材料弹性变形与塑性变形相互关系的探讨

本文通过分析大量试验结果,指出一般金属材料及各向同性、均质、连续性较好的岩石材料,其变形的弹性部分和塑性部分遵循一个规律——弹塑性变形相关律。文章最后从理论上部分论证了这一规律     

基于梯度塑性本构理论的岩样侧向变形分析(Ⅰ):基本理论及本构参数对侧向变形的影响

研究了岩样在单轴压缩条件下轴向应力．侧向或环向变形的全程曲线特征。基于考虑峰值剪切强度后微小结构之间相互影响和作用的梯度塑性理论，得到了由于剪切局部化而引起的侧向塑性变形。利用虎克定律描述了试件的弹性变形，得到了轴向应力．侧向变形全程曲线的解析解。在软化阶段，试件中部侧向变形及对靠近试件上端或下端部位的侧向变形并不相同。与轴向应力．应变曲线可能出现的回跳现象类似。试件中部轴向应力．侧向应变曲线也可能出现回跳现象。在应变软化阶段，与应力．侧向应变曲线相比，应力．环向应变曲线不容易发生回跳现象。若在试件内部出现多条剪切带，则应该以等效剪切带宽度替代本文中的剪切带宽度。随着剪切带倾角、内部长度参数的降低、剪切模量的增加及弹性模量的降低，轴向应力．侧向应变曲线越陡；甚至能出现弹性回跳。     

基于广义热力学的超固结土本构模型

基于广义热力学基本理论,通过考虑塑性剪切变形产生的能量一部分以塑性自由能的形式储存,并且该部分自由能与超固结度相关,结合修正剑桥模型的热力学函数形式建立了适用于超固结土的自由能函数和耗散函数。该耗散函数与当前应力状态无关,相关联流动法则仍然适用。由建立的耗散函数和自由能函数,推导了弹塑性本构关系的屈服函数、流动法则、硬化定律。通过4种不同超固结土的试验结果和计算结果进行比较,验证了模型的合理性。     

Seismic plastic deformation in the free-field

An analytical solution for the free-field seismic elastoplastic deformation of granular dry soil is developed. This solution is possible since the stress field solution from pseudostatic analysis is known at any acceleration level. A plastic potential function with two plastic material parameters is suggested to model the soil. This model can describe both the volume dilation and contraction of soil under shearing. Closed-form deformation solutions are derived for two special cases and the results from a numerical evaluation of the solution are compared with those measured from shaking table tests. From the deformation solution the shape of the horizontal plastic displacement distribution with depth is identical to that for the elastic deformation since both depend only on the distribution of the elastic shear modulus. Copyright © 1999 John Wiley & Sons, Ltd.     

Finite deformation analysis of geomaterials

The mathematical structure and numerical analysis of classical small deformation elasto–plasticity is generally well established. However, development of large deformation elastic–plastic numerical formulation for dilatant, pressure sensitive material models is still a research area. In this paper we present development of the finite element formulation and implementation for large deformation, elastic–plastic analysis of geomaterials. Our developments are based on the multiplicative decomposition of the deformation gradient into elastic and plastic parts. A consistent linearization of the right deformation tensor together with the Newton method at the constitutive and global levels leads toward an efficient and robust numerical algorithm. The presented numerical formulation is capable of accurately modelling dilatant, pressure sensitive isotropic and anisotropic geomaterials subjected to large deformations. In particular, the formulation is capable of simulating the behaviour of geomaterials in which eigentriads of stress and strain do not coincide during the loading process. The algorithm is tested in conjunction with the novel hyperelasto–plastic model termed the B material model, which is a single surface (single yield surface, affine single ultimate surface and affine single potential surface) model for dilatant, pressure sensitive, hardening and softening geomaterials. It is specifically developed to model large deformation hyperelasto–plastic problems in geomechanics. We present an application of this formulation to numerical analysis of low confinement tests on cohesionless granular soil specimens recently performed in a SPACEHAB module aboard the Space Shuttle during the STS‐89 mission. We compare numerical modelling with test results and show the significance of added confinement by the thin hyperelastic latex membrane undergoing large stretching. Copyright © 2001 John Wiley & Sons, Ltd.     

A micro-mechanics-based elastic–plastic model for porous rocks: applications to sandstone and chalk

A micro-mechanics-based elastic–plastic model is proposed to describe mechanical behaviors of porous rock-like materials. The porous rock is considered as a composite material composed of a solid matrix and spherical pores. The effective elastic properties are determined from the classical Mori–Tanaka linear homogenization scheme. The solid matrix verifies a pressure-dependent Mises–Schleicher-type yield criterion. Based on the analytical macroscopic yield criterion previously determined with a nonlinear homogenization procedure (Shen et al. in Eur J Mech A/Solids 49:531–538, 2015), a complete elastic–plastic model is formulated with the determination of a specific plastic hardening law and plastic potential. The micro-mechanics-based elastic–plastic model is then implemented for a material point in view of simulations of homogeneous laboratory tests. The proposed model is applied to describe mechanical behaviors of two representative porous rocks, sandstone and chalk. Comparisons between numerical results and experimental data are presented for triaxial compression tests with different confining pressures, and they show that the micro-mechanical model is able to capture main features of mechanical behaviors of porous rock-like rocks.     

