今日更新：International Journal of Solids and Structures 3 篇，Journal of the Mechanics and Physics of Solids 1 篇，Thin-Walled Structures 6 篇International Journal of Solids and StructuresAnalytical model for flexoelectric sensing of structural response considering bonding complianceSuraj Kumar Rout, Santosh Kapuriadoi:10.1016/j.ijsolstr.2024.113084考虑键合柔度的结构响应挠曲电传感分析模型Flexoelectricity has generated huge interest as an alternative to piezoelectricity for developing electromechanical systems such as actuators, sensors, and energy harvesters. This article presents a generic theoretical framework for the sensing mechanism of a flexoelectric sensor bonded to a host beam through an adhesive layer. The model incorporates piezoelectric and flexoelectric effects and considers both shear-lag and peel stresses at the sensor-beam interface. The formulation also includes the electric field gradient terms that are often overlooked. Consistent one-dimensional constitutive relations and governing equations of equilibrium are derived from the electric Gibb’s energy density function and extended Hamilton’s principle. The sensor is assumed to follow the Euler–Bernoulli beam-type membrane and bending deformation behaviour. Closed-form solutions are obtained for the interfacial stresses by analytically solving a seventh-order non-homogeneous ordinary differential equation, satisfying the stress-free boundary conditions at the sensor edges. The induced electric potential at the sensor top is derived by solving a fourth-order differential equation obtained from the charge balance equation, satisfying the electric boundary conditions. For validation, the sensor output is compared with the results of the existing non-rigid bonding piezoelectric sensor model. Numerical results show a significant impact of non-rigid bonding and the electric field gradient terms on the induced electric potential. Further, the importance of bonding compliance on the interfacial stress distributions is illustrated. Finally, the effects of adhesive and transducer thicknesses on the peak amplitudes of interfacial stresses and sensory potential are presented.柔性电作为压电的替代品，在开发机电系统(如执行器、传感器和能量采集器)方面产生了巨大的兴趣。本文提出了通过粘接层粘接到主梁上的柔性电传感器传感机制的一般理论框架。该模型综合了压电和挠曲电效应，并考虑了传感器梁界面处的剪切滞后和剥离应力。该公式还包括常被忽略的电场梯度项。从电吉布能量密度函数和扩展汉密尔顿原理出发，推导出一维一致的本构关系和平衡控制方程。假设传感器遵循欧拉-伯努利梁型膜和弯曲变形行为。通过解析求解满足传感器边缘无应力边界条件的七阶非齐次常微分方程，得到了界面应力的闭式解。由电荷平衡方程得到满足电边界条件的四阶微分方程，通过求解得到传感器顶部的感应电位。为了验证，将传感器输出与现有非刚性粘结压电传感器模型的结果进行了比较。数值结果表明，非刚性键合和电场梯度项对感应电势有显著影响。此外，还说明了键合顺应性对界面应力分布的重要性。最后，给出了胶粘剂和传感器厚度对界面应力峰值振幅和感觉电位的影响。An alternative stress boundary condition in small deformations and its application to soft elastic composites and structuresMolin Sun, Ming Dai, Peter Schiavonedoi:10.1016/j.ijsolstr.2024.113088小变形的交替应力边界条件及其在软弹性复合材料和结构中的应用Linear elasticity theory has been used extensively in the study of the elastic behavior of various perforated structures and composite materials requiring the accompaniment of appropriate boundary conditions to derive qualitatively correct and quantitatively referential solutions. When incorporating conventional boundary conditions, however, linear elasticity theory fails to predict certain essential phenomena associated with perforate structures and composite materials even when they undergo small deformations. For example, a soft elastic porous medium is appreciably stiffened when inflated despite the fact that the internal air pressure is significantly lower than the modulus of the medium itself. In this paper, we propose an improved stress boundary condition by simply incorporating a small change in the normal to the boundary during deformation. We show via numerical examples that in the context of linear elasticity theory, the use of this improved boundary condition offers the possibility