考虑曲率纵向变形效应的大变形柔性梁刚柔耦合动力学建模与仿真

对在平面内做大范围转动的中心刚体柔性梁系统的动力学进行了研究,建立了考虑大变形效应的系统刚柔耦合动力学模型,并进行了动力学仿真.该动力学模型不但考虑了柔性梁横向弯曲变形和纵向变形(包含轴向拉伸变形和横向弯曲变形而引起的纵向缩短项),还考虑了纵向变形对曲率的影响,称为曲率纵向变形效应.在以往的研究中,柔性梁的横向弯曲变形能往往直接使用柔性梁横向弯曲变形来表达,并没有考虑纵向变形的影响.为了考虑柔性梁纵向变形对横向弯曲变形能的影响,在浮动坐标系下使用柔性梁参数方程形式的精确曲率公式来计算柔性梁的弯曲变形能.在此基础上建立了基于浮动坐标系的考虑曲率纵向变形效应的刚耦合动力学模型.论文给出了数值仿真算例,验证了本文所建的动力学模型既能适用于柔性梁的小变形问题,又能适用于大变形问题,且较现有高次刚柔耦合动力学模型更加适用于大变形问题的处理.论文还通过与能处理柔性梁大变形问题的绝对节点坐标法的比较,验证了模型的正确性.      

Analysis of diffusion induced elastoplastic bending of bilayer lithium-ion battery electrodes

Bilayer electrode, composed of a current collector layer and an active material layer, has great potential in applications of in-situ electrochemical experiments due to the bending upon lithiation. This paper establishes an elastoplastic theory for the lithiation induced deformation of bilayer electrode with consideration of the plastic yield of current collector. It is found that the plastic yield of current collector reduces the restriction of current collector to an active layer, and therefore, enhances in-plane stretching while lowers down the rate of electrode bending. Key parameters that influence the elastoplastic deformation are identified. It is found that the smaller thickness ratio and lower elastic modulus ratio of current collector to an active layer would lead to an earlier plastic yield of the current collector, the larger in-plane strain, and the smaller bending curvature, due to balance between the current collector and the active layer. The smaller yield stress and plastic modulus of current collector have similar impacts on the electrode deformation.     

Diffusion induced stresses in buckling battery electrodes

Highly networked nanostructured battery electrode materials offer the possibility of achieving both rapid battery charge–discharge rates and high storage capacity. Recently, lithium ion battery (LIB) electrodes based on a 2-D honeycomb architecture were shown to undergo remarkable and reversible morphological changes during the lithiation process. Charge–discharge rates in 3-D composite electrode have also been shown to benefit from sandwiching the electrolytically active material between highly conductive ion and electron transport pathways to reduce electrical resistance and solid-state diffusion lengths. In the present work we simulate and analyze the observed morphological changes in honeycomb electrodes, with and without the presence of conductive pathways, during the lithiation–delithiation process. Diffusion induced stresses are analyzed for such structures undergoing elastic–plastic deformation during cycling. The results show that such a periodic, nanostructured electrode geometry allows for the presence of buckling-like deformation modes, which effectively reduce the resulting mechanical stresses that lead to electrode failure.     

Model for charge/discharge-rate-dependent plastic flow in amorphous battery materials

Plastic flow is an important mechanism for relaxing stresses that develop due to swelling/shrinkage during charging/discharging of battery materials. Amorphous high-storage-capacity Li–Si has lower flow stresses than crystalline materials but there is evidence that the plastic flow stress depends on the conditions of charging and discharging, indicating important non-equilibrium aspects to the flow behavior. Here, a mechanistically-based constitutive model for rate-dependent plastic flow in amorphous materials, such as Li_xSi alloys, during charging and discharging is developed based on two physical concepts: (i) excess energy is stored in the material during electrochemical charging and discharging due to the inability of the amorphous material to fully relax during the charging/discharging process and (ii) this excess energy reduces the barriers for plastic flow processes and thus reduces the applied stresses necessary to cause plastic flow. The plastic flow stress is thus a competition between the time scales of charging/discharging and the time scales of glassy relaxation. The two concepts, as well as other aspects of the model, are validated using molecular simulations on a model Li–Si system. The model is applied to examine the plastic flow behavior of typical specimen geometries due to combined charging/discharging and stress history, and the results generally rationalize experimental observations.     

