A linear model of elasto-plastic and adhesive contact deformation

Rigorous non-linear models of elasto-plastic contact deformation are time-consuming in numerical calculations for the distinct element method (DEM) and quite often unnecessary to represent the actual contact deformation of common particulate systems. In this work a simple linear elasto-plastic and adhesive contact model for spherical particles is proposed. Plastic deformation of contacts during loading and elastic unloading, accompanied by adhesion are considered, for which the pull-off force increases with plastic deformation. Considering the collision of a spherical cohesive body with a rigid flat target, the critical sticking velocity and coefficient of restitution in the proposed model are found to be very similar to those of Thornton and Ning’s model. Sensitivity analyses of the model parameters such as plastic, elastic, plastic-adhesive stiffnesses and pull-off force on work of compaction are carried out. It is found that by increasing the ratio of elastic to plastic stiffness, the plastic component of the total work increases and the elastic component decreases. By increasing the interface energy, the plastic work increases, but the elastic work does not change. The model can be used to efficiently represent the force-displacement of a wide range of particles, thus enabling fast numerical simulations of particle assemblies by the DEM.     

钢球和刚性平面弹塑性正碰撞恢复系数研究

采用有限元法(FEM)研究了理想弹性和分段线性/幂指数强化材料钢球与刚性平面的弹性和弹塑性正碰撞。弹性碰撞FEM计算结果和Hertz理论计算结果吻合。弹性碰撞FEM计算结果说明波动效应在球体与刚性平面正碰撞中引起的能量损失可以忽略。弹塑性碰撞的FEM计算结果分别与Johnson和Thornton的理论模型计算结果进行了对比。弹塑性碰撞中,当碰撞速度大于临界速度时发生有限塑性变形,FEM计算结果表明恢复系数与[(v/vy)/(E*/σs)]-0.27成正比。     

Direct measurement of particle–particle interaction using micro particle interaction analyzer (MPIA)

Direct particle–particle contact force measurement was successfully conducted for realistic parameter determination to support discrete element method (DEM) simulation by using a newly developed force measurement of micro particle interaction analyzer (MPIA). In this system particle-to-particle distance and deformation can be controlled by nanometer accuracy. The system can be used for measuring not only short-distance deformation but also long-distance deformation that was validated by both elastic contact and liquid bridge interaction including rupture distance, respectively. Then, the system was applied to obtain plastic normal deformation characteristics such as coefficients of restitution of the spherical granules at low loading force less than 0.5 mN. Granules were prepared from two-stage pressure swing granulation (PSG) technique in a fluidized bed.     

Computer Modeling of the Processes of Elastoplastic Deformation of a WIre in the Course of Winding

An algorithm is proposed for the numerical solution of the problem of elastoplastic torsion of a rod for constant values of a longitudinal force and a torque with regard for the effect of hardening of the material. The dependences of the bending moment, relative elongation, and torsion of the rod on the curvature are obtained. It is shown that the plastic properties of the material of the rod exert significant influence on the numerical results. The three-dimensional diagrams of normal and tangential stresses are presented for different stages of the rod loading.     

X80管线钢不同变形状态的磁记忆检测试验研究

为探明管线钢在不同变形状态的力磁耦合特性,以实现油气管道塑性变形损伤的早期预警,本文开展了 X80管线钢在弹塑性变形阶段的磁记忆检测试验研究.采用疲劳试验机对标准板状试件导入不同变形状态,通过应力-应变监测系统获取试件的实时应变情况,同时利用磁记忆检测仪对卸载后的试件表面磁场强度进行离线扫描.结果表明:在弹性变形阶段,...     

Transformation of sliding motion to rolling during spheres collision

In this research, we have investigated the three-dimensional elastic collision of two balls, based on friction in the tangential plane. Our aim is to offer analytical closed form relations for post collision parameters such as linear and angular velocities, collision time and tangential and normal impulse in three dimensions. To simplify the problem, stick regime is not considered. In other words, balls have a low tangential coefficient of restitution. Sliding, sliding then rolling, and rolling at the beginning of contact are three cases that can occur during impact which have been considered in our research. The normal interaction force is described by the Hertz contact force and dimensionless analysis is used for investigating normal interaction force; furthermore, Coulomb friction is considered during sliding. Experimental data for collisions show when sliding exists through the impact, tangential impulses can be taken as frictional impulses using the Coulomb law if the dynamic regime is not stick regime. To identify transformation of sliding motion to rolling or sticking during the impact process, linear and trigonometric functions are considered as an approximation for the normal interaction force. Afterwards, we have obtained the condition for the possibility of this transformation; moreover, we can estimate the duration of sliding and rolling or sticking. We have obtained an analytical solution for maximum force and deformation, collision time, impulses and post-collision linear and angular velocities in three dimensions.     

