剪切带内部应变(率)分析及基于能量准则的失稳判据

应用应变梯度塑性理论对局部化剪切带内部(塑性)剪应变(率)规律进行了理论分析。研究了剪切降模量及岩石材料内部长度等参数对剪切带内部应变(率)的影响。推导了剪应力(率)与剪切带相对错距(速度)的本构关系。研究了剪切降模量和岩石材料内部长度对剪切带稳定性的影响。将岩石试件直剪试验试验机简化为钢块,采用能量准则对岩石试件(剪切带)及钢块系统的稳定性进行了理论研究,提出了系统失稳判据。研究表明:岩石材料的剪切降模量越大,岩石材料的内部长度越小,试验机的剪切刚度越小及试验机的等效高度越大剪切带--钢块系统越容易失稳。     

考虑应变梯度效应的三点弯梁模型解析研究--第二部分:局部化带的位移及转角

基于梯度塑性理论,分析了应变软化及真实裂纹扩展阶段的局部化带的张拉位移和转角。在弹性阶段,可以由弹性理论来确定二者的关系。真实裂纹出现后,利用平衡条件、几何条件及梯度以来的应变软化本构关系,得到了真实裂纹长度与局部化带长度的关系。当真实裂纹刚出现时,局部化带长度达到最大值。在任何阶段,局部化带到中性轴的距离单调降低,局部化带的张拉位移和转角受梁深、带宽、弹模及下降模量等的影响。弹模及下降模量越大,带宽越小,则局部化带的张拉位移和转角都增加。而且,在前两个阶段,张拉位移都线性增加,但在后两个阶段,转角都非线性增加。     

岩样单轴压缩峰后泊松比理论研究

研究了单轴压缩岩样应变软化阶段侧向应变与轴向应变的比值(峰后泊松比)的变化规律。岩样的塑性变形假设根源于塑性应变局部化。岩样的轴向及侧向变形被分别分为两部分:弹性变形(由虎克定律描述)及由局部化引起的塑性变形(由梯度塑性理论及几何关系确定)。应变软化阶段的轴向应变-侧向应变曲线、轴向应力-轴向应变曲线及轴向应力-侧向应变曲线都得到了实验验证。在峰值强度时,峰后泊松比等于峰前泊松比。当压缩应力降至零时,峰后泊松比达到临界值。该临界值可能比峰前泊松比大,也可能比它小。峰后泊松比还和试件尺寸有关,这与峰前泊松不同。峰后泊松比与轴向压应力之间的关系可能是一条直线,也可能是上凸的,或上凹的。这取决于岩石的本构参数(弹性模量、剪切及软化模量、剪切带宽度及峰前泊松比)、试件的结构尺寸(试件宽度及高度)及剪切带倾角之间的关系。     

考虑一阶和二阶位移梯度的数字图像相关方法在剪切带测量中的比较

当剪切带中存在二阶位移梯度或应变梯度时,研究了两种数字图像相关(DIC)方法在测量位移、应变及应变梯度中的表现。以基于梯度塑性理论的剪切带的位移解作为基础,通过Matlab仿射变换制作了具有不同平均剪切应变和应变梯度的虚拟剪切带。通过对其计算和分析得到了下列结果:当剪切带的平均剪切应变和应变梯度较高时,与只考虑一阶位移梯度的DIC方法相比,考虑二阶位移梯度的DIC方法优势明显,获得的位移、应变及应变梯度结果与理论解比较吻合,由于DIC方法测量的是平均应变,因此,剪切带中心的峰值应变将被低估;当剪切带的平均剪切应变和应变梯度较低时,剪切带中心的峰值应变可能被高估,受标准偏差的影响,考虑二阶位移梯度的DIC方法没有优势。基于上述研究结果,在单向压缩应力控制加载条件下,对砂样从开始加载至宏观裂纹出现之前变形过程中的3种应变场的4种结果进行了分析。由于应变不超过0.25,因而考虑二阶位移梯度的DIC方法的结果并无优势。     

考虑应变梯度效应的三点弯梁模型解析研究--第一部分:局部化带的传播

为分析应变软化和由此带来的应变局部化问题,将梯度塑性理论引入裂纹带模型。以拉应变局部化区域代替裂纹带,在三点弯梁裂纹带(具有一定尺寸的带宽由特征长度确定)内部存在着不均匀分布的拉应变,这与实验结果相符。对拉应变进行积分,得到了拉应变局部化区域的张拉位移的理论表达式,结果表明:该位移与拉应力成线性规律,拉应变局部化区域的宽度越大,弹性模量越小或降模量越小,则该位移越大。此外,采用应力平衡条件、应变软化的本构关系及平截面假定,还得到了拉应变局部化区域的扩展规律,结果表明:下降模量越大、三点弯梁高度越小及弹性模量越小,则在相同的拉应力的情况下,拉应变局部化区扩展的长度越小;抗拉强度对拉应变局部化区扩展长度的最大值没有影响。此外,还研究了梁中部横截面内中性轴到具有最大承载能力的点的距离的变化规律。     

