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1.
Displacement and mixed finite element formulations of shear localization in materials are presented. The formulations are based on hypoplastic constitutive laws for soils and the mixed enhanced treatment involving displacement, strain and stress rates as independently varied fields. Included in these formulations are the standard displacement method, the three‐field mixed formulation, the enhanced assumed strain method and the mixed enhanced strain method. Several numerical examples demonstrating the capability and performance of the different finite element formulations are presented. The numerical results are compared with available experimental data for Hostun RF sand and numerical results for Karlsruhe sand on biaxial tests. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
2.
Modelling of coupled fluid‐mechanical problems in fractured geological media using enriched finite elements 
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下载免费PDF全文 Jose Roberto Silvestre Euripedes do Amaral Vargas Jr. Luiz Eloy Vaz Antonio Claudio Soares 《国际地质力学数值与分析法杂志》2015,39(10):1104-1140
Geological environments, such as petroleum reservoirs, normally exhibit physical discontinuities, for example, fractures and faults. Because of the reduced thickness of these discontinuities, finite element formulations with strong discontinuity have been applied to the numerical modelling of geological environments. Until now, two relevant characteristics of petroleum reservoirs have not been addressed by these formulations. The first is the pore pressure jump in the direction normal to a discontinuity in a fluid‐mechanical coupling condition, which is present primarily in sealing faults owing to the contrast of permeability with the porous medium. The absence of this jump can affect the prediction of the deformability of a physical discontinuity. Furthermore, reservoir models frequently use coarse meshes. Thus, the method used to evaluate the pore pressure in the discontinuity may exhibit a strong dependence relative to the mesh refinement. Based on these characteristics, in this study, a formulation of an enriched finite element for application to coupled fluid‐mechanical problems with pre‐existing physical discontinuities saturated by a single fluid is presented. The formulation employs discontinuous interpolation functions and enables the reproduction of jumps of displacement and pore pressure associated with a discontinuity inside the element without the need to discretise it. An approximation to estimate the pore pressure in the discontinuity was developed, one which seeks to minimise the influence of refinement. The element's response is verified by comparison with a one‐dimensional analytical solution and simple examples that are simulated using commercial software. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
3.
Unbounded plane stress and plane strain domains subjected to static loading undergo infinite displacements, even when the zero displacement boundary condition at infinity is enforced. However, the stress and strain fields are well behaved, and are of practical interest. This causes significant difficulty when analysis is attempted using displacement‐based numerical methods, such as the finite‐element method. To circumvent this difficulty problems of this nature are often changed subtly before analysis to limit the displacements to finite values. Such a process is unsatisfactory, as it distorts the solution in some way, and may lead to a stiffness matrix that is nearly singular. In this paper, the semi‐analytical scaled boundary finite‐element method is extended to permit the analysis of such problems without requiring any modification of the problem itself. This is possible because the governing differential equations are solved analytically in the radial direction. The displacement solutions so obtained include an infinite component, but relative motion between any two points in the unbounded domain can be computed accurately. No small arbitrary constants are introduced, no arbitrary truncation of the domain is performed, and no ill‐conditioned matrices are inverted. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
4.
Modelling shear band is an important problem in analysing failure of earth structures in soil mechanics. Shear banding is the result of localization of deformation in soil masses. Most finite element schemes are unable to model discrete shear band formation and propagation due to the difficulties in modelling strain and displacement discontinuities. In this paper, a framework to generate shear band elements automatically and continuously is developed. The propagating shear band is modelled using discrete shear band elements by splitting the original finite element mesh. The location or orientation of the shear band is not predetermined in the original finite element mesh. Based on the elasto‐perfect plasticity with an associated flow rule, empirical bifurcation and location criteria are proposed which make band propagation as realistic as possible. Using the Mohr–Coulomb material model, various results from numerical simulations of biaxial tests and passive earth pressure problems have shown that the proposed framework is able to display actual patterns of shear banding in geomaterials. In the numerical examples, the occurrence of multiple shear bands in biaxial test and in the passive earth pressure problem is confirmed by field and laboratory observations. The effects of mesh density and mesh alignment on the shear band patterns and limit loads are also investigated. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
5.
