Strain localization and fabric evolution in sand

Strain localization is frequently observed in sand and is considered an important precursor related to major geohazards such as landslides, debris flow and failure of relevant geo-structures. This paper presents a numerical study on strain localization in sand, with a special emphasis on the influence of soil fabric and its evolution on the initiation and development of shear band. In particular, a critical state sand plasticity model accounting for the effect of fabric and its evolution is used in the finite element analysis of plane strain compression tests. It is found that the initiation of shear band is controlled by the initial fabric, while the development of shear band is governed by two competing physical mechanisms, namely, the structural constraint and the evolution of fabric. The evolution of fabric generally makes the sand response more coaxial with the applied load, while the structural constraint induced by the sample ends leads to more inhomogeneous deformation within the sand sample when the initial fabric is non-coaxial with the applied stress. In the case of smooth boundary condition, structural constraint dominates over the fabric evolution and leads to the formation of a single shear band. When the boundary condition is rough, the structural constraint may play a comparable role with fabric evolution, which leads to symmetric cross-shape shear bands. If the fabric is prohibited from evolving in the latter case, a cross-shape shear band pattern is found with the one initiated first by the structural constraint dominating over the second one. In all cases, significantly larger dilation and fabric evolution are observed inside the shear band than outside. The simulated shear band orientation coincides with the Roscoe’s angle for cases with high confining pressure and lies in between the Roscoe’s angle and Arthur’s angle for the low confining pressure cases.     

Finite strain analysis of crack tip fields in incompressible hyperelastic solids loaded in plane stress

A new method is developed to determine the dominant asymptotic stress and deformation fields near the tip of a Mode-I traction free plane stress crack. The analysis is based on the fully nonlinear equilibrium theory of incompressible hyperelastic solids. We show that the dominant singularity of the near tip stress field is governed by the asymptotic solution of a linear second order ordinary differential equation. Our method is applicable to any hyperelastic material with a smooth work function that depends only on the trace of the Cauchy-Green tensor and is particularly useful for materials that exhibit severe strain hardening. We apply this method to study two types of soft materials: generalized neo-Hookean solids and a solid that hardens exponentially. For the generalized neo-Hookean solids, our method is able to resolve a difficulty in the previous work by Geubelle and Knauss (1994a). Our theoretical results are compared with finite element simulations.     

Effects of temperature and thermo-mechanical couplings on material instabilities and strain localization of inelastic materials

A general framework for rate-independent, small-strain, thermoinelastic material behaviour is presented, which includes thermo-plasticity and -damage as particular cases. In this context, strain localization and the development of material instabilities are investigated to highlight the roles of thermal effects and thermomechanical couplings. During a loading process, it is shown that two conditions play the essential roles and correspond to the singularity of the isothermal and the adiabatic acoustic tensors. Under quasi-static conditions, strain localization (in a classical sense) may occur when either of these two conditions is met. It involves a jump in temperature rate in the latter case, whereas temperature rate remains continuous in the former, but a discontinuity in the spatial derivatives of the heat flux must occur. This is consistent with the condition of stationarity of acceleration waves, which are shown to be homothermal and propagate with a velocity related to the eigenvalues of the isothermal acoustic tensor. A linear perturbation analysis further clarifies the above findings. In particular, for a quasi-static path of an infinite medium, failure of positive definiteness of either of the acoustic tensors corresponds to bifurcations in wave-like modes of arbitrary wave-length and infinite rate of growth. Under dynamic conditions, unbounded growth of perturbations is associated only to the short wavelength regime and corresponds to divergence growth or flutter phenomena relative to the isothermal acoustic tensor.     

Damage evaluation and damage localization of rock

Knowledge of damage accumulation and corresponding failure evolution are prerequisite for effective maintenance of civil engineering so as to avoid disaster. Based on statistical mesoscopic damage mechanics, it was revealed that there are three stages in the process of deformation, damage and failure of multiscale heterogeneous elastic–brittle medium. These are uniformly distributed damage, localized damage and catastrophic failure. In order to identify the transitions from scattering damage to macroscopically localized one, a condition for damage localization was given. The experiments of rock under uniaxial compression with the aid of observations of acoustic emission and speckle correlation do support the concept of localization. This provides a potential approach to properly evaluate damage accumulation in practice. In addition, it is found in the experiments that catastrophic failure displays critical sensitivity. This gives a helpful clue to the prediction of catastrophic failure.     

