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1.
Boris Jeremi&#x; Gerik Scheuermann Jan Frey Zhaohui Yang Bernd Hamann Kenneth I. Joy Hans Hagen 《国际地质力学数值与分析法杂志》2002,26(10):925-944
We present a novel technique for visualizing tensors in three dimensional (3D) space. Of particular interest is the visualization of stress tensors resulting from 3D numerical simulations in computational geomechanics. To this end we present three different approaches to visualizing tensors in 3D space, namely hedgehogs, hyperstreamlines and hyperstreamsurfaces. We also present a number of examples related to stress distributions in 3D solids subjected to single and load couples. In addition, we present stress visualizations resulting from single‐pile and pile‐group computations. The main objective of this work is to investigate various techniques for visualizing general Cartesian tensors of rank 2 and it's application to geomechanics problems. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
2.
基于内变量和张量函数表示定理的本构方程 总被引：2，自引：2，他引：0
针对各向同性材料,基于张量函数表示定理,建立了本构关系的张量不变性表示,其中,3个不可约基张量取决于应力的0～2次幂,且相互正交,3个系数由塑性应变增量和应力的不变量表示。基于塑性应变增量的不变量定义内变量,本构关系归结为确定内变量的演化。使用张量函数表示定理,给出了内变量演化方程的一般表达式,它取决于应力不变量的增量,因而与主轴旋转无关。讨论了如何根据试验资料和引入适当的假定,确定具体的演化方程。通过与塑性势理论和多重屈服面理论进行比较,表明所建模型是这些理论的最一般表示,且简捷直观、使用方便。 相似文献
3.
This paper presents novel visualization techniques to simplify representation of the fourth‐order material stiffness tensor as a set of three‐dimensional geometric objects. Stiffness visualization aids in understanding the complex stiffness characteristics of highly non‐linear constitutive models including modelled material anisotropy and loading path dependent stiffness variation. Stiffness visualization is relevant for understanding the relationship of material stiffness to global behaviour in the analysis of a boundary value problem. The spherical pulse stiffness visualization method, developed in the acoustics field, is extended to visualize stiffness of geomaterials using three three‐dimensional objects. This method is limited to relatively simple constitutive models with symmetric stiffness matrices insensitive to loading magnitude and direction. A strain dependent stiffness visualization method is developed that allows the examination of material stiffness for a range of loading directions and is suitable for highly non‐linear and path dependent material models. The proposed stiffness visualization can be represented as 3‐D, 2‐D and 1‐D objects. The visualization technique is used to represent material stiffness and its evolution during simulated soil laboratory tests and deep excavation construction. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
4.
A granular material consists of an assemblage of particles with contacts newly formed or disappeared, changing the micromechanical structures during macroscopic deformation. These structures are idealized through a strain space multiple mechanism model as a twofold structure consisting of a multitude of virtual two‐dimensional mechanisms, each of which consists of a multitude of virtual simple shear mechanisms of one‐dimensional nature. In particular, a second‐order fabric tensor describes direct macroscopic stress–strain relationship, and a fourth‐order fabric tensor describes incremental relationship. In this framework of modeling, the mechanism of interlocking defined as the energy less component of macroscopic strain provides an appropriate bridge between micromechanical and macroscopic dilative component of dilatancy. Another bridge for contractive component of dilatancy is provided through an obvious hypothesis on micromechanical counterparts being associated with virtual simple shear strain. It is also postulated that the dilatancy along the stress path beyond a line slightly above the phase transformation line is only due to the mechanism of interlocking and increment in dilatancy due to this interlocking eventually vanishing for a large shear strain. These classic postulates form the basis for formulating the dilatancy in the strain space multiple mechanism model. The performance of the proposed model is demonstrated through simulation of undrained behavior of sand under monotonic and cyclic loading. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
5.