基于能量原理的岩样单轴压缩剪切破坏失稳判据

利用能量原理对倾斜的剪切带-带外弹性岩石构成的系统的稳定性进行了研究。单轴压缩岩样沿轴向的变形被分解为两部分,带外弹性岩石压缩引起的变形和剪切带错动引起的变形。后者与剪切带的相对剪切变形具有简单的几何关系。系统的总势能由剪切带的弹性及耗散势能和带外弹性岩石对剪切带所作的外力功构成。剪切带的弹性及耗散势能与剪切带的体积有关系。剪切带的尺寸由梯度塑性理论确定。将系统的总势能对相对剪切变形求一阶导数(等于零),得到了弹性岩石的平衡条件。将总势能对相对剪切变形求二阶导数(小于零),得到了系统的失稳判据。它综合反映了岩石材料弹性及应变软化阶段本构参数(弹性模量及软化模量)、剪切带之外弹性岩石的尺寸、剪切带的尺寸及系统的结构形式(剪切带倾角)对系统稳定性的影响。失稳判据比以往所得到的失稳判据更严格,更精确,更具有广泛意义。     

混凝土坝地震动力损伤分析

基于塑性损伤本构理论,将损伤变量作为内变量,在Drucker-Prager本构模型中引入损伤变量,考虑材料损伤引起的材料劲度的退化,基于非关联流动法则计算材料的塑性应变,根据材料的有效塑性应变计算损伤量,考虑到张开裂缝闭合时材料弹性劲度的恢复,推导了考虑塑性损伤的混凝土动态本构关系,并给出了内变量的计算步骤和动力方程的迭代格式。最后利用建立的动态本构模型对Koyna重力坝进行了非线性地震响应时程分析,并给出了关键时刻坝体最大受拉损伤分布,结果表明在坝颈和坝基处出现了较大的损伤,坝颈处的损伤最终形成由下游向上游的开裂破坏,这与该坝的实际震害较为一致。     

基于局部位移场最小二乘拟合数字图像相关方法的剪切带应变测量

采用局部位移场最小二乘拟合数字图像相关方法测量了虚拟剪切带的应变,并将测量结果与中心差分方法的结果和理论解进行了对比,主要研究了计算窗口尺寸和子区尺寸的影响。研究发现:当子区尺寸较小且应变计算窗口尺寸较大时,局部位移场最小二乘拟合数字图像相关方法的测量结果接近于理论解;对于测量单轴压缩条件下低液限黏土试样破坏过程中的应变场,局部位移场最小二乘拟合方法的测量结果比中心差分方法测量结果更准确,有助于对剪切带应变的准确测量。     

针刺C/C-SiC复合材料剪切非线性本构关系

为研究针刺C/C-SiC复合材料的剪切损伤行为,首先,进行了面内剪切加卸载实验,并利用SEM对复合材料的剪切破坏形貌进行了观测;然后,建立了一种塑性与损伤相结合的非线性本构模型描述复合材料的非线性力学行为,以幂函数描述等效塑性应变与等效应力的关系;最后,基于剪切强度的Weibull分布规律提出了一种指数型损伤变量表征剪切刚度的退化,并通过实验数据拟合得到模型中的参数。结果表明:复合材料在卸载后存在明显的残余应变,卸载模量随载荷的增加不断降低,表现出明显的剪切非线性特征;大量无纬布纤维束和纤维单丝拔出,且易在针刺部位发生破坏;由于针刺部位等缺陷的不规律分布,剪切强度存在一定的分散性,符合指数型Weibull统计分布规律;复合材料的剪切非线性主要由基体开裂和纤维/基体界面脱粘等内部损伤引起,从宏观上可以解释为塑性变形和刚度性能折减。所得结论表明本构模型能够很好地表征C/C-SiC复合材料的面内剪切非线性行为。      