基于SMP破坏准则的土体弹塑性动力本构模型

利用土体的塑性流动理论,提出了用于描述饱和砂土动力反应性质的弹塑性本构模型。土体总的变形由三部分组成:即弹性应变、与体积屈服机制相关的塑性应变和与剪切屈服机制相关的塑性应变。土体在初始加载与卸载和重新加载阶段性质的差别通过采用不同的模型参数加以反映。该模型能够较为准确地描述饱和砂土在单调加载和循环加载条件下的反应性质。     

Problems of the mathematical theory of plasticity

This paper gives the results of investigations aimed at the development and elaboration of a theory for the relationships governing plastic-deformation processes in the contemporary mathematical theory of plasticity. We discuss its two main classical directions: the theory of flow and the theory of processes. The first direction is based on the concept of existence of a limiting surface and the possibility of decomposition of strains into elastic and plastic components. On the contrary, the second direction, which is progressing rapidly, does not use the concept of existence of limiting surfaces and does not allow decomposition of strains into elastic and plastic components except for the cases of simple loading and simple unloading. It is thought that in complex loading and complex unloading the deformation is elastoplastic (partially plastic or partially elastic). We believe that these two directions in the theory of plasticity in the case of complex loading will eventually approach each other because they are intended for the investigation of the mechanisms of the same physicomechanical processes of plastic deformation of various media. This work shows one possibility of such approach. Tver' State Technical University, Tver', Russia. Translated from Problemy Prochnosti, No. 1, pp. 22–41, January–February, 2000.     

静动力弹塑性分析的杆系离散单元计算理论研究

杆系离散单元法的现有研究成果均假定接触本构模型的切向弹簧仅用于描述剪力引起的纯剪切变形,这与弯曲梁理论下剪力引起的变形情况不相符。该文针对该问题重新定义了切向弹簧,并根据能量等效原理系统推导了不考虑或考虑剪切变形工况接触本构模型的切向接触刚度系数计算公式。在此基础上,提出了杆系离散单元精细塑性铰法以描述结构的塑性开展问题,推导了颗粒间的弹塑性接触本构模型。采用自编程序对两个大型网壳结构分别进行了静、动力弹塑性行为分析,验证了接触本构模型正确性和精细塑性铰法的适用性。该文将杆系离散单元法的基本计算理论系统化,并补充了杆系离散单元法的弹塑性计算理论,为结构静、动力分析提供了新思路。     

Energy absorption during compression and impact of dry elastic-plastic spherical granules

The discrete modelling and understanding of the particle dynamics in fluidized bed apparatuses, mixers, mills and others are based on the knowledge about the physical properties of particles and their mechanical behaviour during slow, fast and repeated stressing. In this paper model parameters (modulus of elasticity, stiffness, yield pressure, restitution coefficient and strength) of spherical granules (γ-Al₂O₃, zeolites 4A and 13X, sodium benzoate) with different mechanical behaviour have been measured by single particle compression and impact tests. Starting with the elastic compression behaviour of granules as described by Hertz theory, a new contact model was developed to describe the force-displacement behaviour of elastic-plastic granules. The aim of this work is to understand the energy absorption during compression (slow stressing velocity of 0.02 mm/s) and impact (the impact velocity of 0.5–4.5 m/s) of granules. For all examined granules the estimated energy absorption during the impact is found to be far lower than that during compression. Moreover, the measured restitution coefficient is independent of the impact velocity in the examined range and independent of the load intensity by compression (i.e. maximum compressive load). In the case of repeated loading with a constant load amplitude, the granules show cyclic hardening with increasing restitution coefficient up to a certain saturation in the plastic deformation. A model was proposed to describe the increase of the contact stiffness with the number of cycles. When the load amplitude is subsequently increased, further plastic deformation takes place and the restitution coefficient strongly decreases.     

