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Hongxiang Tang - One of the best experts on this subject based on the ideXlab platform.
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an anisotropic elastoplastic Cosserat Continuum model for shear failure in stratified geomaterials
Engineering Geology, 2021Co-Authors: Hongxiang Tang, Wencheng Wei, Xiaoyu Song, Feng LiuAbstract:Abstract In this article, we formulate an anisotropic elastoplastic Cosserat continua model for shear failure in stratified geomaterials. Considering the dip angle between local and global coordinates of a formation, a Cosserat elastic anisotropy constitutive matrix under plane strain condition is derived, and cohesion anisotropy is reflected using a microstructural tensor combined-stress invariant method. A Cosserat Continuum finite element model and consistent algorithm are developed to consider the characteristics of elastic anisotropy, strength anisotropy, and strain softening. The simulation of a stratified geomaterial sample under uniaxial compression condition shows that the elastic anisotropy has an evident influence on the deformation pattern. It is also demonstrated that dip angle could significantly impact macroscopic failure modes, uniaxial compressive strength, and macroscopic equivalent elastic modulus. The stability analysis of a layered slope demonstrates that the strength anisotropy has a considerable influence on the overload safety factor of the slope and can be a trigger of the formation of shear bands in such slopes. Furthermore, the dip angle of the structural plane also affects the stability of the stratified slope, which is controlled by both the block and structural surface. By comparing the numerical results of the classical Continuum model and the Cosserat Continuum model, it is proved that the numerical model considering the elastoplastic anisotropy and strain softening under the Cosserat Continuum theory overcomes the ill-posedness of mesh sensitivity and maintains the well-posedness of the strain localization problem. Thus, the proposed model is useful for modeling shear failure in stratified geomaterials.
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scaled boundary polygon formula for Cosserat Continuum and its verification
Engineering Analysis With Boundary Elements, 2021Co-Authors: Kai Chen, Hongxiang Tang, Degao Zou, Jingmao Liu, Yue ZhuoAbstract:Abstract Cosserat Continuum method can be used to solve stress concentration of holes. However, with the shape limitation of its elements, it is worthwhile to improve the element quality so that this method can be universal and feasible to complex situations. In this paper, a flexible polygonal Cosserat Continuum analysis method is firstly deduced and numerically developed based on the theory of Scaled Boundary FEM. Stress concentration on the holes embedded in different structures is then investigated using the proposed method and verified against theoretical solution, which not only shows good agreement, but also reasonably weakens the stress concentration. The proposed method can closely replicate the theoretical solution for the case when the material is nearly incompressible (Poisson's ratio close to 0.5), also indicating the robustness of this method. Additionally, complex polygonal elements can be solved directly, coupling the quadtree and polygon discretization techniques seamlessly, wherein the efficiency and convenience are improved for processing complex geometries. The proposed method can provide important technical support for stress concentration analysis of structures with complex holes, and contribute to facilitating shape optimization of holes design.
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an isogeometric approach to biot Cosserat Continuum for simulating dynamic strain localization in saturated soils
Computers and Geotechnics, 2021Co-Authors: Feng Zhu, Hongxiang Tang, Xue Zhang, George PapazafeiropoulosAbstract:Abstract The Biot-Cosserat Continuum theory is combined with isogeometric analysis (Biot-CIGA) to simulate dynamic strain localization in saturated soils. The results demonstrate that Biot-CIGA can solve the ill-posed problem of saturated soils caused by strain-softening properties and non-associated flow rules, thereby obtaining a convergent, mesh-independent numerical solution. Compared with the finite element analysis of Biot-Cosserat Continuum (Biot-CFEA), the high-order continuity of Biot-CIGA provides a smooth pore pressure gradient field and thus ensures the local mass balance of pore fluids. Additionally, the Biot-CIGA describes the inflow and outflow of pore fluids in the element, which means it is able to accurately simulate the volumetric strain of the element. Simulation results also show that the Biot-CIGA method can also effectively alleviate the mesh distortion in shear bands when materials experience large deformation. Last but not least, because Biot-CIGA adopts NURBS as its shape functions, it can conduct simulations directly on CAD models, which not only maintains the precise geometry, but also avoids an expensive intermediate meshing step.