This paper develops a novel return mapping algorithm for the numerical integration of general isotropic finite strain elastoplastic constitutive models for geomaterials. The constitutive formulation is founded on multiplicative decomposition of the deformation gradient. The logarithmic strain measure as well as the exponential approximation of the plastic flow rule is utilized to restore the standard infinitesimal format return mapping algorithm. Central to the algorithm is the exploitation of a set of three mutually orthogonal unit base tensors for the representation of constitutive relations and the corresponding integration of the rate form of the constitutive equations. The base tensors constitute a local cylindrical coordinate system in the principal space, which allows to formulate the return mapping algorithm in the three‐dimensional space and reduce the dimension of the problem to be analyzed from six down to three. With the proposed approach, direct determination of the principal axes and the transformation procedure between the general space and the principal space, as required in traditional spectral decomposition, are avoided. Furthermore, the matrices that are involved in the inversion evaluation take simple forms, leading to extremely easy inverse computation. As a result, the consistent tangent operator can be streamlined into a form simpler and more compact than those by conventional integration methods. Following the formulation of the integration procedure, a numerical experiment is performed to assess the accuracy and efficiency of the proposed algorithm. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
6.
The average seismic strain rate is estimated for the seismotectonic zone of the northern/central parts of the Gulf of Suez. The principal strain rate tensor and velocity tensor were derived from a combination of earthquake focal mechanisms data and seismic moment of small-sized earthquakes covering a time span of 13 years (1992–2004). A total of 17 focal mechanism solutions have been used in the calculation of the moment tensor summation. The local magnitudes (MLs) of these events range from 2.8 to 4.7. The analysis indicates that the dominant mode of deformation in the central and northern parts of the Gulf of Suez is extension at a rate of 0.008 mm/year in N28°E direction and a small crustal thinning of 0.0034 mm/year. This low level of strain means that this zone experienced a little seismic deformation. There is also a right lateral shear motion along the ESE–WNW direction. This strain pattern is consistent with the predominant NW–SE normal faulting and ESE–WNW dextral transtensive faults in this zone. Comparing the results obtained from both stress and strain tensors, we find that the orientations of the principal axes of both tensors have the same direction with a small difference between them. Both tensors show a predominantly extensional domain. The nearly good correspondence between principal stress and strain orientations in the area suggests that the tectonic strength is relatively uniform for this crustal volume. 相似文献
7.
A matrix relating stress and elastic strain tensors for anisotropic particulate materials has been derived. The magnitude of the matrix depends on the state of the material anisotropy. Anisotropy in granular materials depends on strain because normal and tangential particle contact forces, as well as the spatial distribution of the contacts, vary with stress and strain. However, the rotation tensor and the strain tensor cannot be independent; they must satisfy certain constraints to meet the requirement for macroscopic stress tensor symmetry. These conditions and constraints lead to the derivation of the matrix presented in this article. The principal directions of the stress tensor and strain tensor are generally not coincident, and the values of deformation parameters, Young's modulus and Poisson's ratio, are direction dependent; these two aspects are also discussed in this paper. Whereas this matrix can be used in static numerical analyses for elastic problems, we note that this relationship can also be used as a basis upon which to derive a fully incremental stress–strain relationship for anisotropic granular materials in the plastic state, where the anisotropy is evolving with strain. 相似文献
8.
In this paper, a study is made of the generalization of constitutive models for geomaterials from two‐dimensional stress and strain states to three‐dimensional stress and strain states. Existing methods of model generalization are reviewed and their deficiencies are highlighted. A new method is proposed based on geometries of the model imprints on two normal planes. Using the proposed method, various three‐dimensional failure criterions suitable for geomaterials are implemented directly into a two‐dimensional model and the generalized model is identical to its original form for the axially symmetric condition. To demonstrate the application of the proposed method, the Modified Cam Clay model is extended using the Matsuoka–Nakai failure criterion. Simulations of soil behaviour for loading in the principal stress space are presented and analysed. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
9.
Wheeler, Sharma and Buisson proposed an elasto‐plastic constitutive model for unsaturated soils that couples the mechanical and water retention behaviours. The model was formulated for isotropic stress states and adopts the mean Bishop's stress and modified suction as stress state variables. This paper deals with the extension of this constitutive model to general three‐dimensional stress conditions, proposing the generalized stress–strain relationships required for the numerical integration of the constitutive model. A characteristic of the original model is the consideration of a number of elasto‐plastic mechanisms to describe the complex behaviour of unsaturated soils. This work presents the three‐dimensional formulation of these coupled irreversible mechanisms in a generalized way including anisotropic loading. The paper also compares the results from the model with published experiments performed under different loading conditions. The response of the model is very satisfactory in terms of both mechanical and water retention behaviours. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
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11.