Anomalous behavior revisited: Dynamic response of elastic-plastic structures

Based on the minimum principle of acceleration in the elastic-plastic continua under finite deformation, the dynamic response of an elastic-perfectly plastic pin-ended beam subjected to rectangular impulse loading is studied with the help of a numerical approach. The calculated results once again show the anomalous behavior of the beam during its response process, which was previously found in [1]. By carefully analyzing the instantaneous distribution of the bending moment, the membrane force, the curvature and displacement during the response process, it is concluded that the interactive effect between the geometry and materials nonlinearities of the structure is the key reason for leading to the anomalous behavior. This will be helpful for clarifying some misunderstandings in explaining the problem before. Project supported by the National Natural Science Foundation of China.     

圆柱壳纯弯曲时塑性失稳临界曲率半径模型

薄壁管材在等曲率矫直生产中,塑性失稳临界曲率半径作为重要的工艺参数,直接决定了设备结构和产品质量。而目前现场仍沿用经验图表结合人工经验和反复试矫对其进行估定,亟待建立针对性的临界曲率半径数学模型以指导生产。在力学建模和分析时,就是确定具有初始曲率的圆柱壳体在纯弯曲条件下塑性失稳的临界曲率半径,为此从旋转壳体一般几何方程出发,基于J2形变理论和能量理论,运用里茨法建立了圆柱壳体在纯弯曲条件下塑性失稳时的临界弯矩,以此确定了临界曲率半径模型,并给出了数值解法。应用ANSYS/LS-DYNA进行了有限元动态仿真试验,证明了模型是近似正确的,并通过仿真对比分析证明了轴向起皱先于截面畸变是圆柱壳体在纯弯曲条件下塑性失稳的主要模态。     

Approximate estimation of hardening-softening behaviour of circular pipes subjected to pure bending

An approximate method for describing the plastic hardeningsoftening behaviour of circular pipes subjected to pure bending is presented. Theoretical estimation based on the uniform ovalization model and local collapse model proposed in the paper is incorporated to give several simple formulations with reasonable accuracy for determining the relationship between bending moment (M) and curvature (k) in the purely bended pipes. Attention is focused on the critical curvature associated with maximum resistant moment and the maximum change in the original diameter before the end of uniform ovalization stage as well as the local collapse behaviour. Some comparisons between analytical results and experimental results are made in order to examine the theory.     

铁磁矩形简支板的磁弹塑性弯曲行为分析

基于广义变分原理得到的磁力计算公式,采用塑性增量理论,Mises屈服准则和有效的增量有限元计算方法,研究了线性强化材料铁磁矩形板的磁弹塑性弯曲行为。在文中定量模拟了铁磁简支矩形板在外加磁场作用下的挠度特征曲线,铁磁板发生塑性变形时的构型图和不同外加磁场下的中截面构型,以及铁磁板在卸载后的残余挠度特征曲线等力学特征,分析了塑性区域随磁场增加而扩展的情况。数值结果表明:当铁磁矩形板上的部分区域发生塑性屈服后,其变形明显大于相同磁场条件下铁磁板发生的弹性变形值;且随着外加磁场倾角的增大(0°<α≤45°),铁磁板进入塑性屈服状态的临界屈服磁场值减小;铁磁板的中截面构形为双半波型,其塑性区域由铁磁板两侧挠度最大的区域向板的中心区域扩展,板的中心最后进入塑性区域等。     