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numerical simulation of strain localization based on Cosserat Continuum theory and isogeometric analysis
Computers and Geotechnics, 2021Co-Authors: Hongxiang Tang, Feng Zhu, Dixiong Yang, George PapazafeiropoulosAbstract:Abstract The Cosserat Continuum theory is combined with isogeometric analysis (Cos-IGA) to simulate strain localization problems of geomaterials. The results demonstrate that the numerical solution based on Cos-IGA is convergent and mesh-independent and that the Cos-IGA method can capture the initiation and propagation of the shear band as strain localization problem involved. The Cos-IGA method can also effectively alleviate the influence of mesh distortion in the shear zone, even in the case of large deformations. Further, the Cos-IGA method reduces computational cost and eliminates errors caused by geometric discretization compared with the Cos-FEA method. It suggests that the C 2 cubic (three-order) basis function for Cos-IGA is the best choice for simulating strain localization problems considering computational cost and convergence.
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elastoplastic Cosserat Continuum model considering strength anisotropy and its application to the analysis of slope stability
Computers and Geotechnics, 2020Co-Authors: Hongxiang Tang, Wencheng Wei, Feng Liu, Guoqing ChenAbstract:Abstract Aiming at solving the problems of strength anisotropy and strain localization of cohesive soil, Pietruszczak’s method, in which the microstructure tensor is combined with stress invariance, is developed to analyze the cohesion anisotropy and is introduced into the Drucker-Prager constitutive model under Cosserat Continuum theory. A consistent algorithm of the corresponding constitutive model is derived. The characteristics of strength anisotropy and the reliability of the developed numerical method are verified by the experiments in laboratory. The importance and necessity of developing the numerical model with strength anisotropy under the framework of Cosserat theory are evaluated via simulation of a plane strain compression model. It indicates that the degree of the cohesion anisotropy has an important influence on the bearing capacity, and that the numerical model can overcome the ill-posedness of the mesh sensitivity and maintain the well-posedness of the strain localization problem. Furthermore, the effects of strength anisotropy and strain softening on the safety factor of the slope are analyzed via the gravity increase method. It is demonstrated that the Cosserat Continuum model can effectively overcome the problems of mesh-dependence encountered by the classical Continuum model and yield a reasonable safety factor with mesh refinement.
A R Khoei - One of the best experts on this subject based on the ideXlab platform.
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3d finite element modeling of shear band localization via the micro polar Cosserat Continuum theory
Computational Materials Science, 2010Co-Authors: A R Khoei, S Yadegari, S O R BiabanakiAbstract:In this paper, a micro-polar Continuum model is presented based on the Cosserat theory for 3D modeling of localization phenomena. Since the classical Continuum model suffers from the pathological mesh-dependence in strain localization problem, the governing equations are regularized by adding the rotational degrees-of-freedom to conventional degrees-of-freedom. The fundamental relations in three-dimensional Cosserat Continuum are presented and the internal length parameters are introduced in the elasto-plastic constitutive matrix to control the shear bandwidth. The mesh independency of Cosserat model in strain-softening problem is verified and the effect of internal parameters is investigated. The efficiency of proposed computational algorithm is demonstrated by 3D numerical simulations of the vertical cut, slope problem and a tensile specimen. A comparison is performed between the classical and Cosserat theories and the effect of internal length parameter is demonstrated.