In this paper, we consider the upscaling of Hooke's law and its parameters on the fine scale, to a similar law with upscaled parameters on a larger scale. It is assumed that the fine scale material properties of the rock are imperfectly layered. In the governing equations, the deviations from perfect layering introduce a small parameter that can be used in perturbation series expansions for the stress, the strain, and the displacement. In the approximation of order zero the upscaled compliance matrix contains the well-known Backus parameters; this approximation holds exactly for a perfect layering. However, many natural rock types are imperfectly layered and in that case the approximation of order zero may not be sufficiently accurate. Therefore, we consider also the first order corrections. The derivation and results are presented both for the most general case and for the much simpler case in which the fine scale Poisson ratio may be assumed constant. From thermodynamic principles, it follows that the compliance tensor is symmetric on the fine scale. However, it is shown that the argument for symmetry cannot be extended to upscaled rigidities. One of the most important conclusions is that upscaled compliance tensors are nonsymmetric when there are trends in the deviations from perfect layering. 相似文献
12.
基于复合材料以及连续介质损伤理论,给出了岩石材料的各向异性损伤破坏模型。通过引入与岩石材料单轴加载行为相对应的特征模态构成的四阶对称损伤张量,描述了岩石材料的损伤演化过程,其中对不同主应变方向采用不同的损伤变量,而对同一主应变方向拉压时的损伤则采用不同的损伤变量来描述。在数值模拟岩石破坏过程的程序中,采用了张量分解的方法。将该模型编写用户材料子程序,并嵌入到大型有限元分析程序ABAQUS中,通过ABAQUS/EXPLICIT SOLVER的显式有限元算法求解。利用此程序对岩石材料的单轴压缩进行了数值模拟。 相似文献
13.
岩体水力学基础（七）：岩体水力学参数的确定方法 总被引：15，自引：2，他引：13
仵彦卿 《水文地质工程地质》1998,25(2):42-48
本文在对参数的内涵分析的基础上,提出了参数的类型及其概念。介绍了岩体渗透系数张量确定的统计学方法、野外抽（压）水试验方法、数学模型反演求解方法,以及应力与渗透系数关系参数的确定方法。 相似文献
14.
The 10 June 2012 Mw 6.0 aftershock sequence in southwestern Anatolia is examined. Centroid moment tensors for 23 earthquakes with moment magnitudes (Mw) between 3.7 and 6.0 are determined by applying a waveform inversion method. The mainshock is a shallow focus strike-slip with reverse component event at a depth of 30 km. The seismic moment (Mo) of the mainshock is estimated as 1.28 × 1018 Nm and rupture duration of the Fethiye mainshock is 38 s. The focal mechanisms of the aftershocks are mainly strike-slip faulting with a reverse component. The geometry of the focal mechanisms reveals a strike-slip faulting regime with NE–SW trending direction of T-axis in the entire activated region. A stress tensor inversion of focal mechanism data is performed to obtain a more accurate picture of the Fethiye earthquake stress field. The stress tensor inversion results indicate a predominant strike-slip stress regime with a NW–SE oriented maximum horizontal compressive stress (SH). According to variance of the stress tensor inversion, to first order, the Fethiye earthquake area is characterized by a homogeneous interplate stress field. The Coulomb stress change associated with the mainshock and the largest aftershock are also investigated to evaluate any significant enhancement of stresses along the Gulf of Fethiye and surrounding region. Positive lobes with stress more than 0.4 bars are obtained, indicating that these values are large enough to increase the Coulomb stress failure towards NNW–SSE and E–W directions. 相似文献
15.
The restrictions imposed by the form-invariance principle on the structure of the elasto-plastic constitutive law for small strains are examined. It is shown that the yield and plastic potential functions may depend on the joint invariants of the stress and plastic strain tensors in addition to their dependence on the direct invariants of these tensors and additional scalar hardening parameters such as the plastic work; inclusion of the joint invariants as parameters in the constitutive functions allows for induced anisotropy during plastic deformation. It is demonstrated that the physical meaning of the joint invariants is related to the deviation of the principal directions of the stress tensor from those of the plastic strain tensor. It is also shown that only three cases of anisotropy (orthorhombic, transverse and isotropy) are possible in the types of material models discussed herein. The model proposed in this paper does not imply coaxiality between the principal directions of the stress and, plastic strain increment tensors; however, implications of the assumption of coaxiality on the structure of the constitutive equations is investigated. It is shown that coaxiality does not necessarily imply isotropy, but no deviations from coaxiality can be expected in isotropic materials. 相似文献
16.