弹塑性耦合应变定义与本构方程

岩石屈服之后,弹性参数随塑性变形而变化,即岩石具有弹塑性耦合特征。在弹塑性耦合框架和现有应变分类、定义、本构方程研究的基础上,主要做了以下工作：结合岩石压缩试验,从损伤和塑性变形角度分析了弹性参数随塑性演化的现象;重点研究了加载增量步的应变特征,将与加载应力增量对应的应变增量分解为符合广义Hooke定律的弹性应变增量 、不符合广义Hooke定律的弹性应变增量 和塑性应变增量 ;通过采用加载增量步之后的弹性参数将 与 构造弹性关系,分别在应变空间和应力空间中建立了适用于加载、中性变载和卸载条件的本构方程;对表征物质微观结构变化的内变量进行了讨论。所提出的应变分类和定义方法概念清晰,适合于应变强化阶段和应变软化阶段,且所建立的弹塑性耦合本构方程能够反映不同加载条件对弹性参数变化速率的影响,符合岩石的弹塑性耦合力学特性。     

A Transversely Isotropic Damage Model for Boom Clay

Boom clay can be considered as a transversely isotropic geomaterial. However, due to lack of experimental evidence and data base, it is still difficult to describe the transversely isotropic plastic behavior of this argillaceous rock. In this paper, we present first, by means of an experimental approach, the main features of the mechanical properties of Boom clay. Then, combining the transversely isotropic elastic model and the modified Mohr–Coulomb criterion, a suitable constitutive model is introduced so as to fully describe the mechanical behavior of the studied material, in which, an elastic damage law which takes into consideration, the transversely isotropic effect, a plastic hardening law and a plastic damage law were introduced to describe the nonlinear elastic, hardening and softening behavior of Boom clay. As a preliminary step, the evolution law of both elastic moduli and Poisson’s ratio during the elastic stage was obtained by direct analysis of the test data. The synchronism of the elastic damage in both transversal and axial directions was proved by this method. Some of the parameters of the model in the elastic stage were also determined by direct analysis method and further verified by back analysis. Other unknown parameters in the model were determined by back analysis.     

Micromechanical viscoelasto‐plastic models and finite element implementation for rate‐independent and rate‐dependent permanent deformation of stone‐based materials

This paper presents parallel and serial viscoelasto‐plastic models to simulate the rate‐independent and the rate‐dependent permanent deformation of stone‐based materials, respectively. The generalized Maxwell viscoelastic and Chaboche's plastic models were employed to formulate the proposed parallel and serial viscoelasto‐plastic constitutive laws. The finite element (FE) implementation of the parallel model used a displacement‐based incremental formulation for the viscoelastic part and an elastic predictor—plastic corrector scheme for the elastoplastic component. The FE framework of the serial viscoelasto‐plastic model employed a viscoelastic predictor—plastic corrector algorithm. The stone‐based materials are consisted of irregular aggregates, matrix and air voids. This study used asphalt mixtures as an example. A digital sample was generated with imaging analysis from an optically scanned surface image of an asphalt mixture specimen. The modeling scheme employed continuum elements to mesh the effective matrix, and rigid bodies for aggregates. The ABAQUS user material subroutines defined with the proposed viscoelasto‐plastic matrix models were employed. The micromechanical FE simulations were conducted on the digital mixture sample with the viscoelasto‐plastic matrix models. The simulation results showed that the serial viscoelasto‐plastic matrix model generated more permanent deformation than the parallel one by using the identical material parameters and displacement loadings. The effect of loading rates on the material viscoelastic and viscoelasto‐plastic mixture behaviors was investigated. Permanent deformations under cyclic loadings were determined with FE simulations. The comparison studies showed that the simulation results correctly predicted the rate‐independent and rate‐dependent viscoelasto‐plastic constitutive properties of the proposed matrix models. Overall, these studies indicated that the developed micromechanical FE models have the abilities to predict the global viscoelasto‐plastic behaviors of the stone‐based materials. Copyright © 2009 John Wiley & Sons, Ltd.     

