liquefaction state in relation to granular anisotropy are also explored and discussed.
The concept of the critical state in granular soils needs to make proper reference to the fabric ... more The concept of the critical state in granular soils needs to make proper reference to the fabric structure that develops at critical state. This study identifies a unique property associated with the fabric structure relative to the stresses at critical state. A unique relationship between the mean effective stress and a fabric anisotropy parameter, K, defined by the first joint invariant of the deviatoric stress tensor and the deviatoric fabric tensor, is found at critical state, and is path-independent. Numerical simulations using the discrete-element method under different loading conditions and intermediate principal stress ratios identify a unique power law for this relationship. Based on the findings, a new definition of critical state for granular media is proposed. In addition to the conditions of constant stress and unique void ratio required by the conventional critical state concept, the new definition imposes the additional constraint that K reaches a unique value at critical state. A unique spatial critical state curve in the three-dimensional space K–e–p' is found for a granular medium, the projection of which onto the e–p' plane turns out to be the conventional critical state line. The new critical state concept provides an important reference state for a soil to reach, based on which the key concepts in the constitutive modelling of granular media, including the choice of state parameters, dilatancy relation and non-coaxiality, are reassessed, and future exploratory topics are discussed.
This paper presents a micro-mechanical study on the characteristics of shear-induced anisotropy i... more This paper presents a micro-mechanical study on the characteristics of shear-induced anisotropy in granular media. Based on three-dimensional Discrete Element Method (DEM) simulations, the distinct features associated with the evolution of internal granular structure and different anisotropy sources during drained/undrained shearing of granular samples are carefully examined. The study finds that static liquefaction occurs when the geometrical anisotropy in a sample dominates the mechanical anisotropy in the overall shear strength, and the weak force network features an exceptionally high proportion of sliding contacts and develops certain degree of anisotropy. Phase transformation corresponds to a transitional, unstable state associated with a dramatic change in both coordination number and the proportion of sliding contacts in all contacts. The critical state in a granular material is always associated with a highly anisotropic fabric structure wherein both the critical void ratio and critical fabric anisotropy are uniquely related to the mean effective stress. The relations provide a more comprehensive definition for the critical state in granular media with proper reference to the critical fabric anisotropy.
A hierarchical multiscale modeling approach is used to investigate three-dimensional (3D) strain ... more A hierarchical multiscale modeling approach is used to investigate three-dimensional (3D) strain localization in granular media. Central to the multiscale approach is a hierarchical coupling of finite element method (FEM) and discrete element method (DEM), wherein the FEM is employed to treat a boundary value problem of a granular material and the required constitutive relation for FEM is derived directly from the DEM solution of a granular assembly embedded at each of the FEM Gauss integration points as the representative volume element (RVE). While being effective in reproducing the complex mechanical responses of granular media, the hierarchical approach helps to bypass the necessity of phenomenological constitutive models commonly needed by conventional FEM studies and meanwhile offers a viable way to link the macroscopic observations with their underlying microscopic mechanisms. To model the phenomenon of strain localization, key issues pertaining to the selection of proper RVE packings are first discussed. The multiscale approach is then applied to simulate the strain localization problem in a cubical specimen and a cylindrical specimen subjected to either conventional triaxial compression (CTC) or conventional triaxial extension (CTE) loading, which is further compared to a case under plane-strain biaxial compression (PBC) loading condition. Different failure patterns, including localized, bulging and diffuse failure modes, are observed and analyzed. Amongst all testing conditions, the PBC condition is found most favorable for the formation of localized failure. The CTC test on the cubical specimen leads to a 3D octopus-shaped localization zone, whereas the cylindrical specimen under CTC shows seemingly bulging failure from the outlook but rather more complex failure patterns within the specimen. The CTE test on a uniform specimen normally ends in a diffuse failure. Different micro mechanisms and controlling factors underlying the various interesting observations are examined and discussed.
This paper extends the hierarchical multiscale approach developed earlier by the authors to model... more This paper extends the hierarchical multiscale approach developed earlier by the authors to model the coupled hydro-mechanical behaviour for saturated granular soils. Based on a hierarchical coupling of the finite element method (FEM) and the discrete element method (DEM), the approach employs the FEM to solve a boundary value problem while using the DEM to derive the required nonlinear material responses at each FEM Gauss integration point. It helps to bypass the phenomenological constitutive model required in the conventional FEM simulations and offers a natural pathway for scale bridging. The current extension features further key consideration of the coupled hydro-mechanical behaviour in a saturated granular soil due to the presence of pore fluid and its flow. By invoking Terzaghi’s effective stress principle, a View the MathML source–p formulation is proposed for the multiscale framework to derive the effective stress from DEM solution of the representative volume element (RVE) embedded at each Gauss point which is then superimposed with the pore fluid pressure to obtain the total stress in solving the coupled governing equations for a fluid–solid mixture. This extension greatly enriches the predictive capacity of the multiscale approach for simulating saturated granular soils relevant to a wide variety of important civil/mining applications. The new approach is first benchmarked by closed-form solutions to classical 1D and 2D consolidation problems. It is then applied to simulate globally undrained biaxial compression tests on both dense and loose soils subjected to large deformation. We further discuss interesting fluid flow patterns and the failure modes (both localisation and diffuse liquefaction) observed from the simulations and provide detailed cross-scale analyses.