On the Elastic and Plastic Strain Decomposition in Granular Materials

An impressive number of constitutive relations have been developed in the past few decades. With respect to the class of elastoplastic phenomenological models, elastic and plastic strain decomposition is generally stated as a basic assumption, so as to treat the elastic (i.e., recoverable) and plastic (i.e., unrecoverable) parts of the strains separately. For incrementally nonlinear relations, this decomposition is not possible. In the first part of this paper a detailed discussion of elastic and plastic decomposition is presented. Then the paper expands the debate on this crucial point by addressing the question of defining elastic (or plastic) deformation specifically for granular materials, considering two complementary approaches. An incrementally nonlinear model is used first and then a multi-scale approach is considered to examine the compatibility of this partition from a micromechanical point of view, with the usual definition of both elastic and plastic incremental strains. Finally, micro-structural considerations show that only a fraction of the elastic strain energy can be recovered, whatever the unloading path, after an incremental loading path inducing both elastic and plastic mechanisms.     

Finite element analysis of vickers indentation cracking processes in brittle solids using elements exhibiting cohesive post-failure behaviour

The cracking processes during the indentation test of brittle solids is simulated by means of the finite element method (FEM) using elements exhibiting cohesive post-failure behaviour and alumina as the model material. The results show that at low indentation loads, median cracks could nucleate at full loading but Palmqvist cracks only nucleate in the unloading stage and that they may not join up even after full unloading. Such cracks are stable as they are embedded in a region of high hydrostatic compression throughout the indentation test. At high indentation loads, both median and Palmqvist cracks nucleate early during the loading stage and coalesce to form a half-penny crack on further loading. Although the cracks are embedded in a region of high hydrostatic compression during loading, an annular tensile region eventually develops in between the cracked material beneath the indenter and the surrounding uncracked material during the unloading stage of the macro-indentation. This not only provides the driving force for existing cracks to grow but also new crack systems to form. The present work shows that for brittle solids with negligible plastic deformation, the mismatch in elastic recovery between the cracked and uncracked bodies on unloading plays an important role in indentation fracture processes.     

A new boundary element technique without domain integrals for elastoplastic solids

A simple idea is proposed to solve boundary value problems for elastoplastic solids via boundary elements, namely, to use the Green's functions corresponding to both the loading and unloading branches of the tangent constitutive operator to solve for plastic and elastic regions, respectively. In this way, domain integrals are completely avoided in the boundary integral equations. Though a discretization of the region where plastic flow occurs still remains necessary to account for the inhomogeneity of plastic deformation, the elastoplastic analysis reduces, in essence, to a straightforward adaptation of techniques valid for anisotropic linear elastic constitutive equations (the loading branch of the elastoplastic constitutive operator may be viewed formally as a type of anisotropic elastic law). Numerical examples, using J₂‐flow theory with linear hardening, demonstrate that the proposed method retains all the advantages related to boundary element formulations, is stable and performs well. The method presented is for simplicity developed for the associative flow rule; however, a full derivation of Green's function and boundary integral equations is also given for the general case of non‐associative flow rule. It is shown that in the non‐associative case, a domain integral unavoidably arises in the formulation. Copyright © 2005 John Wiley & Sons, Ltd.     

不同初始磁状态U75V钢变形阶段的磁记忆参数表征

通过对经退磁处理和未消磁的U75V钢光滑试件进行静载拉伸试验研究了初始磁状态对试件表面磁信号的影响。结果表明:消磁试件长度范围内的表面磁场在弹性阶段呈现很好的线性分布。进入塑性后,切向磁场出现局部弯曲。利用切向磁场均值和法向磁场斜率变化可以区分弹塑性阶段以及确定弹性阶段的应力幅值;未消磁试件随着载荷增加其表面磁场波动幅度减小,由初始无规律分布逐渐转向磁有序状态。利用未消磁试件长度范围外的磁记忆信号曲线的磁场均值及斜率变化可以有效表征不同的变形阶段。     

单层网壳结构弹塑性屈曲分析的离散单元法研究

该文提出离散元塑性区法,即将任意2个球元的接触截面划分成若干小面积,通过各小面积的应力状态描述整个截面的塑性发展过程,较离散元塑性铰法更精确。该文推导了杆系离散元截面应变增量计算公式,建立了截面在三维应力-应变状态下的结构弹塑性本构方程、加卸载准则、截面内力积分公式以及计算分析流程。离散元弹塑性屈曲分析的追踪策略与弹性屈曲分析完全相同,即仍采用离散元力控制法或位移控制法。采用Fortran语言自编程序对若干单层网壳结构算例进行弹塑性屈曲分析,验证了离散元塑性区法的正确性和适用性,拓宽了离散单元法在工程领域的应用范围,为结构分析提供了新路径。     