岩土材料应变局部化的有限元分析方法

采用有限单元法分析岩土材料的应变局部化时经常会遇到单元尺寸敏感性问题和网格锁定问题。自适应网格技术能够有效地解决网格锁定问题,但仍然无法克服计算结果对单元尺寸的依赖性,尽管在一维情况下被证明是可行的。复合体理论(均匀化理论)和弱非连续有限元方法可以成功地解决岩土材料的单元尺寸敏感性问题,在一维情况下两类方法实际上是一致的。本文针对岩土材料应变局部化的有限元新技术所存在的若干问题进行了详细的讨论,并给出了有关算例。     

Boundary effects on behaviour of granular material during plane strain compression

The paper investigates the boundary effect on the behaviour of granular materials during plane strain compression using finite element method. A micro-polar hypoplastic constitutive model was used. The numerical calculations were carried out with different initial densities and boundary conditions. The behaviour of initially dense, medium dense and loose sand specimen with very smooth or very rough horizontal boundary was investigated. The formation of shear zones gave rise to different global and local stress and strain. Comparisons of the mobilized internal friction, dilatancy and non-coaxiality between global and local quantities were made.     

Anisotropic plastic stress field at a mixed-mode crack tip under plane and anti-plane strain

On condition that any perfectly plastic stress component at a crack tip is nothingbut the function ofθ.by making use of equilibrium equations,anisotropic plastic stress-strain-rate relations,compatibility equations and Hill anisotropic plastic yieldcondition,in the present paper,we derive the generally analytical expressions of theanisotropic plastic stress field at a mixed-mode crack tip under plane and anti-planestrain.Applying these generally analytical expressions to the mixed-mode cracks,wecan obtain the analytical expressions of anisotropic plastic stress fields at the tips ofmixed-modeⅠ-Ⅲ,Ⅱ-ⅢandⅠ-Ⅱ-Ⅲcracks.     

Size-effects in plane strain sheet-necking

A finite strain generalization of the strain gradient plasticity theory by Fleck and Hutchinson (J. Mech. Phys. Solids 49 (2001a) 2245) is proposed and used to study size effects in plane strain necking of thin sheets using the finite element method. Both sheets with rigid grips at the ends and specimens with shear free ends are analyzed. The strain gradient plasticity theory predicts delayed onset of localization when compared to conventional theory, and it depresses deformation localization in the neck. The sensitivity to imperfections is analyzed as well as differently hardening materials.     

ONSET CONDITION OF STRAIN LOCALIZATION IN MATRIX OF SATURATED POROUS MEDIA

Introduction Strainlocalizationofgeomaterialsisoneofmostpopularfailuretypesinnature,which canbeshowedaslandslidesandmudflowsinmountainousareasunderincessantorheavy raining,especiallythevegetationisseverelydamagedbywoodsharvest;pipingeffect,a typeoflocalfa…     

Three-dimensional characterization of strain localization bands in high-resolution elastoplastic polycrystals

In crystalline materials, the experimental observation of the localization of plastic strains in particular directions is generally restricted to the surface of a sample containing some hundreds of grains, because of the difficulties underlying microstructural analysis. In these conditions, the determination of the morphological characteristics of localization can be limited by the poor statistical representativity of the domain of observation. The purpose of this work is to extend the analysis of localization – localization bands or else – to the 3D elastoplastic strain fields of a high-resolution representative volume element of a polycrystal.     

饱和多孔介质中的混合有限元法和有限应变下应变局部化分析

对基于Biot理论的饱和多孔介质中动力-渗流耦合分析提出了一个耦合场混合元．固相位移、应变和有效应力以及流相压力、压力梯度和Darcy速度在单元内均处理为独立变量分别插值．基于胡海昌-Washizu三变量广义变分原理给出的饱和多孔介质动力-渗流耦合问题控制方程的单元弱形式，导出了单元公式．进一步导出了考虑压力相关非关联塑性的非线性单元公式和发展了相应的一致性算法．对几何非线性分析，采用了共旋公式途径．数值结果例题显示所发展耦合场混合元模拟大应变下由应变软化引起以应变局部化为特征的渐进破坏现象的性能．     

Stress–strain behaviour of poly(ethylene terephthalate) (PET) during large plastic deformation by plane strain compression: the relation between stress–strain curve and thermal history, temperature and strain rate

This study presents an experimental investigation of the large plastic deformation of poly(ethylene terephthalate) (PET) submitted to plane strain compression. PET samples, obtained by injection moulding, annealed and non-annealed, were deformed using a specific compression device developed for this purpose. The obtained stress–strain curves at different temperatures and strain rates are useful for engineering applications and show a significant temperature dependence and a minor dependence on the strain rate. A softening temperature as a minimum temperature necessary to initiate deformation when a minimum, almost zero, stress is applied is introduced. This temperature, at the zero stress and strain limit, we denominate “Stress–Strain independent softening Temperature (T _SOF)”. The T _SOF values, 104 and 113°C for non-annealed and annealed PET, respectively, have been obtained using three different strain rates, indicating that the property is sensitive to the thermal history of the material.     

