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1.
Summary Failure of earth structures or laboratory specimens of soils is often characterized by the existence of bands or surfaces at which strain localizes. Numerical simulation of shear band development has attracted the attention of many research groups during past years. Here it is proposed that adaptive remeshing techniques can be applied to better simulate strain localization problems in geotechnique. The algorithm has been previously applied to compressible fluid dynamics problems to capture discontinuities such as shocks. A new refinement functional has been introduced to improve quality of produced meshes. Finally, the algorithm is applied to solve inception and development of shear bands on both homogeneous stress fields and non-homogeneous stress fields.
Adaptive Netzverfeinerung bei Problemen mit Scherfugen-Lokalisierung
Übersicht Das Versagen von Erdbauwerken oder Bodenproben im Labor ist oft durch die Existenz von Flächen mit lokalisierter Deformation gekennzeichnet. Zahlreiche Forschungsgruppen haben sich in den letzten Jahren mit der numerischen Simulation der Scherfugen-Bildung beschäftigt. Zur Verbesserung der Simulation von Scherfugen-Lokalisierung bei bodenmechanischen Problemen wird in diesem Beitrag eine adaptive Netzverfeinerung vorgeschlagen. Dieser Weg wurde schon früher in der Dynamik kompressibler Flüssigkeiten beschritten, um Unstetigkeiten wie Schockfronten zu erfassen. Als Kriterium für die Verfeinerung des Netzes wird in diesem Beitrag ein neues Funktional benutzt. Schließlich wird der Algorithmus auf den Beginn und die Weiterentwicklung von Scherfugen bei homogenen und inhomogenen Spannung zuständen angewandt.


Presented at the workshop on Numerical Methods for Localization and Bifurcation of Granular Bodies, held at the Technical University of Gdansk (Poland), September 25–30, 1989  相似文献   

2.
The tensile deformation localization and the shear band fracture behaviors of sheet metals with strong anisotropy are numerically simulated by using Updating Lagrange finite element method, Quasi-flow plastic constitutive theory[1] and B-L planar anisotropy yield criterion[2]. Simulated results are compared with experimental ones. Very good consistence is obtained between numerical and experimental results. The relationship between the anisotropy coefficientR and the shear band angle θ is found. The project supported by the National Natural Science Foundation of China and the Excellent Youth Teacher Foundation of the State Education Commission of China  相似文献   

3.
Summary The main objective of the present paper is the development of a viscoplastic regularization procedure valid for an adiabatic dynamic process for multi-slips of single crystals. The next objective is to focus attention on the investigation of instability criteria, and particularly on shear band localization conditions.To achieve this aim, an analysis of acceleration waves is given, and advantage is taken of the notion of the instantaneous adiabatic acoustic tensor. If zero is an eigenvalue of the acoustic tensor, then the associated discontinuity does not propagate, and one speaks of a stationary discontinuity. This situation is referred to as the strain localization condition, and corresponds to a loss of hyperbolicity of the dynamical equations. It has been proved that for an, adiabatic process of rate-dependent (elastic-viscoplastic) crystal, the wave speed of discontinuity surface always remains real and different from zero. It means that for this case the initial-value problem is well-posed. However, for an adiabatic process of rate-independent(elastic-plastic) crystal, the wave speed of discontinuity surface can be equal zero. Then the necessary condition for a localized plastic deformation along the shear band to be formed is as follows: the determinant of the instantaneous adiabatic acoustic tensor is equal to zero. This condition for localization is equivalent to that obtained by using the standard bifurcation method. Based on this idea, the conditions for adiabatic shear band localization of plastic deformation have been investigated for single crystals. Particular attention has been focused on the discussion of the influence of thermal expansion, thermal plastic, softening and spatial covariance effects on shear band localization criteria for a planar model of an f.c.c. crystal undergoing symmetric primary-conjugate double slip. The results obtained have been compared with available experimental observations.Finally, it is noteworthy that the viscoplasticity regularization procedure can be used in the developing of an unconditionally stable numerical integration algorithm for simulation of adiabatic inelastic flow processes in ductile single crystals, cf. [21].The paper has been prepared within research programme sponsored by the Committee of Scientific Research under Grant 3 P404 031 07.  相似文献   