Poroelastic two‐phase material modeling: theoretical formulation and embedded finite element method implementation 下载免费PDF全文
下载免费PDF全文 Nathan Benkemoun Rachel Gelet Emmanuel Roubin Jean‐Baptiste Colliat 《国际地质力学数值与分析法杂志》2015,39(12):1255-1275
This paper presents the formulation of FEMs for the numerical modeling of a poroelastic two‐phase (aggregates/mixture phase) solid. The displacement and pressure fields are decomposed, following the Enhanced Assumed Strain (EAS) method, into a regular part and an enhanced part. This leads to discontinuous strain and pressure gradient fields allowing to capture the jump in mechanical and hydrical properties passing through the interface between the aggregates and the mixture phase. All these enhanced fields are treated in the context of the embedded FEM through a local enhancement of the finite element interpolations as these jumps appear. The local character of these interpolations leads after a static condensation of the enhanced fields to a problem exhibiting the same structure as common poroelastic finite element models but incorporating now the mechanical and hydrical properties of a two‐phase solid. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
6.
It is well established that severe numerical difficulties may arise when the displacement finite element method is used to analyse the behaviour of incompressible solids and this is particularly true for axisymmetric problems. These numerical difficulties are caused by excessive kinematic constraints and are reflected by strong oscillations in the calculated stress distribution and overestimations of collapse loads. The purpose of this paper is to present new displacement finite element formulations which are particularly suitable for axisymmetric analysis of incompressible materials. A direct comparison is made of the performance of various displacement finite elements in the analysis of elastic or plastic incompressible materials under axisymmetric loading conditions. Particular attention is focused on the performance of various axisymmetric displacement elements in predicting the stress field of incompressible or nearly incompressible materials. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
7.
Frictional slip plane growth by localization detection and the extended finite element method (XFEM)
This paper is concerned with developing a numerical tool for detecting instabilities in elasto‐plastic solids (with an emphasis on soils) and inserting a discontinuity at these instabilities allowing the boundary value problem to proceed beyond these instabilities. This consists of implementing an algorithm for detection of strong discontinuities within a finite element (FE) framework. These discontinuities are then inserted into the FE problem through the use of a displacement field enrichment technique called the extended finite element method (XFEM). The newly formed discontinuities are governed by a Mohr–Coulomb frictional law that is enforced by a penalty method. This implementation within an FE framework is then tested on a compressive soil block and a soil slope where the discontinuity is inserted and grown according to the localization detection. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
8.
P. H. Morris 《国际地质力学数值与分析法杂志》2005,29(2):127-140
Analytical solutions are presented for linear finite‐strain one‐dimensional consolidation of initially unconsolidated soil layers with surcharge loading for both one‐ and two‐way drainage. These solutions complement earlier solutions for initially unconsolidated soil layers without surcharge and initially normally consolidated soil layers with surcharge. Small‐strain solutions for the consolidation of initially unconsolidated soil layers with surcharge loading are also presented, and the relationship between the earlier solutions for initially unconsolidated soil without surcharge and the corresponding small‐strain solutions, which was not addressed in the earlier work, is clarified. The new solutions for initially unconsolidated soil with surcharge loading can be applied to the analysis of low stress consolidation tests and to the partial validation of numerical solutions of non‐linear finite‐strain consolidation. They also clarify a formerly perplexing aspect of finite‐strain solution charts first noted in numerical solutions. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
9.
Strain localization developing inside soft rock specimens is examined through experimental observation and numerical simulation. In the experimental study, soft rock specimens are sheared at different strain rates under plane strain conditions and deformation and strain localization characteristics are analysed. Transition of localization mode from highly localized mode for higher strain rate to distributed and diffused mode of strain localization for lower strain rates was observed. In the numerical study, simulations of plane strain compression tests are carried out at different strain rates by using an overstressed‐type elasto‐viscoplastic model in finite element computations. The role of strain rates on setting gradients of strain fields across shear band is clarified. The probable mechanism for transition of localization mode is discussed. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
10.
In geomechanics, limit analysis provides a useful method for assessing the capacity of structures such as footings and retaining walls, and the stability of slopes and excavations. This paper presents a finite element implementation of the kinematic (or upper bound) theorem that is novel in two main respects. First, it is shown that conventional linear strain elements (6‐node triangle, 10‐node tetrahedron) are suitable for obtaining strict upper bounds even in the case of cohesive‐frictional materials, provided that the element sides are straight (or the faces planar) such that the strain field varies as a simplex. This is important because until now, the only way to obtain rigorous upper bounds has been to use constant strain elements combined with a discontinuous displacement field. It is well known (and confirmed here) that the accuracy of the latter approach is highly dependent on the alignment of the discontinuities, such that it can perform poorly if an unstructured mesh is employed. Second, the optimization of the displacement field is formulated as a standard second‐order cone programming (SOCP) problem. Using a state‐of‐the‐art SOCP code developed by researchers in mathematical programming, very large example problems are solved with outstanding speed. The examples concern plane strain and the Mohr–Coulomb criterion, but the same approach can be used in 3D with the Drucker–Prager criterion, and can readily be extended to other yield criteria having a similar conic quadratic form. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
11.
