Granular vortices: Identification,characterization and conditions for the localization of deformation

We relate the micromechanics of vortex evolution to that of force chain buckling and, on this basis, formulate the conditions for strain localization in a continuum model of dense granular media. Using the traditional bifurcation analysis of shear bands, we show that kinematic vortex fields are in fact solutions to the boundary value problem satisfying null boundary conditions. To establish an empirical basis for our study, we first develop a method to identify the location of the core and boundary of each vortex from a given displacement field in two dimensions. We then employ this method to characterize the residual deformation field (i.e., the deviation of particle motions from the continuum deformation) in a physical experiment and a discrete element simulation of dense granular samples submitted to biaxial compression. Vortices in the failure regime are essentially confined to the shear band. Primary vortices, the clear majority, rotate in the same direction as the shear band; secondary vortices, the so-called wakes, rotate in the opposite direction. Primary vortices align in spatial succession along the central axis of the band; wakes form next to the band boundaries, in between and beside two adjacent primary vortices. Force chain buckling, the governing mechanism for shear bands, is responsible for vortex formation in the failure regime. Vortex dynamics are consistent with stick-slip dynamics. From quiescent conditions of jamming or stick, vortical motions arise from force chain buckling and associated relative particle rotations and sliding; these in turn precipitate intermittent periods of unjamming or slip, evident in the attendant drops in stress ratio and bursts in both kinetic energy and local nonaffine deformation. A kinematic vortex field inside shear bands is proposed that is consistent with the equations of continuum mechanics and the underlying instability of force chain buckling: such a field is periodic with a repeating unit cell comprising a primary vortex at the center of the band, with two trailing wakes close next to the band boundaries.     

基于介观力学信息的颗粒材料损伤——愈合与塑性宏观表征

本文在二阶计算均匀化框架下提出了颗粒材料损伤--愈合与塑性的多尺度表征方法. 颗粒材料结构在宏观尺度模型化为梯度Cosserat连续体,在其有限元网格的每个积分点处定义具有离散颗粒介观结构的表征元. 建立了表征元离散颗粒系统的非线性增量本构关系. 表征元周边介质作用于表征元边界颗粒的增量力与增量力偶矩以表征元边界颗粒的增量线位移与增量转动角位移、当前变形状态下表征元离散介观结构弹性刚度、以及凝聚到表征元边界颗粒的增量耗散摩擦力表示. 基于平均场理论与Hill定理,导出了基于介观力学信息的梯度Cosserat连续体增量非线性本构关系. 在等温热动力学框架下定义了表征颗粒材料各向异性损伤--愈合和塑性的损伤、愈合张量因子与综合损伤、愈合效应的净损伤张量因子和塑性应变. 此外,定义了损伤和塑性耗散能密度与愈合能密度,以定量比较材料损伤、愈合、塑性对材料失效的效应. 应变局部化数值例题结果显示了所建议的颗粒材料损伤--愈合--塑性表征方法的有效性.      

颗粒柱塌落中的尺寸效应和瞬态流变性研究

颗粒材料是自然界和工程中广泛存在和普遍应用的材料,泥石流、滑坡和混凝土等均可视为颗粒材料。颗粒材料研究有助于更好地控制相关自然灾害或利用其某些特性。对颗粒材料柱体的塌落动力学研究不仅可以方便理解颗粒材料在瞬态流动时的流变性,还可以引申到泥石流等岩土材料的运动与堆积形态。本文利用扩展多面体离散单元法对颗粒堆积柱的塌落进行了细致的研究,探索高宽比、摩擦系数以及颗粒柱相对尺寸等对柱体塌落的影响。对颗粒集合进行分网并分析每个网格内的应力与应变率之间的关系,讨论其瞬态本构关系。相关研究对于深入理解颗粒材料重力流的动力学性质以及颗粒集合体的堆积形态具有重要意义。     