4.
Q. Sun  S. Song  J. Liu  M. Fei  F. Jin 《力学快报》2013,3(2):021008
Granular materials exhibit abundant dissipations due to fluctuations in both granular motions and configurations (i.e., granular skeleton) evolutions. Twin granular temperatures Tk and Te are introduced accounting for two types of fluctuations, and the so-called twin granular temperatures theory is established as an extension of granular solid hydrodynamics. By using simulations, the nonaffine deformations in a 2D assembly are simulated by using discrete element methods. By analogizing with microdamages in deformed solids, double scalar damage variables, DP and Dq, are proposed to describe the deformed granular solid under triaxial compressions. Granular flows are found intrinsically turbulent due to the presence of Tk and the Naiver–Stokes equation is obtained for granular flows.  相似文献   

5.
6.
A constitutive relation that accounts for the thermally activated dislocation motion and microstructure interaction is used to study the stability of a homogeneous solution of equations governing the simple shearing deformations of a thermoviscoplastic body. An instability criterion and an upper bound for the growth rate of the infinitesimal deformations superimposed on the homogeneous solution are derived. By adopting Wright and Ockendon's postulate, i.e., the wavelength of the dominant instability mode with the maximum growth rate determines the minimum spacing between shear bands, the shear band spacing is computed. The effect of the initial dislocation density, the nominal strain-rate, and parameters describing the initial thermal activation and the initial microstructure interaction on the shear band spacing are delineated.  相似文献   

7.
8.
Plastic flow localization in ductile materials subjected to pure shear loading and uniaxial tension is investigated respectively in this paper using a reduced strain gradient theory, which consists of the couple-stress (CS) strain gradient theory proposed by Fleck and Hutchinson (1993) and the strain gradient hardening (softening) law (C–W) proposed by Chen and Wang (2000). Unlike the classical plasticity framework, the initial thickness of the shear band and the strain rate distribution in both cases are predicted analytically using a bifurcation analysis. It shows that the strain rate is obviously non-uniform inside the shear band and reaches a maximum at the center of the shear band. The initial thickness of the shear band depends on not only the material intrinsic length lcs but also the material constants, such as the yield strength, ultimate tension strength, the linear hardening and softening shear moduli. Specially, in the uniaxial tension case, the most possible tilt angle of shear band localization is consistent qualitatively with the existing experimental observations. The results in this paper should be useful for engineers to predict the details of material failures due to plastic flow localization.  相似文献   

9.
The paper outlines a relaxation method based on a particular isotropic microstructure evolution and applies it to the model problem of rate independent, partially damaged solids. The method uses an incremental variational formulation for standard dissipative materials. In an incremental setting at finite time steps, the formulation defines a quasi-hyperelastic stress potential. The existence of this potential allows a typical incremental boundary value problem of damage mechanics to be expressed in terms of a principle of minimum incremental work. Mathematical existence theorems of minimizers then induce a definition of the material stability in terms of the sequential weak lower semicontinuity of the incremental functional. As a consequence, the incremental material stability of standard dissipative solids may be defined in terms of weak convexity notions of the stress potential. Furthermore, the variational setting opens up the possibility to analyze the development of deformation microstructures in the post-critical range of unstable inelastic materials based on energy relaxation methods. In partially damaged solids, accumulated damage may yield non-convex stress potentials which indicate instability and formation of fine-scale microstructures. These microstructures can be resolved by use of relaxation techniques associated with the construction of convex hulls. We propose a particular relaxation method for partially damaged solids and investigate it in one- and multi-dimensional settings. To this end, we introduce a new isotropic microstructure which provides a simple approximation of the multi-dimensional rank-one convex hull. The development of those isotropic microstructures is investigated for homogeneous and inhomogeneous numerical simulations.  相似文献   