A novel hierarchical multiscale model has been applied to simulate the thick-walled hollow cylind... more A novel hierarchical multiscale model has been applied to simulate the thick-walled hollow cylinder tests in dry sand and to investigate the corresponding shear failures. The combined finite-element method and discrete-element method (FEM/DEM) model employs the FEM as a vehicle to advance the solution for a macroscopic non-linear boundary value problem incrementally. It is, meanwhile, free of conventional macroscopic phenomenological constitutive law, which is replaced by discrete-element simulations conducted with representative volume elements (RVEs) associated with the Gauss quadrature points of the FEM mesh. Numerical simulations proposed by the authors indicate that this multiscale approach is capable of replicating the evolution of cavity pressure during cavity expansion – before and after the onset of strain localisation – in qualitative agreement with laboratory tests. In particular, the curvilinear shear bands observed from experiments have been reproduced numerically. The information provided by the mesoscale DEM and the macroscale FEM reveals a close linkage between significant particle rotations taking place inside the dilative shear bands and the highly anisotropic microstructural attributes of the associated RVEs.
This paper presents a multiscale investigation on the interplay among inherent anisotropy, fabric... more This paper presents a multiscale investigation on the interplay among inherent anisotropy, fabric evolution and strain localisation in granular soils, based on a hierarchical multiscale framework with rigorous coupling of the finite-element method (FEM) and discrete-element method (DEM). DEM assemblies with elongated particles are generated to simulate inherent anisotropy and are embedded to the Gauss points of the FEM mesh to derive the required constitutive relation. Specimens prepared with different bedding plane angles are subjected to biaxial shear under either smooth or rough loading platens. Key factors and physical mechanisms contributing towards the occurrence and development of strain localisation are examined. The competing evolutions of two sources of anisotropy, one related to particle orientations and the other related to contact normals, are found to underpin the development of the shear band. A single band pattern is observed under smooth boundary conditions, and its orientation relative to the bedding plane depends critically on the relative dominance between the two anisotropies. Under rough boundary conditions, the non-coaxial material response and the boundary constraint jointly lead to cross-shaped double shear bands. The multiscale simulations indicate that the DEM assemblies inside the shear band(s) undergo extensive shearing, fabric evolution and particle rotation, and may reach the critical state, while those located outside the shear band(s) experience mild loading followed by unloading. The particle-orientation-based fabric anisotropy needs significantly larger shear and dilation for mobilisation than the contact-normal based one. The asynchrony in evolution of the two fabric anisotropies can cause non-coaxial responses for initially coaxial packings, which directly triggers strain localisation.
International Journal for Numerical and Analytical Methods in Geomechanics
We pay a revisit to some classical geomechanics problems using a novel computational multiscale m... more We pay a revisit to some classical geomechanics problems using a novel computational multiscale modelling approach. The multiscale approach employs a hierarchical coupling of the finite element method (FEM) and the discrete element method. It solves a boundary value problem at the continuum scale by FEM and derives the material point response from the discrete element method simulation attached to each Gauss point of the FEM mesh. The multiscale modelling framework not only helps successfully bypass phenomenological constitutive assumptions as required in conventional modelling approaches but also facilitates effective cross-scale interpretation and understanding of soil behaviour. We examine the classical retaining wall and footing problems by this method and demonstrate that the simulating results can be well validated and verified by their analytical solutions. Furthermore, the study sheds novel multiscale insights into these classical problems and offers a new tool for geotechnical engineers to design and analyse geotechnical applications based directly upon particle-level information of soils.
International Journal for Numerical Methods in Engineering
A hierarchical multiscale framework is proposed to model the mechanical behaviour of granular med... more A hierarchical multiscale framework is proposed to model the mechanical behaviour of granular media. The framework employs a rigorous hierarchical coupling between the FEM and the discrete element method (DEM). To solve a BVP, the FEM is used to discretise the macroscopic geometric domain into an FEM mesh. A DEM assembly with memory of its loading history is embedded at each Gauss integration point of the mesh to serve as the representative volume element (RVE). The DEM assembly receives the global deformation at its Gauss point from the FEM as input boundary conditions and is solved to derive the required constitutive relation at the specific material point to advance the FEM computation. The DEM computation employs simple physically based contact laws in conjunction with Coulomb's friction for interparticle contacts to capture the loading-history dependence and highly nonlinear dissipative response of a granular material. The hierarchical scheme helps to avoid the phenomenological assumptions on constitutive relation in conventional continuum modelling and retains the computational efficiency of FEM in solving large-scale BVPs. The hierarchical structure also makes it ideal for distributed parallel computing to fully unleash its predictive power. Importantly, the framework offers rich information on the particle level with direct link to the macroscopic material response, which helps to shed lights on cross-scale understanding of granular media. The developed framework is first benchmarked by a simulation of single-element drained test and is then applied to the predictions of strain localisation for sand subject to monotonic biaxial compression, as well as the liquefaction and cyclic mobility of sand in cyclic simple shear tests. It is demonstrated that the proposed method may reproduce interesting experimental observations that are otherwise difficult to be captured by conventional FEM or pure DEM simulations, such as the inception of shear band under smooth symmetric boundary conditions, non-coaxial granular response, large dilation and rotation at the edges of shear band and critical state reached within the shear band.