The present study investigates propagation of a cohesive crack in non‐isothermal unsaturated porous medium under mode I conditions. Basic points of skeleton deformation, moisture, and heat transfer for unsaturated porous medium are presented. Boundary conditions on the crack surface that consist of mechanical interaction of the crack and the porous medium, water, and heat flows through the crack are taken into consideration. For spatial discretization, the extended finite element method is used. This method uses enriched shape functions in addition to ordinary shape functions for approximation of displacement, pressure, and temperature fields. The Heaviside step function and the distance function are exploited as enrichment functions for representing the crack surfaces displacement and the discontinuous vertical gradients of the pressure and temperature fields along the crack, respectively. For temporal discretization, backward finite difference scheme is applied. Problems solved from the literature show the validity of the model as well as the dependency of structural response on the material properties and loading. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
12.
冲击荷载下土体位移特征研究 总被引：10，自引：0，他引：10
建立了冲击荷载作用下土体动力压密有限元方程及其数值计算方法。用Ansys-Ls-dyna软件包对山西化肥厂地基冲击荷载作用后土体的动力响应进行了分析,得出了冲击荷载作用下分层土体中的位移分布特征及其它们的变化过程,计算结果与实测结果吻合较好。研究结果表明：冲击荷载作用下土体位移的影响范围为一椭球体。侧向加固半径距荷载作用中心接近2D(D为夯锤直径),荷载作用中心下加固深度能达到2D甚至更大。 相似文献
13.
This paper presents a relatively simple method for three‐dimensional liquefaction analysis of granular soil under offshore foundations. In this method, the Mohr–Coulomb model, which defines the elasto–plastic stress–strain relationship under monotonic loading, is modified to accommodate the plastic strains generated by cyclic loading. The effects of cyclic loading, evaluated from the results of laboratory tests on saturated samples of soil, are incorporated into the model. The method is implemented in an efficient finite element program for analyses of three‐dimensional consolidating soil. The practicability of the model is demonstrated by analysis of a typical offshore foundation, and the predictions of the numerical analysis are compared with the observed behaviour of the foundation. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
14.
模拟三维裂纹问题的扩展有限元法 总被引：4，自引：1，他引：3
扩展有限元法是一种在常规有限元框架内求解强和弱不连续问题的新型数值方法,其计算网格与不连续面相互独立,因此模拟移动不连续面时无需对网格进行重新剖分。给出了模拟三维裂纹问题的扩展有限元法。在常规有限元位移模式中,基于单位分解的思想加进一个阶跃函数和二维渐近裂尖位移场,反映裂纹处位移的不连续性。用两个水平集函数表示裂纹。采用线性互补法求解裂纹面非线性接触条件,不需要迭代,提高了计算效率。采用两点位移外推法计算裂纹前缘应力强度因子。给出了3个三维弹性静力问题算例,其结果显示了所提方法能获得高精度的应力强度因子,并能有效地处理裂纹面间的接触问题,同时表明扩展有限元结合线性互补法求解不连续问题具有较好的前景。 相似文献
15.
针对岩石类材料压剪破坏,国内外学者做了大量真实岩石和模型材料的试验,并进行相应的数值模拟工作。但由于试验结果往往具有很强的离散性,且对影响试验结果的各因素缺乏系统地理论分析,加之传统常规有限元在处理裂纹这类强不连续问题时存在很大的困难,如在裂尖附近的高应力区需要剖分令人难以接受的密度的网格,同时在模拟裂纹生长时还需要对网格进行重新剖分,操作繁琐复杂,效率极低,因此,针对压剪复合断裂翼裂纹扩展规律的研究始终没有取得令人满意的成果。对原生裂纹的几何形态,主裂纹面与其间填充物的相互作用对翼裂纹起裂角的影响做了系统的理论分析,并利用扩展有限元对翼型裂纹扩展全过程进行数值模拟,与理论分析结果对比,吻合良好。相关成果为以后针对压剪复合断裂的研究提供了理论分析框架,同时对今后相关试验的开展具有理论指导作用 相似文献
16.