Deformation and Mechanical Characteristics of Compacted Binary Mixtures of Plastic (Microcrystalline Cellulose), Elastic (Sodium Starch Glycolate), and Brittle (Lactose Monohydrate) Pharmaceutical Excipients

This work studies the tensile strength, coherence, elastic, and plastic energy of single and bi-component compacted tablets consisting of (i) microcrystalline cellulose (MCC) PH 102 as a plastic material, (ii) (SSG) as an elastic material, and (iii) alpha lactose monohydrate as a brittle material by direct compression. Compacted tablets were studied with various mass ratios formed at an ultimate compaction stress of 150 MPa. The loading and unloading stages of the compaction process for the single and binary tablets were evaluated based on the energies derived from the force-displacement data obtained. The resulting tablet quality was measured in terms of the tensile strength. Material that exhibit predominantly plastic deformation (MCC) shows a dominant property over elastically deforming sodium starch glycolate (SSG) and brittle (lactose) materials during the loading and unloading stages of the compaction process. In conclusion, the tensile strength of the formed tablets depends directly on the plastic energy and indirectly on the elastic energy and is negatively affected by the presence of a brittle material.     

A Lagrangian model for hardening behaviour of materials at finite deformation based on the right plastic stretch tensor

In this paper a modified multiplicative decomposition of the right stretch tensor is proposed and used for finite deformation elastoplastic analysis of hardening materials. The total symmetric right stretch tensor is decomposed into a symmetric elastic stretch tensor and a non-symmetric plastic deformation tensor. The plastic deformation tensor is further decomposed into an orthogonal transformation and a symmetric plastic stretch tensor. This plastic stretch tensor and its corresponding Hencky’s plastic strain measure are then used for the evolution of the plastic internal variables. Furthermore, a new evolution equation for the back stress tensor is introduced based on the Hencky plastic strain. The proposed constitutive model is integrated on the Lagrangian axis of the plastic stretch tensor and does not make reference to any objective rate of stress. The classic problem of simple shear is solved using the proposed model. Results obtained for the problem of simple shear are identical to those of the self-consistent Eulerian rate model based on the logarithmic rate of stress. Furthermore, extension of the proposed model to the mixed nonlinear isotropic/kinematic hardening behaviour is presented. The model is used to predict the nonlinear hardening behaviour of SUS 304 stainless steel under fixed end finite torsional loading. Results obtained are in good agreement with the available experimental results reported for this material under fixed end finite torsional loading.     

Effect of grain size on cyclic microplasticity of ECAP processed commercial pure magnesium

Equal channel angular pressing (ECAP) was performed on the extruded commercial pure magnesium at 250 °C for 4 passes. Heat treatments were carried out to modify the microstructures. The cyclic plastic deformation behavior of pure Mg with different grain sizes in microstrain region was studied by tensile loading and unloading experiments. The microplastic deformation process of pure Mg can be divided into two stages. In the first stage, pronounced plastic deformation associated with dislocation motion on basal plane is initiated at several MPa. The materials are softened and characterized by low friction stresses and hardening exponents. The microplastic deformation enters into region II above the strain of about 8 × 10^?4. Annihilation and tangle of dislocations lead to the increase of hardening exponents and friction stresses. Pure Mg shows a very pronounced anelastic behavior during cyclic microplastic deformation, which results in a rapid increase of modulus defect, effectively decreasing the elastic modulus by up to 60 %. Grain size has a marked effect on microplastic deformation behavior of pure Mg. With increasing the grain size, the specimen shows a more pronounced microstrain and anelastic behavior.     

吸能型防冲立柱液体冲击问题研究

针对冲击作用下加入吸能构件后液压立柱的液体冲击问题,对扩径式构件在不同加载下的变形行为和特性进行分析,建立基于LuGre模型的吸能构件能量吸收模型。基于液体冲击定解问题的一般方程进行吸能构件及立柱系统顶板来压液体冲击理论和仿真分析,得到吸能构件对立柱内液体冲击的影响规律。结果表明:最大静摩擦力和库伦摩擦力对应吸能构件峰值承载力以及稳定变形阶段反作用力,鬃毛刚度和微观阻尼系数影响吸能构件弹性变形过度到塑性变形时的力-位移特性;随着扩径式构件的变形过程,吸能构件对立柱液体冲击的影响作用分为近似弹性、柔性让位吸能和刚性三个阶段。