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an enriched fem model for simulation of localization phenomenon in Cosserat Continuum theory
Computational Materials Science, 2008Co-Authors: A R Khoei, Kamran KarimiAbstract:Abstract The standard finite element models, i.e. the finite element methods that use the classical Continuum models, suffer from the excessive mesh dependence when a strain-softening model is used. It cannot converge to a meaningful solution and the governing differential equation loses the ellipticity. This paper presents an enriched finite element algorithm for simulation of localization phenomenon using a higher order Continuum model based on the Cosserat Continuum theory. The governing equations are regularized by adding the rotational degrees-of-freedom to the conventional degrees-of-freedom and including the internal length parameter in the model. The extended finite element method (X-FEM) is employed, in which the discontinuity interfaces are represented independent of element boundaries and the process is accomplished by partitioning the domain with some triangular sub-elements whose Gauss points are used for integration of the domain of elements. Finally, several numerical examples are analyzed to demonstrate the efficiency of the mixed XFEM – Cosserat Continuum model in shear band localization.
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h adaptive mesh refinement for shear band localization in elasto plasticity Cosserat Continuum
Communications in Nonlinear Science and Numerical Simulation, 2005Co-Authors: A R Khoei, A R Tabarraie, S A GharehbaghiAbstract:In this paper, an h-adaptive mesh refinement is presented based on the gradient of deformation in the modeling of localization due to material instability. As the classical Continuum models suffer from pathological mesh dependence in the strain-softening models, the governing equations are regularized by adding rotational degrees-of-freedom to the conventional degrees-of-freedom. Adaptive strategy using element elongation is applied to compute the distribution of required element size using the estimated error distribution. Once the new element size and its alignment have been indicated, an automated procedure is used to construct the mesh according to a predetermined size and elongation distribution. Finally, the efficiency of the proposed model and computational algorithms is demonstrated by several numerical examples. Clearly, a finite shear bandwidth is achieved and the load–displacement curves is uniformly converged upon mesh refinement. It is shown that the h-adaptive remeshing using Cosserat Continuum can be effectively used in the modeling of localization phenomena.
Elena F Grekova - One of the best experts on this subject based on the ideXlab platform.
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plane waves in the linear elastic reduced Cosserat medium with a finite axially symmetric coupling between volumetric and rotational strains
Mathematics and Mechanics of Solids, 2016Co-Authors: Elena F GrekovaAbstract:We consider plane waves in the linear elastic reduced Cosserat Continuum, a medium where point-bodies have independent rotational and translational degrees of freedom, but couple stresses are zero,...
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nonlinear isotropic elastic reduced Cosserat Continuum as a possible model for geomedium and geomaterials spherical prestressed state in the semilinear material
Journal of Seismology, 2012Co-Authors: Elena F GrekovaAbstract:We suggest a nonlinear elastic reduced Cosserat Continuum as a possible model for geomedium and geomaterials and also for a soil or rock with heterogeneities. If a medium has a block structure, or if it contains heterogeneities that may have their proper rotational dynamics, the presence of rotational degrees of freedom may influence wave propagation and stability of the medium. In the reduced Cosserat model, translations and rotations are independent, the medium resists to the rotation of each “particle” relatively to the background Continuum, but it does not resist to the gradient of rotation. We consider a nonlinear spherical stress state in an isotropic elastic reduced Cosserat material. We write down small deviations from this nonlinear equilibrium. They coincide in form with the equations of the linear elastic isotropic reduced Cosserat Continuum. Depending on the level of the stress and on the type of elastic energy, the equilibrium can be stable or unstable. In the domain of stability, shear–rotational wave demonstrates dispersion. There is a resonant frequency corresponding to the independent rotational oscillations. The bulk plane shear–rotational wave has a forbidden band of frequencies. In this zone, the shear–rotational wave localises near heterogeneities or external sources. We show that for a semilinear medium (medium with large deformations but linear dependence of stress on the strain tensor), strong compression leads to the material instability caused by shear perturbations, and strong tension for some class of parameters yields in instability caused by rotational perturbations.
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waves in linear elastic media with microrotations part 2 isotropic reduced Cosserat model
Bulletin of the Seismological Society of America, 2009Co-Authors: Elena F Grekova, M A Kulesh, G C HermanAbstract:In this article, we consider a problem of the surface elastic wave propagation within the framework of the isotropic Cosserat Continuum. The medium deformation in this model is described not only by the displacement vector but also by a kinematically independent rotation vector. We discuss the general solution of equations of motion. This solution describes the following wave types: longitudinal and transverse bulk waves, Rayleigh wave, surface transverse wave in a half-space as well as Lamb wave and transverse wave in a thin layer. Within the framework of Cosserat Continuum, both the Rayleigh and surface transverse waves in a half-space are dispersive. The transverse wave in a thin layer and the surface transverse wave in a half-space do not have any analogies in the classical elasticity theory.