of predicting the influence of initial or residual stress in a perforated structure on the elastic response of the structure to external loadings (which can never be captured with the use of conventional boundary conditions). We perform also large-deformation-based finite element simulations to verify the accuracy of the closed-form results obtained from the improved boundary condition for a soft elastic perforated structure with initial internal pressure. We believe that the idea presented in this paper will extend the applicability of linear elasticity theory and yield more accurate referential analytic results for soft elastic structures and composites.线性弹性理论已广泛应用于研究各种穿孔结构和复合材料的弹性行为，需要适当的边界条件来推导定性正确和定量参考解。然而，当结合传统的边界条件时，线弹性理论无法预测与射孔结构和复合材料相关的某些基本现象，即使它们发生了很小的变形。例如，软弹性多孔介质在膨胀时明显变硬，尽管内部空气压力明显低于介质本身的模量。在本文中，我们提出了一种改进的应力边界条件，通过简单地将变形过程中法向边界的小变化结合起来。我们通过数值例子表明，在线性弹性理论的背景下，使用这种改进的边界条件提供了预测穿孔结构中初始应力或残余应力对结构对外部载荷的弹性响应的影响的可能性(使用传统边界条件永远无法捕获)。我们还进行了基于大变形的有限元模拟，以验证由改进的边界条件获得的封闭形式结果的准确性，该结果适用于具有初始内压的软弹性穿孔结构。我们相信，本文提出的思想将扩展线弹性理论的适用性，并为软弹性结构和复合材料提供更准确的参考分析结果。A non-isothermal breakage-damage model for plastic-bonded granular materials incorporating temperature, pressure, and rate dependenciesYazeed Kokash, Richard Regueiro, Nathan Miller, Yida Zhangdoi:10.1016/j.ijsolstr.2024.113085结合温度、压力和速率依赖性的塑料粘结颗粒材料的非等温断裂-损伤模型Plastic-bonded granular materials (PBM) are widely used in industrial sectors, including building construction, abrasive applications, and defense applications such as plastic-bonded explosives. The mechanical behavior of PBM is highly nonlinear, irreversible, rate dependent, and temperature sensitive governed by various micromechanical attributions such as grain crushing and binder damage. This paper presents a thermodynamically consistent, microstructure-informed constitutive model to capture these characteristic behaviors of PBM. Key features of the model include a breakage internal variable to upscale the grain-scale information to the continuum level and to predict grain size evolution under mechanical loading. In addition, a damage internal state variable is introduced to account for the damage, deterioration, and debonding of the binder matrix upon loading. Temperature is taken as a fundamental external state variable to handle non-isothermal loading paths. The proposed model is able to capture with good accuracy several important aspects of the mechanical properties of PBM, such as pressure-dependent elasticity, pressure-dependent yield strength, brittle-to-ductile transition, temperature dependency, and rate dependency in the post-yielding regime. The model is validated against multiple published datasets obtained from confined and unconfined compression tests, covering various PBM compositions, confining pressures, temperatures, and strain rates.塑料粘结颗粒材料(PBM)广泛应用于工业领域，包括建筑施工、磨料应用和国防应用，如塑料粘结炸药。PBM的力学行为是高度非线性的、不可逆的、速率依赖的和温度敏感的，受各种微观力学属性(如颗粒破碎和粘结剂损伤)的控制。本文提出了一个热力学一致的、微观结构的本构模型来捕捉PBM的这些特征行为。该模型的主要特征是引入破碎内变量，将粒度信息提升到连续体水平，并预测机械载荷下的粒度演变。此外，还引入了损伤内部状态变量来解释加载时粘结剂基体的损伤、劣化和脱粘。将温度作为处理非等温加载路径的基本外部状态变量。该模型能够很好地捕捉到PBM力学性能的几个重要方面，如压力相关弹性、压力相关屈服强度、脆性到延性转变、屈服后状态下的温度依赖性和速率依赖性。该模型通过从承压和无承压压缩试验中获得的多个公开数据集进行验证，涵盖了不同的PBM成分、围压、温度和应变率。Journal of the Mechanics and Physics of SolidsHall effect and topological phase transition of nonlinear elastic wave metamaterials with local resonatorsTai-Lai Yang, Yi-Ze Wangdoi:10.1016/j.jmps.2024.105889具有局部谐振腔的非线性弹性波超材料的霍尔效应和拓扑相变This work reports the amplitude-induced topological phase transition and Hall effect in nonlinear elastic waves metamaterials with local resonators. The multi scale method is employed to analyze nonlinear effects on the Bragg scattering and locally resonant band gaps. The amplitude-induced band inversion and topological edge states are numerically investigated. A