Quantification of large and localized deformation in granular materials

Quantifying large deformation in granular assemblies using concepts originating from continuum mechanics is a challenging task because of (1) the discontinuous nature of granular displacement, which does not allow the definition of a continuum measure of deformation, and (2) the almost inevitable shear band localization. These problems exist in both real-world granular materials and their numerical idealizations using particle-based simulations. In this work a new method is developed in order to address these issues. Instead of creating a meshed equivalent continuum for quantifying small engineering strains, the new method performs independent random queries on the velocity gradient characteristics of arbitrary sub-domains in the assembly through the novel concept of overlapping reference triangles, thus, enabling rigorous handling of large deformations which are usually associated with localization. The proposed method is illustrated and validated by discrete element method (DEM) simulation of a biaxial compressive test, in which apparent shear banding takes place. The homogenized deformation quantifications based on the new method match the estimations from the imposed boundary conditions. The numerical examples are also applied to (1) quantifying the heterogeneous distribution of deformation over the specimen, (2) visualizing the nucleation process of shear bands, and (3) characterizing shear flow patterns in shear bands. An investigation on the effects of the reference triangle sizes yields some inspiring and practically significant results.     

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。     

Modeling shear localization along granular soil–structure interfaces using elasto-plastic Cosserat continuum

The current study presents finite element simulations of shear localization along the interface between cohesionless granular soil and bounding structure under large shearing movement. Micro-polar (Cosserat) continuum approach is applied in the framework of elasto-plasticity in order to overcome the numerical problems of localization modeling seen in the conventional continuum mechanics. The effects of different micro-polar kinematic boundary conditions, along the interface, on the evolution and location of shear band are shown by the numerical results. Furthermore, shear band thickness is also investigated for its dependence on the initial void ratio, vertical pressure and mean grain size. Here, the distribution and evolution of static and kinematic quantities are the main focuses regarding infinite layer of micro-polar material during plane shearing, especially with advanced large movement of bounding structure. The influence of such movement has not been investigated yet in the literature. Based on the results obtained from this study, shear localization appears parallel to the direction of shearing. It occurs either in the middle of granular layer or near boundaries, regarding the assumed micro-polar kinematic boundary conditions at the bottom and top surfaces of granular soil layer. Narrower shear band is observed in lower rotation resistance of soil particles along the interface. It is emphasized that the displacement magnitude of bounding structure has significant effect on the distribution and evolution of state variables and polar quantities in the granular soil layer. However, continuous displacement has no meaningful effect on the thickness of shear band. Here, smooth distributions of void ratio and shear stress components are obtained within the shear band, what the other previous numerical investigations did not receive. Despite indirect linking of Lade’s model to the critical state soil mechanics, state variables tend towards asymptotical stationary condition in large shear deformation.     

基于细观拓扑结构演化的颗粒材料剪胀性分析

剪胀性是包括岩土材料在内的摩擦性颗粒材料的重要特征之一,其形成机制与颗粒体系内部拓扑结构的演化有关.基于颗粒体系细观数据,可对颗粒体系内部的拓扑结构特征及演化进行分析,进而建立拓扑演化与宏观剪胀变形之间的联系.采用离散单元法,根据密实、中密和松散摩擦性颗粒材料双轴试验的宏微观数据,从拓扑参量演化及接触网络拓扑变化所引起...     

散体介质SHPB被动围压试验体应力计算的理论修正方法

SHPB被动围压试验为探究散体介质在爆炸和冲击荷载作用下的力学行为提供了一个行之有效的方法。针对相关试验设计和计算中存在的弊端和不足,借助经典板壳理论将SHPB被动围压试验中用于约束散体介质的刚性套筒简化为受均匀带状内压作用的圆柱形壳体。理论计算了套筒径向位移、环向应变与均匀带状内压及套筒几何、力学参数的关系,得到了套筒径向位移、环向应变沿其轴向的分布规律;分析了套筒长度、厚度、内外径以及均匀带状内压宽度之间等无量纲几何参数对计算结果的影响;将理论计算结果与试验和数值模拟结果进行对比,验证了理论计算结果的正确性。本文中提出的理论修正方法可为指导散体介质SHPB被动围压试验提供参考。     