考虑非局部应变梯度效应的轴对称压电纳米圆板热-力-电耦合振动EI北大核心CSCD

基于非局部应变梯度理论和Mindlin板理论,研究了热‐力‐电多场耦合下轴对称压电纳米圆板的振动特性。通过Hamilton原理推导了非局部应变梯度本构框架内的运动方程,采用微分求积法数值求解了理论模型微分方程组,分析了压电纳米圆板的振动固有频率受内尺度参数与外场参数的影响。压电纳米圆板的固有频率随着非局部参数的增大而减小,随着应变梯度特征参数的增大而增大。当非局部参数小于应变梯度特征参数时,纳米圆板表现出刚度硬化行为;当非局部参数大于应变梯度特征参数时,表现出刚度软化行为。当非局部参数等于应变梯度特征参数时,纳米圆板的刚度退化为相应的经典连续介质理论结果。此外,固有频率随着径向压力和正电压的增大而减小,随着径向拉力和负电压的增大而增大,随着温差的增加而小幅减小。特别地,研究发现当径向载荷和电压增大到一定程度时,纳米圆板出现了振动失稳现象,并分析了非局部参数与应变梯度特征参数对失稳临界径向载荷及临界电压的影响。     

深部岩石渐进破损本构模型及其应用

深部岩石力学特性的数理描述与深部岩体的灾害控制密切相关。从岩石破坏过程和破坏机制出发,将代表性体元(RVE)划分为弹性区及剪切局部化带两个部分;并把剪切局部化带内的变形过程抽象为胶结强度弱化及摩擦强度增强两个阶段,重点考虑了这两个阶段一前一后发挥作用的破坏本质;同时采用细观链式模型及均匀化方法将破坏过程的细观特征与宏观力学特性相结合,建立了岩石局部化渐进破损本构模型的理论公式。模型计算结果与Yumlu和Ozbay试验结果吻合较好,证明了所提出模型的正确性。通过变化模型中的参数,进一步对深部岩石的局部化渐进破坏特征进行了分析,揭示了试样呈现"尺寸效应"、"形状效应"、应变软化及II型应力-应变曲线的内在原因及影响因素。     

Discontinuous displacement approximation for capturing plastic localization

It is proposed to capture localized plastic deformation via the inclusion of regularized displacement discontinuities at element boundaries (interfaces) of the finite element subdivision. The regularization is based on a kinematic assumption for an interface that resembles that which is pertinent to the classical shear band concept. As a by-product of the regularization, an intrinsic band width is introduced as a ‘constitutive’ property rather than a geometric feature of the finite element mesh. In this way the spurious mesh sensitivity, which is obtained when the displacement approximation is continuous, can be avoided. Another consequence is that the interfacial relation between the elements is derived directly from the conventional constitutive properties of the continuously deforming material. An interesting feature is that the acoustic tensor will not only play a role for diagnosing discontinuous bifurcation but will also serve as the tangent stiffness tensor of the interface (up to within a scalar factor). An analytical investigation of the behaviour of the interface is carried out and it is shown that dilatation may indeed accompany slip within a ‘shear’ band for a general plasticity model. The significance of proper mesh alignment is demonstrated for a simple problem in plane strain and plane stress. It is shown that a unique structural post-peak response (in accordance with non-linear fracture mechanics) can be achieved when the plastic softening modulus is properly related to the bandwidth. The paper concludes with a numerical simulation of the gradual development of a shear band in a soil slope.     

Assessment of small fatigue crack growth driving forces in single crystals with and without slip bands

Strain localization under low amplitude cyclic loading is a manifestation of plastic irreversible deformation associated with early crack growth. However, traditional constitutive models cannot usually reproduce strain localization in smooth single crystals, which can affect crack growth predictions for crystallographic fatigue cracks. This work analyzes the influence of bands of localized plastic shear strain on the cyclic crack tip displacement and on a fatigue indicator parameter by making special provision of a crack along the interface of a deformation band. Furthermore, the quality of local and volume-averaged fatigue indicator parameters are assessed using finite element models of a Cu single crystal cycled to induce plastic deformation under multiple loading conditions.     

Gradient damage models coupled with plasticity: Variational formulation and main properties

A variational formulation is proposed for a family of elastic–plastic–damage models within the framework of rate-independent materials. That consists first in defining the total energy which contains, in particular, a gradient damage term and a term which represents the plastic dissipation but depends also on damage. Then, the evolution law is deduced from the principles of irreversibility, stability and energy balance. Accordingly, the plastic dissipation term which appears both in the damage criterion and the plastic yield criterion plays an essential role in the damage–plasticity coupling. Suitable constitutive choices on how the plastic yield stress decreases with damage, allows us to obtain a rich variety of coupled responses. A particular attention is paid on the equations which govern the formation of cohesive cracks where the displacement is discontinuous and the plasticity localizes. In the one-dimensional traction test where the solution is obtained in a closed form, we show that, because of damage localization, a cohesive crack really appears at the center of the damage zone before the rupture and the associated cohesive law is obtained in closed form in terms of the constitutive parameters. A Finite Element discrete version of the energy functional is used to simulate a two-dimensional traction test over a rectangular domain with mixed boundary conditions; again a localized band of plastic strain is generated seemingly independent of the mesh size.