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wave propagation in rocks modeled as reduced Cosserat Continuum with weak anisotropy
67th EAGE Conference & Exhibition, 2005Co-Authors: Elena F Grekova, G C HermanAbstract:P164 0-000 WAVE PROPAGATION IN ROCKS MODELED AS Abstract REDUCED Cosserat Continuum WITH WEAK ANISOTROPY ELENA F. GREKOVA 1 and GERARD C.HERMAN 2 1 Institute for Problems in Mechanical Engineering of Russian Academy of Sciences St. Petersburg Russia 2 Shell International E & P and Delft University The Netherlands Wave propagation in rocks can exhibit frequency dependence and attenuation due to the complex microstructure. From this frequency dependence important microscale properties of the rock can be obtained with the aid of an appropriate constitutive model. Well established effective medium methods do not address this frequency dependence. We develop the reduced
Mustafa I Alsaleh - One of the best experts on this subject based on the ideXlab platform.
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the evolution of shear bands in sand numerical investigations based on an elasto plastic Cosserat Continuum approach
International Workshop on Bifurcation and Degradation in Geomaterials, 2014Co-Authors: Babak Ebrahimian, Mustafa I AlsalehAbstract:This research is focused on the numerical investigations of the evolution of shear bands and polar effects within a planar layer of cohessionless and dry sand material under shearing. In this regard, micro-polar (Cosserat) Continuum is used to account for micro-rotations, couple stresses and size effect in sand. In particular, extending the non-polar version of the employed elasto-plastic soil model is presented within the framework of Cosserat Continuum. Non-linearity is considered in constitutive relations and geometry for the finite element implementation. It is demonstrated that strain localization with a finite thickness occurs under large quasi-static shearing. Location, thickness and evolution of strain localization are strongly affected by the rotating resistance of boundary grains of sand layer and the boundary conditions of entire system. The localization patterns are different within finite and infinite shear layers, depending on the prescribed lateral boundary conditions.
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modeling shear localization along granular soil structure interfaces using elasto plastic Cosserat Continuum
International Journal of Solids and Structures, 2012Co-Authors: Babak Ebrahimian, Asadollah Noorzad, Mustafa I AlsalehAbstract:Abstract The current study presents finite element simulations of shear localization along the interface between cohesionless granular soil and bounding structure under large shearing movement. Micro-polar (Cosserat) Continuum approach is applied in the framework of elasto-plasticity in order to overcome the numerical problems of localization modeling seen in the conventional Continuum mechanics. The effects of different micro-polar kinematic boundary conditions, along the interface, on the evolution and location of shear band are shown by the numerical results. Furthermore, shear band thickness is also investigated for its dependence on the initial void ratio, vertical pressure and mean grain size. Here, the distribution and evolution of static and kinematic quantities are the main focuses regarding infinite layer of micro-polar material during plane shearing, especially with advanced large movement of bounding structure. The influence of such movement has not been investigated yet in the literature. Based on the results obtained from this study, shear localization appears parallel to the direction of shearing. It occurs either in the middle of granular layer or near boundaries, regarding the assumed micro-polar kinematic boundary conditions at the bottom and top surfaces of granular soil layer. Narrower shear band is observed in lower rotation resistance of soil particles along the interface. It is emphasized that the displacement magnitude of bounding structure has significant effect on the distribution and evolution of state variables and polar quantities in the granular soil layer. However, continuous displacement has no meaningful effect on the thickness of shear band. Here, smooth distributions of void ratio and shear stress components are obtained within the shear band, what the other previous numerical investigations did not receive. Despite indirect linking of Lade’s model to the critical state soil mechanics, state variables tend towards asymptotical stationary condition in large shear deformation.