Fabric and connectivity as field descriptors for deformations in granular media

Granular materials involve microphysics across the various scales giving rise to distinct behaviours of geomaterials, such as steady states, plastic limit states, non-associativity of plastic and yield flow, as well as instability of homogeneous deformations through strain localization. Incorporating such micro-scale characteristics is one of the biggest challenges in the constitutive modelling of granular materials, especially when micro-variables may be interdependent. With this motivation, we use two micro-variables such as coordination number and fabric anisotropy computed from tessellation of the granular material to describe its state at the macroscopic level. In order to capture functional dependencies between micro-variables, the correlation between coordination number and fabric anisotropy limits is herein formulated at the particle level rather than on an average sense. This is the essence of the proposed work which investigates the evolutions of coordination number distribution (connectivity) and anisotropy (contact normal) distribution curves with deformation history and their inter-dependencies through discrete element modelling in two dimensions. These results enter as probability distribution functions into homogenization expressions during upscaling to a continuum constitutive model using tessellation as an abstract representation of the granular system. The end product is a micro-mechanically inspired continuum model with both coordination number and fabric anisotropy as underlying micro-variables incorporated into a plasticity flow rule. The derived plastic potential bears striking resemblance to cam–clay or stress–dilatancy-type yield surfaces used in soil mechanics.     

岩石试件端面摩擦效应数值模拟研究

试件端面摩擦效应直接影响试件内的塑性等效应变、侧向位移的分布和单元应力应变曲线。本文运用ANSYS中的接触单元模拟了平面应变状态下端面摩擦效应对塑性等效应变、侧向位移和单元应力应变曲线的影响,得到了不同摩擦系数时塑性等效应变及侧向位移的渐进变化形式。当接触面摩擦较小时,塑性等效应变图案为上下两个X形网络,侧向位移上下分布均匀;当接触面摩擦增大时,塑性等效应变网络向中部靠拢并且明显增大,侧向位移上下分布不均匀,中部较上下端面位移大;当试件端面侧向位移被限制,即摩擦力很大时,塑性等效应变网络变为一个X形局部化带,侧向位移分布更加不均匀,中部明显隆起。     

A real-space phase field model for the domain evolution of ferromagnetic materials

A real-space phase field model based on the time-dependent Ginzburg–Landau (TDGL) equation is developed to predict the domain evolution of ferromagnetic materials. The phase field model stems from a thermodynamic theory of ferromagnetic materials which employs the strain and magnetization as independent variables. The phase field equations are shown to reduce to the common micromagnetic model when the magnetostriction is absent and the magnitude of magnetization is constant. The strain and magnetization in the equilibrium state are obtained simultaneously by solving the phase field equations via a nonlinear finite element method. The finite-element based phase field model is applicable for the domain evolution of ferromagnetic materials with arbitrary geometries and boundary conditions. The evolution of magnetization domains in ferromagnetic thin film subjected to external stresses and magnetic fields are simulated and the magnetoelastic coupling behavior is investigated. Phase field simulations show that the magnetization vectors form a single magnetic vortex in ferromagnetic disks and rings. The configuration and size of the simulated magnetization vortex are in agreement with the experimental observation, suggesting that the phase field model is a powerful tool for the domain evolution of ferromagnetic materials.     

二元复合材料板的自由振动: 半解析法

二元复合材料板是超材料板结构中常见的单元之一. 针对由材料参数相差两个量级的基体和嵌入体组成的二元复合材料板, 提出结构自由振动的半解析模型, 并对其振动特性进行了研究. 基于区域分解法和二元材料的分布, 将二维平板分解成两个子区域. 通过在振型函数中附加区域试函数, 来描述复合材料板面内刚度突变引起局部位移和转角的非光滑性. 基于二元复合材料板的基本边界条件和两子区连接处的变形协调条件, 构造了新的振型函数. 基于经典薄板理论, 利用带特殊试函数的里兹法, 求得不同几何构型下二元复合材料板的固有频率和振型, 并研究了嵌入体的尺寸和位置对结构振动特性的影响规律. 通过收敛分析并与有限元仿真结果对比, 验证了本文方法的准确性. 研究结果表明: 传统的全局试函数在分析具有振动局部化的模态时会得到不准确的结果, 而附加区域试函数可以显著提高里兹法的收敛速度以及结果的准确性; 嵌入体位置对低阶固有频率的作用不明显, 却能显著改变低阶振型节线的分布和振动局部化发生的区域.      

Global–local analysis of granular media in quasi-static equilibrium

A method of global–local analysis is developed for quasi-static equilibrium problems for granular media. The two-scale modeling based on mathematical homogenization theory enables us to formulate two separate boundary value problems in terms of macro- and microscales. The macroscale problem governs the equilibrium of a global structure composed of granular assemblies, while the microscale one is posed for the particulate nature of a local structure with the friction-contact mechanism between particles. The local structure is identified with a periodic representative volume element, or equivalently, a unit cell, over which averaging is performed. The mechanical behavior of unit cells is analyzed by a discrete numerical model, in which spring and friction devices connect rigid particles, whereas the continuum-based finite element method is used for the macroscopic one. Representative numerical examples are presented to demonstrate the capability of the proposed two-scale analysis method for granular materials.     