spin Hall insulator is generated by a honeycomb lattice to show how the nonlinearity affects the frequencies of doubly degenerate states. By adjusting the nonlinear elastic wave amplitude, topological phase transition is achieved due to the intercellular and intracellular coupling. The transition from topological boundary states to bulk states is observed by increasing nonlinear elastic wave amplitude. Bidirectional and unidirectional transmissions of topological interface states with amplitude-induced properties can also be realized, which demonstrates robustness against both corners and defects. Furthermore, experiment is performed to support theoretical predictions of topological phase transition and Hall effect of nonlinear elastic wave.本文报道了具有局部谐振腔的非线性弹性波超材料的振幅诱导拓扑相变和霍尔效应。采用多尺度方法分析了非线性效应对Bragg散射和局部谐振带隙的影响。数值研究了振幅诱导的带反演和拓扑边缘状态。利用蜂窝晶格产生自旋霍尔绝缘子，以说明非线性对双简并态频率的影响。通过调节非线性弹性波的振幅，实现细胞间和细胞内耦合的拓扑相变。通过增加非线性弹性波的振幅，观察到拓扑边界态向体态的转变。具有幅值诱导特性的拓扑界面态的双向和单向传输也可以实现，对拐角和缺陷都具有鲁棒性。此外，实验还支持了非线性弹性波的拓扑相变和霍尔效应的理论预测。Thin-Walled StructuresModeling and Motion Analysis of Flexible Legged Robots using the Finite Particle MethodYing Yu, Jingwen Liu, Yugen You, Qilin Tan, Xinzhuo Xu, Yanfeng Zheng, Zhun Fandoi:10.1016/j.tws.2024.112491基于有限粒子法的柔性腿机器人建模与运动分析Robotics with flexible legs have attracted significant attention. Engineers often design and analyze the motion of legged robots from kinematic and biomimetic perspective. However, the influence of flexibility of the feet on robot locomotion is often not given sufficient considerations, which is also very crucial to the motion posture of the flexible legged robots, especially as the soft robots design becomes increasingly popular. The mainly difficulties lies in the traditional numerical methods in handling the dynamic motion analysis with both large rigid motion and large deformation. In this paper, the finite particle method (FPM) is used to simulate the motion and deformation coupled problems of the flexible six-legged robot. A shell-based particle model of a six-leg robot and the contact model between legs and ground are built. Without iterative and modification of the FPM analytical framework, structural nonlinearity is efficiently handled after eliminating rigid body motions by a fictitious reverse motion. The motion and deformation of a single leg with varying leg thickness, locomotion speed, and leg-to-ground friction coefficients were simulated. By analyzing the stress distribution in the leg and the number of contact points with the ground, the mechanical leg was optimized in design. Furthermore, the motion and deformation of the entire six-legged robot were simulated using the FPM. The numerical results' feasibility was validated through comparison with experimental data obtained from robot walking tests. The proposed method effectively simulates the motion and deformation of flexible robots, providing significant insights for the design of soft robots.具有柔性腿的机器人引起了人们的极大关注。工程师经常从运动学和仿生学的角度设计和分析有腿机器人的运动。然而，足部柔韧性对机器人运动的影响往往没有得到充分的考虑，这对柔性足部机器人的运动姿态也是至关重要的，尤其是在软性机器人设计日益流行的今天。传统的数值方法在处理大刚性运动和大变形的动力运动分析时存在较大的困难。本文采用有限粒子法对柔性六足机器人的运动与变形耦合问题进行了仿真。建立了六足机器人的壳粒子模型和腿与地面的接触模型。无需迭代和修改FPM分析框架，通过虚拟的反向运动消除刚体运动后，可以有效地处理结构非线性。模拟了不同腿厚、运动速度和腿对地摩擦系数下单腿的运动和变形。通过分析机械腿的应力分布和与地面接触点的数量，对机械腿进行了优化设计。此外，利用FPM对整个六足机器人的运动和变形进行了仿真。通过与机器人行走实验数据的对比，验证了数值结果的可行性。该方法有效地模拟了柔性机器人的运动和变形，为柔性机器人的设计提供了重要的参考。