冻土蠕变的渐进屈服准则

基于冻土蠕变的现象分析表明，冻土蠕变的破坏是由于冻土中非弹性变形积累的结果，在冻土的任何变形阶段都存在着非弹性变形。非弹性变形的积累在一定条件下导致了冻土渐进屈服的出现，渐进屈服反过来又促进了冻土蠕变的进一步增加。     

Explicit solutions for the instantaneous undrained contraction of hollow cylinders and spheres in porous elastoplastic medium

In this article we present closed‐form solutions for the undrained variations in stress, pore pressure, deformation and displacement inside hollow cylinders and hollow spheres subjected to uniform mechanical pressure instantaneously applied to their external and internal boundary surfaces. The material is assumed to be a saturated porous medium obeying a Mohr–Coulomb model failure criterion, exhibiting dilatant plastic deformation according to a non‐associated flow rule which accounts for isotropically strain hardening or softening. The instantaneous response of a porous medium submitted to an instantaneous loading is undrained, i.e. without any fluid mass exchange. The short‐term equilibrium problem to be solved is now formally identical to a problem of elastoplasticity where the constitutive equations involve the undrained elastic moduli and particular equivalent plastic parameters. The response of the model is presented (i) for extension and compression undrained triaxial tests, and (ii) for unloading problems of hollow cylinders and spheres through the use of appropriately developed closed‐form solutions. Numerical results are presented for a plastic clay stone with strain hardening and an argilite with strain softening. The effects of plastic dilation, of the strain softening law and also of geometry of the cavity on the behaviour of the porous medium have been underlined. Analytical solutions provide valuable benchmarks enabling various numerical methods in undrained conditions with a finite boundary to be verified. Copyright © 2002 John Wiley & Sons, Ltd.     

一种气泡轻质土路基受载-破坏模型试验

针对某原型工程采用的新型气泡轻质填土路基,通过室内相似模型试验和UDEC数值模拟相结合分析的手段,研究该气泡轻质土路基在受载-破坏过程中的变形特征和受力破坏机制,得到了该过程中路基内部的应变变化、应力分布以及沉降变形规律等数据。研究表明：该种气泡轻质土路基在受载-破坏过程中,内部老路基首先发生变形,当荷载达到175 kPa后,中层左侧轻质土路基内部最先发生塑性变形直至破坏;轻质土路基与老路基交接处易受老路基沉降变形与轻质土路基破坏变形的共同作用而产生弯剪破坏裂缝,最终导致路基失稳;该气泡轻质土路基受载-破坏模式是一个由内而外的从弹性变形到塑性屈服,最终发生弯剪破坏的过程,即先局部破坏再整体失稳;纵向上老路基的应力传递比轻质土路基小;一定荷载范围（小于100 kPa）内,路基变形程度与路基深度成反比。     

Modeling of elastic anisotropy due to one-dimensional plastic consolidation of clays

Experiments indicate that in one-dimensionally consolidated natural clays the elastic anisotropy is much stronger than the plastic strain anisotropy. Moreover, the elastic anisotropy appears to be dependent on the pre-consolidation strain. Coupled elasto-plastic constitutive law is shown to be able to simulate these anisotropy effects of natural clay deposits. In this law the elastic potential is not only a function of stress, but additionly of the plastic strain. The plastic strain comprises the geological process of pre-consolidation idealized as an one-dimensional plastic straining as well as a mechanically induced strain due to engineering activity. Calibration of the model and simulation of some stress paths are presented and related to the classical experimental results by Mitchell (1972).     

Template elastic‐plastic computations in geomechanics

In this paper we present a new approach to computations in elasto‐plastic geomechanics. The approach is based on the object oriented design philosophy and observations on similarity of most incremental elastic–plastic material models. This new approach to elastic–plastic computations in geomechanics allows for creation of template material models. The analysis of template material models will in turn allow for an easy implementation of other elastic–plastic material models based on the object oriented design principles. Furthermore we present some illustrative implementation details. Finally we present analysis results that emphasize features of template elastic–plastic computations in geomechanics. Copyright © 2002 John Wiley & Sons, Ltd.     

大理岩弹塑性耦合特性试验研究

大量研究表明,岩石经历塑性变形时其弹性参数会发生变化,即存在弹塑性耦合现象。为了研究岩石的弹塑性耦合特性,进行了两种大理岩的循环加、卸载试验。试验结果表明:与常规试验对比,循环加、卸载试验对岩石的变形、强度及破坏形态影响较小;弹性参数随塑性变形的变化显著,考虑弹塑性耦合时,弹性参数取体积模量和剪切模量更为合适;基于Mohr-Coulomb屈服准则,计算得到了强度参数,即黏聚力和内摩擦角随塑性内变量的演化规律。所得结论将为岩石弹塑性耦合本构模型的建立提供基本的试验支持。     

The impact of analogue material properties on the geometry,kinematics, and dynamics of convergent sand wedges