基于拓扑优化的新型蜂窝结构设计

可变体飞行器若要实现机翼后掠角、面积和前后缘弯度等参数的大幅度变化,机翼蒙皮需要具有光滑的气动外形、大变形、高承载以及驱动力小的特点。针对柔性蒙皮的需求,本文利用拓扑优化方法设计了一种新型零泊松比蜂窝结构,通过有限元仿真与U形蜂窝结构和余弦形蜂窝结构进行对比,验证其变形和承载等性能。以最大应变2%为基准,比较了三种蜂窝结构的变形能力。结果表明,新型蜂窝结构的拉伸变形量高达75%,分别是U形蜂窝结构和余弦形蜂窝结构的1.7倍和2.1倍。在最大位移量相同时,所需驱动力分别是U形蜂窝结构和余弦形蜂窝结构的0.51倍和0.28倍,表明新型蜂窝结构具有很大的易变形能力。当蜂窝结构的橡胶蒙皮受到相同压强载荷且处于初始未拉伸状态/拉伸状态时,新型蜂窝结构橡胶蒙皮的最大法向位移量分别是U形蜂窝橡胶蒙皮和余弦形蜂窝橡胶蒙皮的0.4倍/0.56倍和0.29倍/0.42倍,表明新型蜂窝结构具有良好的面外承载能力。另外,通过适当增加壁厚,可以提高新型蜂窝结构本身的抗弯曲能力。分析结果表明,本文设计的新型蜂窝结构具备大变形、高承载以及驱动力小的优点。     

Elastic–plastic behavior of a semicircular frame being pressed against a rigid plane

As a simplified structural model, a semicircular frame is used to study the crashworthiness behavior of an aircraft fuselage. The quasi-static large elastic-plastic deformation of a semicircular frame in the process of its being pressed against a rigid ground is analyzed. First, based on the linear elastic assumption, the quasi-static large deformation contact process of the frame can be divided into three phases, i.e., point contact, line contact and post-buckling. By means of a shooting method, the relations between the displacement and contact force as well as the distribution of bending moment in the three phases are obtained. Then, by assuming an elastic, perfectly-plastic moment-curvature relationship for the semi-circular frame, the contact process is analyzed in detail to reveal the plastic collapse mechanism, the traveling of plastic hinge and the force-displacement relationship. In order to verify the analysis, a preliminary experiment was conducted, in which two types of half rings with clamped ends were pressed by a rigid plate. In addition, a numerical simulation is also conducted by employing ABAQUS to analyze both rectangular cross-sectional beam and I-beam. Finally, the theoretical predictions are compared with the experimental results and numerical solutions, showing that the elastic-plastic analysis can predict the contact process very well.     

端部受斜撞击作用悬臂梁的弹塑性动力响应模式

基于大变形动力控制方程并利用有限差分离散分析,研究了斜撞击作用下弹塑性悬臂梁的动力响应．通过对屈服函数以及弯矩、轴力在动力响应过程中分布规律的分析,阐明了斜撞击下恳臂梁的弹塑性动力响应模式和斜撞击的轴向分量对变形机制的影响．研究表明,弹塑性响应过程可划分为四个阶段,对应的变形模式为：“压缩塑性区扩展”模式,“广义移行塑性铰”和“压缩塑性区收缩”混合模式,“驻定塑性铰”模式,“弹性自由振动”模式．与刚塑性分析所假定的两相变形模式比较,弹塑性应响分析证实了响应早期的瞬态轴向压缩模式和梁根部“驻定塑性铰”模式的存在性,肯定了刚塑性分析所假定变形模式的主要特征．斜撞击的轴向分量在撞击发生的瞬时主导了梁的变形,使梁呈现同承受横向冲击明显小同的变形规律．随着响应的深入,轴向分量迅速衰减,其对截面屈服的贡献非常微弱,由横向分量引起的弯曲挠动在大部分时间内主导和控制梁的变形．数值计算结果表明,斜撞击载荷的质量、撞击速度和角度是影响梁动力响应的重要因素．     