岩土类颗粒物质宏-细观力学研究进展

岩土类颗粒物质在自然界、工程建设以及日常生活中普遍存在,其运动特性的研究在力学界已经开展了几十年.在近20年开展的一系列小尺寸物理实验中,颗粒物质表现出许多新奇现象,人们从物理角度开展了系统研究,在统计力学中,颗粒固体的流体动力学等理论研究以及实验检测技术等方面都取得突破性进展,深刻地揭示了颗粒材料的物理机制,促使力学...     

基于试验与有限元耦合技术的延性材料全程单轴本构关系获取方法

摘 要: 材料拉伸直至断裂的全程单轴本构关系对材料大变形和断裂机理研究具有重要意义。传统拉伸试验获取的材料真应力-真应变曲线在试样颈缩后不可测。借助可以精确测量三维变形的DIC(Digital image correlate) 技术和有限元分析技术(Finite element analysis),本文提出了基于漏斗试样拉伸试验获取材料全程单轴本构关系的新方法,即TF(Test and FEA)方法。该方法将TF方法获取的材料全程单轴应力应变关系曲线作为有限元软件中的材料本构关系对漏斗试样拉伸变形过程进行模拟,其模拟载荷-位移曲线、漏斗根部直径-位移曲线和漏斗变形轮廓线等均与试验结果吻合良好,试样表面模拟应变也与DIC测试结果吻合, 根据不同半径漏斗试样模拟获得的全程真应力-真应变曲线保持良好一致性。最后,还对试样颈缩断面的力学行为进行了讨论,并给出了304不锈钢、汽轮机叶片材料2Cr12Ni4Mo3VNBN和 1Gr12Ni3Mo2VN、汽轮机转子材料30Cr2Ni4MoV的全程单轴本构关系模型参数、破断应力和破断应变。     

Mixed numerical–experimental technique for orthotropic parameter identification using biaxial tensile tests on cruciform specimens

This paper presents a mixed numerical–experimental method for the identification of the four in-plane orthotropic engineering constants of composite plate materials. A biaxial tensile test is performed on a cruciform test specimen. The heterogeneous displacement field is observed by a CCD camera and measured by a digital image correlation (DIC) technique. The measured displacement field and the subsequently computed strain field are compared with a finite element simulation of the same experiment. The four independent engineering constants are unknown parameters in the finite element model. Starting from an initial value, these parameters are updated till the computed strain field matches the experimental strain field. Two specimen geometries are used: one with a centered hole to increase the strain heterogeneity and one without a hole. It is found that the non-perforated specimen yields the most accurate results.     

Modeling of textural anisotropy in granular materials with stochastic micro-polar hypoplasticity

The paper deals with a numerical analysis of the effect of textural anisotropy on the behaviour of cohesionless granular materials with consideration of shear localization. For a simulation of the mechanical behaviour of a granular material during a monotonic deformation path, an isotropic micro-polar hypoplastic constitutive model was used. To describe textural effects, spatially correlated random fields of the initial void ratio were subject to rotation against the horizontal axis. The 2D random fields were generated using a conditional rejection method. The results were compared with those obtained with an anisotropic micro-polar constitutive model for a uniform distribution of the initial void ratio. The calculations were carried out with an initially dense granular specimen during plane strain compression under constant lateral pressure.     

Experimental and numerical investigations of the deformation of soft materials under tangential loading

The surface ‘tensile test’, in which tangential loads are applied through surface mounted adhesive tapes, is a viable method for the assessment of mechanical properties of soft materials, particularly biological soft materials in vivo. In the present work the deformation pattern and force–displacement relationship in the surface tensile test were experimentally investigated using surface displacement analysis (SDA) and numerically simulated using finite element modelling. The experimental and FE results showed close agreement using silicone rubber as a model material. The force–displacement relationship was found to be dependent on the tape separations. SDA measurements and FE simulation showed that the displacement and strain fields were not uniform and the distribution pattern varies with tape separation. A combined experimental–numerical approach to inversely extract material properties using multiple tests with different length scales is proposed and assessed using a model material.