Simulation of geodynamic processes in sandbox experiments requires analogue materials with a deformation behaviour that reproduces the deformation mechanisms of typical crustal rocks. We present data on the frictional strength of different sand types employing static and dynamic shear tests. The sand types analysed are characterised by an elastic/frictional plastic mechanical behaviour with a transient strain-hardening and strain-softening phase prior to transition to stable sliding. This is in conflict with the standard assumption of an ideal cohesionless Coulomb-material with constant frictional properties. The influence of the identified transient material properties on the kinematics, growth mechanisms, and internal deformation patterns of convergent sand wedges results in characteristic wedge segments which vary—depending on material compaction—between wedges with well defined segments (i.e. frontal-deformation zone, frontal-imbrication zone and internal-accumulation zone) with straight slopes and wedges with a continuous convex topographic profile. For most materials, only the frontal part of the wedge is critical during experimental runs. Taper and strength of the wedge segments can be shown to be controlled by the frictional properties of active faults. Wedge segmentation is controlled by a bulk-strength increase toward the rear of the wedge due to fault rotation in mechanically less-favourable orientations and plastic material hardening. The limit between the frontal critical parts of a wedge and internal stable parts is largely controlled by a critical state of stress upon which either renewed failure or fault inactivation occurs. On this basis, we suggest that critical-taper analysis of wedges must be restricted to specific kinematic segments. Comparison of the experimental results with the Nankai accretionary wedge suggests that our interpretation also applies to natural convergent wedges. Moreover, we provide constraints for the selection of adequate granular analogue materials to simulate typical crustal rocks in natural convergent wedges.     

模拟应变软化岩石三轴试验过程曲线

在经典弹塑性理论框架下,认为岩石材料在应变软化过程中遵守摩尔-库仑强度准则,塑性变形服从非关联流动法则。对两组岩石在三轴试验中呈现的应变软化行为进行了分析,获取了峰值前后强度参数的大小。采用应变软化模拟方法,将应力-应变曲线峰后应变软化阶段简化为一系列应力跌落和塑性流动的脆塑性过程,在给定的强度参数演化规律基础上,得到了岩石的应力-应变曲线、侧向应变-轴向应变曲线、体应变-轴向应变曲线和塑性体应变-轴向塑性应变曲线。模拟得到的应力-应变曲线与试验结果吻合较好,其他曲线与相关试验测试规律基本一致。研究成果对确定岩石强度参数与认识岩石峰后强度演化规律有一定的指导意义。     

生态护坡基材土-岩接触面原位剪切试验研究

基材土-岩接触面剪切力学性能是生态护坡体系长久稳定的关键,相关研究可为解决基材脱落难题、完善生态防护技术体系提供必要依据和指导。采用自制的原位剪切仪对4种不同粗糙起伏的基材土-岩接触面进行了原位剪切试验,结果表明,基材土-岩接触面剪切应力-位移表现出典型的软化特性,具有明显的初始线弹性变形、弹塑性变形、峰后软化以及残余剪切变形4个阶段。分析发现,文中试验条件下凸起高度算数平均偏差Ra在4 mm以下时,峰值剪切强度增加速度较快,随后呈逐渐减弱趋势;残余剪切强度、峰值剪切位移以及进入残余阶段的剪切位移与粗糙凸起高度算数平均偏差呈近线性正相关关系。可见实施生态护坡时合理地控制坡面粗糙起伏,有助于提高土-岩接触面峰值剪切强度和残余剪切强度,改善其变形性能,对防护体系的长期整体稳定具有促进作用。     

一种基于弹性能释放率的岩石新型统计损伤本构模型

为了揭示岩石变形的破坏机理以及岩石材料产生损伤的本质原因,文章对岩石材料变形规律和力学特性进行分析后,再以损伤变量作为影响岩石变形和力学性能变化的内变量,采用能量原理、有效应力原理和统计损伤理论构建了一种基于弹性能释放率的新型岩石统计损伤本构模型。该损伤模型进一步完善了岩石损伤本构模型的理论体系,弥补了传统损伤模型无法合理解释引发岩石破坏原因的不足。利用岩石试验数据对损伤模型的参数进行确定,并将损伤演化模型代入弹性能-应变模型中,分析在加载过程中岩石弹性能变化的规律。结果表明:模型曲线与试验曲线在峰前变形阶段几乎重合,说明损伤模型可以很好地反映岩石的变形特性;在初始加载阶段,岩石的损伤变量随着轴向应变的增大而增大,说明在荷载作用下,岩石内部裂隙逐渐发展发育,使得岩石材料的损伤逐步积累;在围压达到10 MPa以上时,损伤-应变曲线基本重合。同时,在初始加载时刻,损伤-应变曲线增长率急剧上升,大约在岩石应变为0.01%时,损伤-应变曲线趋于平稳变化状态;且由于岩石在峰值应力点附近损伤迅速累积,进而使得损伤变量在数值上快速增大到1,这说明了围压的增大使得岩石破坏极限得到显著的提升。