阴极充氢对结构钢裂尖形变行为的影响

采用微机控制激光散斑干涉技术，原位研究了结构钢单边缺口预裂纹试样在３．５％Ｎａｄ水溶液中，－１４００ｍＶ（ＳＣＥ）电位下阴极完氢６小时前后，裂尖材料形变行为的变化。同时，还对充氢与未充氢条件下光滑圆柱试样的应力－应变行为进行了对比研究，用扫描电镜观察了断口形貌。结果表明：由于氢的进入，使材料的加工硬化程度加剧，从而导致了变形困难。     

泡沫铝在SHPB高温动态下的变形过程研究

利用分离式Hopkinson压杆(SHPB)实验装置研究轻质泡沫铝在动态压缩下的温度相关性,重点设计了一种基于SHPB的可视化高温炉,在此基础上通过高速摄影观测泡沫铝试件在高低温且动态压缩下的变形过程。动态加载下的实验结果表明：常温下,胞壁在变形过程中易于观察到屈曲失稳、撕裂、弯曲等现象,且在压缩的过程中碎片飞溅;高温下材料软化较明显,呈现出更多的塑性弯曲现象,但是屈曲失稳与撕裂的现象并不显著,变形过程中并无碎片产生。     

Localization and propagation of curvature under pure bending in steel tubes with Lüders bands

The paper examines the plastic bending of steel tubes exhibiting Lüders bands through a combination of experiments and analyses. In pure bending experiments on tubes with diameter-to-thickness ratio of 18.8 tested under end-rotation control, following the elastic regime the moment initially traced a somewhat ragged plateau. At the beginning of the plateau Lüders bands appeared on the tension and compression sides of the cross section and simultaneously the curvature localized in one or two short zones while the rest of the tube maintained a much lower curvature. As the rotation of the ends was increased, one of the higher curvature zones spread at a nearly steady rate, affecting an increasingly larger part of the tube. When the whole tube was deformed to the higher curvature, the moment started to gradually increase while the tube deformed uniformly. A moment maximum was eventually attained and the structure failed by localized diffuse ovalization without any apparent effect from the initial Lüders bands-induced propagating instability. The problem was analyzed using 3D finite elements with a fine mesh. The material was modeled as an elastic–plastic solid with an up–down–up response over the extent of the Lüders strain, followed by hardening. The calculated response reproduced all major structural events observed experimentally including the initiation of the Lüders deformation, the moment plateau that followed, its extent, and the curvature localization and propagation associated with it. As in the experiments, once the high curvature extended over the whole tube length, the response of the tube became stable and the curvature uniform. With further bending the increasing ovalization induced a limit moment at a very high curvature.     

Experimental study and electromechanical model analysis of the nonlinear deformation behavior of IPMC actuators

This paper develops analytical electromechanical formulas to predict the mechanical deformation of ionic polymer–metal composite(IPMC) cantilever actuators under DC excitation voltages. In this research, IPMC samples with Pt and Ag electrodes were manufactured, and the large nonlinear deformation and the effect of curvature on surface electrode resistance of the IPMC samples were investigated experimentally and theoretically. A distributed electrical model was modified for calculating the distribution of voltage along the bending actuator. Then an irreversible thermodynamic model that could predict the curvature of a unit part of an IPMC actuator is combined with the electrical model so that an analytical electromechanical model is developed. The electromechanical model is then validated against the experimental results obtained from Pt-and Ag-IPMC actuators under various excitation voltages. The good agreement between the electromechanical model and the actuators shows that the analytical electromechanical model can accurately describe the large nonlinear quasi-static deflection behavior of IPMC actuators.     

广义双重抗侧力结构体系的统一位移计算理论

在广义概念上将建筑结构视为由同时考虑弯曲变形、剪切变形的两种子结构组成的双重抗侧力结构体系, 提出弹性阶段广义双重结构水平位移的统一的计算方法. 子结构单独承受水平外载荷时其内力与变形的关系服从Timoshenko剪切梁基本理论, 在子结构协同工作的基础上, 采用水平变形连续化的计算方法, 建立了广义双重抗侧力结构体系的统一位移微分方程, 以结构承受均布载荷作用为例推导出两个子结构的弯曲变形、剪切变形及结构总水平位移的通用解析表达式. 对框架-剪力墙结构与广义双重结构的位移微分方程式、微分方程特解、水平位移解析解进行了全面对比分析, 证明了框架-剪力墙结构是隶属于广义双重结构体系的一种具体表现形式; 算例分析表明, 对于一般中高层双重抗侧力结构, 采用解析法计算所得的位移结果能够满足一般工程设计的精度要求.      