NIED seismic moment tensor catalogue for regional earthquakes around Japan: quality test and application 总被引：4，自引：0，他引：4
We have examined the quality of the National Research Institute for Earth Science and Disaster Prevention (NIED) seismic moment tensor (MT) catalogue obtained using a regional broadband seismic network (FREESIA). First, we examined using synthetic waveforms the robustness of the solutions with regard to data noise as well as to errors in the velocity structure and focal location. Then, to estimate the reliability, robustness and validity of the catalogue, we compared it with the Harvard centroid moment tensor (CMT) catalogue as well as the Japan Meteorological Agency (JMA) focal mechanism catalogue. We found out that the NIED catalogue is consistent with Harvard and JMA catalogues within the uncertainty of 0.1 in moment magnitude, 10 km in depth, and 15° in direction of the stress axes. The NIED MT catalogue succeeded in reducing to 3.5 the lower limit of moment magnitude above which the moment tensor could be reliably estimated. Finally, we estimated the stress tensors in several different regions by using the NIED MT catalogue. This enables us to elucidate the stress/deformation field in and around the Japanese islands to understand the mode of deformation and applied stress. Moreover, we identified a region of abnormal stress in a swarm area from stress tensor estimates. 相似文献
17.
This paper presents a fabric tensor-based bounding surface model accounting for anisotropic behaviour (e.g. the dependency of peak strength on loading direction and non-coaxial deformation) of granular materials. This model is developed based on a well-calibrated isotropic bounding surface model. The yield surface is modified by incorporating the back stress which is proportional to a contact normal-based fabric tensor for characterising fabric anisotropy. The evolution law of the fabric tensor, which is dependent on both rates of the stress ratio and the plastic strain, rules that the material fabric tends to align with the loading direction and evolves towards a unique critical state fabric tensor under monotonic shearing. The incorporation of the evolution law leads to a rotational hardening of the yield surface. The anisotropic critical state is assumed to be independent of the initial values of void ratio and fabric tensor. The critical state fabric tensor has the same intermediate stress ratio (i.e. b value) and principal directions as the critical state stress tensor. A non-associated flow rule in the deviatoric plane is adopted, which is able to predict the non-coaxial flow naturally. The stress–strain relation and fabric evolution of model predictions show a satisfactory agreement with DEM simulation results under monotonic shearing with different loading directions. The model is also validated by comparing with laboratory test results of Leighton Buzzard sand and Toyoura sand under various loading paths. The comparison results demonstrate encouraging applicability of the model for predicting the anisotropic behaviour of granular materials.
相似文献18.
In this paper a micro‐polar continuum approach is proposed to model the essential properties of cohesionless granular materials like sand. The model takes into account the influence of particle rotations, the mean grain size, the void ratio, the stresses and couple stresses. The constitutive equations for the stresses and couple stresses are incrementally non‐linear and based on the concept of hypoplasticity. For plane strain problems the implementation of the model in a finite element program is described. Numerical studies of the evolution of micro‐polar effects within a granular strip under plane shearing are presented. It is shown that the location and evolution of shear localization is strongly influenced by the initial state and the micro‐polar boundary conditions. For large shearing the state quantities tend towards a stationary state for which a certain coupling between the norm of the stress deviator and the norm of the couple stress tensor can be derived. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
19.
Coupled bonded particle and lattice Boltzmann method for modelling fluid–solid interaction 
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下载免费PDF全文 This paper presents a two‐dimensional coupled bonded particle and lattice Boltzmann method (BPLBM) developed to simulate the fluid–solid interactions in geomechanics. In this new technique, the bonded particle model is employed to describe the inter‐particle movement and forces, and the bond between a pair of contacting particles is assumed to be broken when the tensile force or tangential force reaches a certain critical value. As a result the fracture process can be delineated based on the present model for the solid phase comprising particles, such as rocks and cohesive soils. In the meantime, the fluid phase is modelled by using the LBM, and the immersed moving boundary scheme is utilized to characterize the fluid–solid interactions. Based on the novel technique case studies have been conducted, which show that the coupled BPLBM enjoys substantially improved accuracy and enlarged range of applicability in characterizing the mechanics responses of the fluid–solid systems. Indeed such a new technique is promising for a wide range of application in soil erosion in Geotechnical Engineering, sand production phenomenon in Petroleum Engineering, fracture flow in Mining Engineering and fracture process in a variety of engineering disciplines. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献