The expression of stress and strain at the tip of three-dimensional notch

ＴＨＥＥＸＰＲＥＳＳＩＯＮＯＦＳＴＲＥＳＳＡＮＤＳＴＲＡＩＮＡＴＴＨＥＴＩＰＯＦＴＨＲＥＥ－ＤＩＭＥＮＳＩＯＮＡＬＮＯＴＣＨＱｉａｎＪｕｎ（钱俊）（ＥａｓｔＣｈｉｎａＩｎｓｔｉｔｕｔｅｏｆＴｅｃｈｍｏｌｏｇｙ）ＮａｎｊｉｎｇＬｏｎｇＹｕ－ｑｉｕ（龙驭...     

基于非局部塑性模型的应变局部化理论分析及数值模拟

通过求解一个第二类Fredholm方程,得到了基于非局部塑性软化模型的应变局部化问题理论解,结果表明,只有在当采用过非局部修正形式的非局部塑性软化模型才能得到应变局部化解,且得到的塑性应变分布和荷载响应依赖于所引入的特征长度及过非局部权参数。通过一维应变局部化有限元数值解,验证了非局部理论的引入能克服计算结果的网格敏感...     

The expression of stress and strain at the tip of notch in reissner plate

In this paper, the eigenequation of notch in Reissner plate is derived by the eigenfunction method. Eigenvalues of different notches with different angles are calculated by Muller iteration method.The expression of stress and strain at the tip of notch in Reissner plate is obtained.     

A damage accumulation model for complex strain paths: Prediction of ductile failure in metals

The characterisation of strain path with respect to the directionality of defect formation is discussed. The criterion of non-monotonic strain path is used in the scalar and tensor models for damage accumulation and recovery. Comparable analysis of models and their verification has been obtained by simulation of crack initiation in a two-stage metal forming operation consisting of wire drawing followed by constrained upsetting.     

Creep damage constitutive equations for multi-axial states of stress for 0.5Cr0.5Mo0.25V ferritic steel at 590°C

Multi-axial creep damage constitutive equations are developed for 0.5Cr0.5Mo0.25V ferritic steel at 590°C. It is aimed to overcome the deficiency of inconsistency in predicted and observed creep strains existed in previous formulations [Q. Xu, in: European Conference on Advances in Mechanical Behaviour, Plasticity and Damage, 7–9 November 2000, Tours, France; Creep Damage Mechanics Research Report, The School of Engineering, The University of Huddersfield, 2000; I.J. Perrin, D.R. Hayhurst, J. Strain Anal. 31 (4) (1996) 299]. In this paper, the lifetime and strain at failure are qualitatively validated in a wider range of states of stress by which the capability of producing consistent results is demonstrated.     

高应力岩体爆破卸荷过程中应变率及应变能特征

针对高应力岩体爆破开挖卸载问题,自制了一台轴向加、卸载实验测试平台,通过实验测试获得了爆破卸荷过程中岩杆的动态应变及应变率数据。实测数据表明：开挖面附近岩体的爆破加、卸载以及初始应力卸载应变率均在10⁻¹ s⁻¹量级以上,验证了高地应力区岩体爆破开挖卸荷是一动态过程。建立了初始应力卸载一维力学模型,揭示了卸载波的传播机制;通过分析爆破卸荷过程应变能密度的时空分布特征,建立了应变能密度与各阶段应变率变化规律的联系。结合实测数据,采用隐式-显式顺序求解方法,进一步分析了高应力区岩体爆破卸荷荷载各阶段应变率沿岩杆的变化规律。结果表明：爆破加载阶段的平均应变率沿杆件逐渐衰减,且衰减速度逐渐减小;爆破卸阶段平均应变率沿杆件也呈衰减趋势;而初始应力的应变能稳定释放,其平均应变率无衰减趋势。

     

考虑破碎影响的颗粒材料亚塑性模型及应变局部化模拟

在基于2ndP-K应力率的亚塑性模型基础上,通过引入一个能够考虑颗粒破碎影响的孔隙比-平均压力临界状态方程,形成了一个能够模拟颗粒破碎影响的颗粒材料亚塑性模型,数值算例考查了颗粒破碎对应变局部化模式及位移-承载曲线的影响,结果表明,所建议模型具有模拟破碎对颗粒材料应变局部影响的良好性能。