Research progress in degradation mechanism of silicon anode materials for lithium-ion batteries

硅负极材料由于具有非常高的理论比容量,使之成为锂离子电池极具前景的负极替代材料,然而,硅负极材料在充放电过程中会发生非常大的体积变形,这会引起活性材料的破坏失效,严重影响其电化学循环性能,成为制约其在锂离子电池领域广泛应用的最大瓶颈,本文介绍了硅负极材料的不同结构形态及其在充放电过程中电化学性能的退化机理,并综述了充放电过程中的力学性能演化、相关理论分析、数值模拟计算等方面的最新国际研究进展,展望了硅负极材料力学失效方面的研究重点,     

Cyclic plasticity and shakedown in high-capacity electrodes of lithium-ion batteries

Of all materials, silicon has the highest capacity to store lithium, and is being developed as an electrode for lithium-ion batteries. Upon absorbing a large amount of lithium, the electrode swells greatly, with a volumetric change up to 300%. The swelling is inevitably constrained in practice, often leading to stress and fracture. Evidence has accumulated that the swelling-induced stress can be partially relieved by plastic flow, and that electrodes of small feature sizes can survive many cycles of lithiation and delithiation without fracture. Here we simulate a particle of an electrode subject to cyclic lithiation and delithiation. A recently developed theory of concurrent large swelling and finite-strain plasticity is used to co-evolve fields of stress, deformation, concentration of lithium, and chemical potential of lithium. We identify three types of behavior. When the yield strength is high and the charging rate is low, the entire particle deforms elastically in all cycles. When the yield strength is low and the charging rate is high, the particle (or part of it) undergoes cyclic plasticity. Under intermediate conditions, the particle exhibits the shakedown behavior: part of the particle flows plastically in a certain number of initial cycles, and then the entire particle remains elastic in subsequent cycles. We discuss the effect of the three types of behavior on the capacity and the electrochemical efficiency.     

Micromechanical modelling of the effect of plastic deformation on the mechanical behaviour in pseudoelastic shape memory alloys

Except for the recoverable strain induced by phase transformation, NiTi alloys are very ductile even in the martensite phase. The purpose of the present paper is to study the influence of permanent deformation, which results from plastic deformation of martensite, on the mechanical behaviour of pseudoelastic NiTi alloys. Based on phenomenological theory of martensitic transformation and crystal plasticity, a new three dimensional micromechanical model is proposed by coupling both the slip and twinning deformation mechanisms. The present model is implemented as User MATerial subroutine (UMAT) into ABAQUS/Standard to study the influences of plastic deformation on the stress and strain fields, and on the evolution of martensite transformation. Results show that with the increasing of plastic deformation the residual strain increases and the phase transformation stress–strain curves from the martensite to austenite become steeper and less obvious. Both characteristics, stabilisation of martensite and impedance of the reverse transformation, due to plastic deformation are captured.     

Shear and Bending Response of a Rigid Plastic Circular Plate Struck Transversely by a Mass*

ABSTRACT

A theoretical analysis is presented for the dynamic plastic behavior of a fully clamped rigid, perfectly plastic circular plate struck transversely by a rigid mass at the center. It is shown that the maximum permanent transverse deformation predicted by a theoretical solution, with combined transverse shear and bending, is similar to that from a bending-only solution when the ratio of shear strength to bending capacity υ is sufficiently large. However, when the strength parameter υ is small, the transverse shear deformation dominates the response and the maximum deformation from a combined shear and bending solution increases sharply with a decrease in υ. It is also found that the transverse shear deformation becomes more important with an increase in the dimensionless mass ratio β and is sensitive to the dimensionless radius ρ₀ of the impact area.