10.
11.
The present paper briefly reviews analytical studies of the evolution of thermoplastic shear band, i.e. emergence from uniform deformation, post-instability growth and late stage behaviour. The case studied is the simple shear of temperature and rate-dependent materials with heat transfer. Uniform mode exists before a critical state, if no heat flows out of testpiece. Upon reaching the critical state, bifurcation appears as a result of disturbances, which leads to instability and the formation of narrow shear band. Initially, the band, due to temperature disturbance, can shrink with increasing temperature and strain rate owing to unsteady flow. Then heat conduction dominates and causes the shear band to expand. The postmortem appearance of thermo-plastic shear band manifests itself as balance of plastic work rate and heat diffusion. Melting may also take place within the band.  相似文献   

12.
Strain localization is a well known phenomenon, generally associated with plastic deformation and rupture in solids, especially in geomaterials. In this process, deformation is observed to concentrate in narrow zones called shear bands. This phenomenon has been studied extensively in the last 20 years by different researchers, experimentally, theoretically and numerically. A criterion for the onset of localization can be predicted solely on the basis of the constitutive law of the material, using the so-called shear band analysis. This criterion gives the critical orientation, and the critical stress state and strain for a given loading history. An important point, already stressed by Vardoulakis in 1980, is that in particular, out-of-axes shear moduli play a central role in the criterion. These are the moduli involved in the response to a deviatoric stress increment with principal axes oriented at 45° from total stress principal axes. Out-of-axes shear moduli are difficult parameters to calibrate; common tests, with fixed principal stress and strain directions, do not provide any information on these moduli, as long as they remain homogeneous. Still, real civil engineering and environmental problems are definitely not simple axisymmetric triaxial tests; practical modeling involves complex stress paths, and need complex parameters to be calibrated. Only special tests, like compression–torsion on hollow cylinder tests, or even more complex tests can be used for shear moduli calibration. However, shear band initiation in homogeneous, fixed-axes tests does activate out-of-axes shear. Hence, it is natural that shear band analysis makes shear moduli enter into the analysis.Then, a typical inverse analysis approach can be used here: experimental observation of strain localization in triaxial tests can be used together with a proper shear band analysis for the model considered, in order to determine out-of-axes shear moduli.This approach has been used for a stiff marl in the framework of a calibration study on a set of triaxial tests. The steps of the method are presented, and the bifurcation surface in the stress space is exhibited.  相似文献   

13.
The monitored resonant behavior of fatigue specimens of metastable austenitic stainless steel (AISI304) is correlated with its damage accumulation in the very high cycle fatigue (VHCF) regime. The resonant behavior is studied experimentally and shows a distinct transient characteristic. Microscopic examinations indicate that during VHCF a localized plastic deformation in shear bands arises on the specimen surface. Hence, this work focuses on the effect of damage accumulation in shear bands on the resonant behavior of AISI304 in the VHCF regime. A microstructural simulation model is proposed that takes into account specific mechanisms in shear bands proven by experimental results. The simulation model is solved numerically using the two-dimensional boundary element method and the resonant behavior is characterized by evaluating the force-displacement hysteresis loop. Simulation of shear bands agrees well with microscopic examinations and plastic deformation in shear bands influences the transient characteristic of the resonant behavior.  相似文献   

14.
Summary Antiplane shear problem of an infinite medium containing a circular inclusion of different material is investigated in this article. Perfectly bonding between the matrix and the inclusion, as well as partial debonding in the form of a circumferential crack occurring at the interface of these two constituents, are considered. Using the complex variable method in conjunction with a semi-inversed technique, exact expressions for the stress, displacement and stress intensity factor in the problem are obtained for various external loading conditions, including that brought about by stress singularities. A number of numerical results of stress intensity factors for a partially damaged matrix-inclusion system are given, and a discussion is made on the general features of the antiplane shear problem of inhomogeneous matrix-inclusion systems.
Scherung von perfekten und teilweise beschädigten Matrix-Einschluß-Systemen außerhalb der Ebene
Übersicht In dieser Abhandlung wird das Problem der Scherung au\erhalb der Ebene für einen unendlichen Körper mit einem kreisförmigen Einschluß aus unterschiedlichem Material untersucht. Es wird die perfekte Verbindung zwischen der Matrix und dem Einschluß ebenso wie teilweise Ablösung in der Form eines Umkreisrisses an der Schnittfläche zwischen den beiden Bestandteilen betrachtet. Unter Verwendung der komplexen Variablenmethode in Verbindung mit einem Halbinversionsverfahren werden exakte Ausdrücke für Spannung, Verschiebung und Spannungsintensitätsfaktor für verschiedene äußere Belastungszustände, einschließlich dem Einfluß von Spannungssingularitäten, erhalten. Es werden numerische Ergebnisse für den Spannungsintensitätsfaktor für ein teilweise beschädigtes Matrix-Einschluß-System gegeben, und die allgemeine Form des Problems der Scherung außerhalb der Ebene für ein nicht homogenes Matrix-Einschluß-System wird diskutiert.
  相似文献   