We investigate the local fluctuations in dense granular media subjected to athermal, quasistatic ... more We investigate the local fluctuations in dense granular media subjected to athermal, quasistatic shearing, based on three-dimensional discrete element method simulations. By shearing granular assemblies of different polydispersities under constant-volume constraint, we quantify the characteristics of local structures (in terms of local volume and local anisotropy) and local deformation (using local shear strain and nonaffine displacement). The distribution of the local volume in a granular medium is found unchanged during the entire shearing process, which indicates a constant temperaturelike compactivity for the material. The compactivity is not, however, equilibrated among different particle groups in a polydisperse assembly. The local structures of a disordered granular assembly are inherently anisotropic. The fluctuations in local anisotropy can be well captured by a gamma or mixed-gamma distribution function, which is also unchanged during the shear. The local anisotropic orientation evolves towards the coaxial direction of the stress anisotropy with shear. The deformation characteristics of a jammed granular medium have their origins in the structural amorphousness. The local shear strain field depicts clear shear transformation zones which act as plasticity carriers. The spatial correlation of the local shear strains exhibits a fourfold pattern which is stronger in the stress deviatoric planes than in the stress isotropic plane. The fluctuations of nonaffine displacement suggest an isotropic granular temperature and an isotropic spatial correlation independent of the stress state. Both the local strain and the nonaffine displacement exhibit a power-law decayed distribution with a long-range correlation. We further modify the shear-transformation-zone theory to predict the pressure-dependent constitutive behavior of a sheared granular material and compare its prediction with our simulation data.
This paper presents a micromechanical study on the behavior of granular materials under confined ... more This paper presents a micromechanical study on the behavior of granular materials under confined shear using a three-dimensional Discrete Element Method (DEM). We consider rotational resistance among spherical particles in the DEM code as an approximate way to account for the effect of particle shape. Under undrained shear, it is found rotational resistance may help to increase the shear strength of a granular system and to enhance its resistance to liquefaction. The evolution of internal structure and anisotropy in granular systems with different initial conditions depict a clear bimodal character which distinguishes two contact subnetworks. In the presence of rotational resistance, a good correlation is found between an analytical stress-force-fabric relation and the DEM results, in which the normal force anisotropy plays a dominant role. The unique properties of critical state and liquefaction state in relation to granular anisotropy are also explored and discussed.
The concept of the critical state in granular soils needs to make proper reference to the fabric ... more The concept of the critical state in granular soils needs to make proper reference to the fabric structure that develops at critical state. This study identifies a unique property associated with the fabric structure relative to the stresses at critical state. A unique relationship between the mean effective stress and a fabric anisotropy parameter, K, defined by the first joint invariant of the deviatoric stress tensor and the deviatoric fabric tensor, is found at critical state, and is path-independent. Numerical simulations using the discrete-element method under different loading conditions and intermediate principal stress ratios identify a unique power law for this relationship. Based on the findings, a new definition of critical state for granular media is proposed. In addition to the conditions of constant stress and unique void ratio required by the conventional critical state concept, the new definition imposes the additional constraint that K reaches a unique value at critical state. A unique spatial critical state curve in the three-dimensional space K–e–p' is found for a granular medium, the projection of which onto the e–p' plane turns out to be the conventional critical state line. The new critical state concept provides an important reference state for a soil to reach, based on which the key concepts in the constitutive modelling of granular media, including the choice of state parameters, dilatancy relation and non-coaxiality, are reassessed, and future exploratory topics are discussed.
This paper presents a micro-mechanical study on the characteristics of shear-induced anisotropy i... more This paper presents a micro-mechanical study on the characteristics of shear-induced anisotropy in granular media. Based on three-dimensional Discrete Element Method (DEM) simulations, the distinct features associated with the evolution of internal granular structure and different anisotropy sources during drained/undrained shearing of granular samples are carefully examined. The study finds that static liquefaction occurs when the geometrical anisotropy in a sample dominates the mechanical anisotropy in the overall shear strength, and the weak force network features an exceptionally high proportion of sliding contacts and develops certain degree of anisotropy. Phase transformation corresponds to a transitional, unstable state associated with a dramatic change in both coordination number and the proportion of sliding contacts in all contacts. The critical state in a granular material is always associated with a highly anisotropic fabric structure wherein both the critical void ratio and critical fabric anisotropy are uniquely related to the mean effective stress. The relations provide a more comprehensive definition for the critical state in granular media with proper reference to the critical fabric anisotropy.
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Papers by Ning Guo