Ioannis Stefanou - One of the best experts on this subject based on the ideXlab platform.
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Numerical Analysis of Strain Localization in Rocks with Thermo-hydro-mechanical Couplings Using Cosserat Continuum
Rock Mechanics and Rock Engineering, 2018Co-Authors: Hadrien Rattez, Ioannis Stefanou, Jean Sulem, Manolis Veveakis, Thomas PouletAbstract:A numerical model for thermo-hydro-mechanical strong couplings in an elasto-plastic Cosserat Continuum is developed to explore the influence of frictional heating and thermal pore fluid pressurization on the strain localization phenomenon. This model allows specifically to study the complete stress–strain response of a rock specimen, as well as the size of the strain localization zone for a rock taking into account its microstructure. The numerical implementation in a finite element code is presented, matching adequately analytical solutions or results from other simulations found in the literature. Two different applications of the numerical model are also presented to highlight its capabilities. The first one is a biaxial test on a saturated weak sandstone, for which the influence on the stress–strain response of the characteristic size of the microstructure and of thermal pressurization is investigated. The second one is the rapid shearing of a mature fault zone in the brittle part of the lithosphere. In this example, the evolution of the thickness of the localized zone and the influence of the permeability change on the stress–strain response are studied.
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Strain Localization with Rate Dependent Models Versus Cosserat Continuum: An Illustrative Example
Springer Series in Geomechanics and Geoengineering, 2017Co-Authors: Ioannis Stefanou, Jean SulemAbstract:A simple example of adiabatic shearing of a rock layer under constant shear stress is considered in order to investigate and juxtapose two different modeling frameworks concerning strain localization and shear band thickness. The first framework is the Cauchy Continuum with a rate dependent constitutive law (viscoplasticity). The second modeling framework is Cosserat elastoplasticity. Cosserat Continuum is a special case of higher order continua. It is shown that the conditions for shear band triggering have a similar mathematical form, even though the starting point is different from a physical point of view.
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A limit analysis approach based on Cosserat Continuum for the evaluation of the in-plane strength of discrete media: application to masonry
European Journal of Mechanics - A Solids, 2017Co-Authors: Michele Godio, Ioannis Stefanou, Jean Sulem, Karam Sab, Seddik SakjiAbstract:In the frame of Cosserat Continuum theory, an upscaling procedure for the assessment of the in-plane strength domain of discrete media is developed. The procedure is the extension to the Cosserat Continuum of a procedure initially formulated for the Cauchy Continuum, based on the kinematic approach of limit analysis and the classical homogenisation theory. The extension to the Cosserat Continuum is made in order to take into account the effect of particles' rotation on the strength of the discrete medium. The procedure is illustrated with regard to periodic assemblies of blocks in contact and is then generalised to the whole class of discrete periodic media with particles of the same type. The case of masonry is considered as an application. Strength criteria of columns and walls are formulated in terms of non-symmetric stresses and in-plane couples. The procedure allows to show how the in-plane strength of the medium is reduced as a result of particles' rotation.
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modeling of fault gouges with Cosserat Continuum mechanics influence of thermal pressurization and chemical decomposition as coseismic weakening mechanisms
Journal of Structural Geology, 2012Co-Authors: Emmanuil Veveakis, Jean Sulem, Ioannis StefanouAbstract:In this paper we study the impact of thermal pressurization and mineral decomposition reactions under seismic deformation conditions (e.g., slip rates of about 1 m/s) triggered by shear heating, to the stability of a saturated fault material. By using higher order Continuum considerations, allowing for rotational degrees of freedom to the gouge material, we verify that the micro-inertia of the Cosserat Continuum may regularize the ill-posed problem of simple shear of a fault and that the thermal effects promote localization of deformation into ultra-thin shear bands. It is shown that the width of these structures depends on the parameters of the decomposition reaction considered, obtaining values as low as 100 μm, in agreement with microstructural evidence from natural and artificial faults.