15.
The mechanical condition of shear band bifurcation   总被引:1,自引:0,他引:1  
Based on the understanding of the role played by the strain-softening effect in the formation of shear band bifurcation, this paper investigates (a) What is the most favourable condition that stimulates the occurrence of shear band? (b) With what model and characterizing parameters can the curved type of band bifurcation be simulated?  相似文献   

16.
边坡稳定的剪切带计算   总被引:2,自引:0,他引:2  
为了解决边坡稳定分析中剪切带有限元网格的依赖性问题,采用梯度塑性理论,从本构关系中引入特征长度入手,建立计算模型。提出了一种8节点缩减积分的梯度塑性单元,并采用梯度塑性理论推导了Drucker-Prager屈服准则的软化模型的有限元格式,在ABAQUS中进行了二次开发,嵌入了本文提出的8节点单元和本构模型,并用ABAQUS软件进行了边坡剪切带的计算。计算结果表明,本文提出的方法消除了经典有限元计算的网格依赖性问题,可以得到与单元剖分无关的稳定的剪切带宽度。本文所提出的方法可适用于其他场合的剪切带计算。  相似文献   

17.
Using the inverse method we consider the admissibility of a family of inhomogeneous rectilinear shear deformations in isotropic electroactive materials. Moreover, several boundary value problems related to these deformations are investigated numerically.  相似文献   

18.
We review and compare the phenomenological aspects and physical origin of shear localization and shear banding in various material types, namely emulsions, suspensions, colloids, granular materials, and micellar systems. It appears that shear banding, which must be distinguished from the simple effect of coexisting static-flowing regions in yield stress fluids, occurs in the form of a progressive evolution of the local viscosity toward two significantly different values in two adjoining regions of the fluids in which the stress takes slightly different values. This suggests that from a global point of view, shear banding in these systems has a common physical origin: Two physical phenomena (for example, in colloids, destructuration due to flow and restructuration due to aging) are in competition, and depending on the flow conditions, one of them becomes dominant and makes the system evolve in a specific direction.  相似文献   

19.
The problem of fracture mechanics on nucleation of cracks emanating from circular contours of holes of perforated isotropic solids under longitudinal shear is under consideration. The solution of the equilibrium problem of a perforated solid under longitudinal shear with prefracture zones is reduced to solving an infinite algebraic system and a nonlinear singular integrodifferential equation with a kernel of the Cauchy type. Forces in crack nucleation zones are found by solving these equations. The condition of crack emergence is formulated taking into account the criterion of the limiting discontinuity of material displacements.  相似文献   

20.
In this paper we study the problem of rectilinear shear of a slab of transversely isotropic incompressible non-linearly elastic material. In particular, the material under consideration is a base neo-Hookean model augmented with a function that accounts for the existence of a unidirectional reinforcement. The slab is of infinite length in two dimensions and finite thickness in the other one and is clamped to two rigid plates. Closed form analytic solutions are found for this problem. It is shown that, depending on the reinforcement strength and the fiber orientation in the undeformed configuration, weak solutions, i.e. solutions for which the smoothness required by the differential equations is relaxed, are to be expected. These solutions give rise to fiber kinking. It is shown that: (i) both sides of the kink involve fiber contraction; (ii) a suitable intermediate deformation between the two conjoined kink deformation states is non-elliptic.  相似文献   

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