Behnam V. Damirchi Marcelo R. Carvalho Luís A. G. Bitencourt Osvaldo L. Manzoli Daniel Dias‐da‐Costa 《国际地质力学数值与分析法杂志》2021,45(1):83-107
A new discrete fracture model is introduced to simulate the steady‐state fluid flow in discontinuous porous media. The formulation uses a multi‐layered approach to capture the effect of both longitudinal and transverse permeability of the discontinuities in the pressure distribution. The formulation allows the independent discretisation of mesh and discontinuities, which do not need to conform. Given that the formulation is developed at the element level, no additional degrees of freedom or special integration procedures are required for coupling the non‐conforming meshes. The proposed model is shown to be reliable regardless of the permeability of the discontinuity being higher or lower than the surrounding domain. Four numerical examples of increasing complexity are solved to demonstrate the efficiency and accuracy of the new technique when compared with results available in the literature. Results show that the proposed method can simulate the fluid pressure distribution in fractured porous media. Furthermore, a sensitivity analysis demonstrated the stability regarding the condition number for wide range values of the coupling parameter. 相似文献
17.
Analysis of large deformation of geomaterials subjected to time‐varying load poses a very difficult problem for the geotechnical profession. Conventional finite element schemes using the updated Lagrangian formulation may suffer from serious numerical difficulties when the deformation of geomaterials is significantly large such that the discretized elements are severely distorted. In this paper, an operator‐split arbitrary Lagrangian–Eulerian (ALE) finite element model is proposed for large deformation analysis of a soil mass subjected to either static or dynamic loading, where the soil is modelled as a saturated porous material with solid–fluid coupling and strong material non‐linearity. Each time step of the operator‐split ALE algorithm consists of a Lagrangian step and an Eulerian step. In the Lagrangian step, the equilibrium equation and continuity equation of the saturated soil are solved by the updated Lagrangian method. In the Eulerian step, mesh smoothing is performed for the deformed body and the state variables obtained in the updated Lagrangian step are then transferred to the new mesh system. The accuracy and efficiency of the proposed ALE method are verified by comparison of its results with the results produced by an analytical solution for one‐dimensional finite elastic consolidation of a soil column and with the results from the small strain finite element analysis and the updated Lagrangian analysis. Its performance is further illustrated by simulation of a complex problem involving the transient response of an embankment subjected to earthquake loading. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
18.
Analyses for the response of a linear visco‐elastic system subjected to axi‐symmetric vertical circular loading are presented. Hankel transforms with respect to the radial spatial coordinate are used to reduce the three‐dimensional problem to that involving only a single spatial dimension, which is then discretized using the finite element method. Three techniques are employed to handle the time factor in the visco‐elastic material: (i) direct time integration; (ii) Fourier transforms; and (iii) Laplace transforms. These methods are compared and evaluated through their numerical results. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
19.
The bulk strain induced by excavation of rooms for storage of highly radioactive waste is usually unimportant, but the change in aperture and shear displacement of permeable fractures may be of practical importance. Hence, the normal and shear of such discontinuities have to be considered and are commonly predicted by using special deformation moduli termed “normal” and “shear” stiffnesses in numerical calculations. For the use of some finite element methods, these have to be converted to compression and shear moduli ,which, in turn, requires that the thickness of the discontinuity is known. The normal and shear strain can be expressed in terms of soil mechanical parameters, yielding the compression modulus M and the shear modulus G, with the required form for finite element calculations. By definition they are functions of the normal and shear stiffness Kn and Ks. It is concluded that calculation of the normal and shear strain of discontinuities with clastic fillings by the use of finite element methods and deformation moduli derived from stiffness numbers is very uncertain except when the geometry of the weaknesses can be accurately defined. 相似文献
20.
扩展有限元法是一种在常规有限元框架内求解强和弱不连续问题的新型数值方法,其原理是在裂尖附近用一些奇异函数和沿裂纹面用阶跃函数加强传统有限元的基,以考虑跨过裂纹的位移场的不连续,该加强策略允许计算网格独立于不连续体几何。讨论了扩展有限元法的一些数值方面,主要包括：水平集法确定界面和加强节点与加强方式、裂尖加强范围的选择、J积分区域的确定和积分方案等。 相似文献