Simplified discrete model for axisymmetric dielectric elastomer membranes with robotic applicationsZhaowei Liu, Mingchao Liu, K. Jimmy Hsia, Xiaonan Huang, Weicheng Huangdoi:10.1016/j.tws.2024.112502具有机器人应用的轴对称介质弹性体膜的简化离散模型Soft robots utilizing inflatable dielectric membranes can realize intricate functionalities through the application of non-mechanical fields. However, given the current limitations in simulations, including low computational efficiency and difficulty in dealing with complex external interactions, the design and control of such soft robots often require trial and error. Thus, a novel one-dimensional (1D) discrete differential geometry (DDG)-based numerical model is developed for analyzing the highly nonlinear mechanics in axisymmetric inflatable dielectric membranes. The model captures the intricate dynamics of these membranes under both inflationary pressure and electrical stimulation. Comprehensive validations using hyperelastic benchmarks demonstrate the model’s accuracy and reliability. Additionally, the focus on the electro-mechanical coupling elucidates critical insights into the membrane’s behavior under varying internal pressures and electrical loads. The research further translates these findings into innovative soft robotic applications, including a spherical soft actuator, a soft circular fluid pump, and a soft toroidal gripper, where the snap-through of electroelastic membrane plays a crucial role. Our analyses reveal that the functional ranges of soft robots are amplified by the snap-through of an electroelastic membrane upon electrical stimuli. This study underscores the potential of DDG-based simulations to advance the understanding of the nonlinear mechanics of electroelastic membranes and guide the design of electroelastic actuators in soft robotics applications.利用充气介质膜的软体机器人可以通过非机械领域的应用实现复杂的功能。然而，考虑到目前仿真的局限性，包括低计算效率和难以处理复杂的外部交互，这种软机器人的设计和控制往往需要反复试验。因此，建立了一种新的一维离散微分几何(DDG)数值模型来分析轴对称充气介质膜的高度非线性力学。该模型捕捉到了这些膜在膨胀压力和电刺 激下的复杂动力学。使用超弹性基准的全面验证证明了模型的准确性和可靠性。此外，对机电耦合的关注阐明了膜在不同内部压力和电负载下的行为的关键见解。该研究进一步将这些发现转化为创新的软机器人应用，包括球形软执行器、软圆形流体泵和软环形夹持器，其中电弹性膜的通卡起着至关重要的作用。我们的分析表明，软机器人的功能范围被电刺 激下的电弹性膜的弹跳放大。这项研究强调了基于ddg的模拟在促进对电弹性膜非线性力学的理解和指导软机器人应用中电弹性致动器的设计方面的潜力。Multiscale numerical scheme on shear failure feature of 3DOWC/Cs bar incorporating microlevel uncertainties and coupled constitutive behaviorYanfeng Zhang, Jinlu Sheng, Zhengong Zhou, Zhiyong Tan, Weiguo Lidoi:10.1016/j.tws.2024.112511考虑微观不确定性和耦合本构行为的3DOWC/Cs杆剪切破坏特征多尺度数值格式In contrast to prevalently utilized carbon fiber reinforced plastics (CFRP), the carbon fiber reinforced carbon matrix composites (C/Cs) frequently present significantly divergent mechanics features. The current investigation dedicates to a robust multiscale finite element strategy on shear failure characteristics of three-dimensional orthogonal woven C/Cs (3DOWC/Cs) bolt bar together with relevant experimental measurement for validation, while the off-axial orientation sensibility of structural load-bearing performance and damage mechanism are systematically evaluated. In view of the complicated internal fabric architecture, the predictions are received via hierarchical numerical simulation at micro-, meso-, as well as macroscales. The random distributions of voids and fibers are incorporated to precisely capture the material properties, meanwhile the constitutive laws which embed the combining of Hashin and Puck criterions judging for yarn initial damage, multilinear rule for carbon matrix, and trilinear cohesive zone model (CZM) for interface, are implemented to render the coupling impacts of material behaviors. Besides, the extracted global load-displacement curves and local progressive failure morphologies from macroscale simulation are separately compared with experimental acquisitions to verify the accuracy of proposed modelling and to expose the damage mechanism of specimens with various off-axis angles. The contribution of this research lies in accurate quantification for microlevel uncertainties via modified stochastic algorithms, and applicable constitutive frame severally matching each material component to portray the distinctive mechanical particularities of 3DOWC/Cs.i与目前广泛使用的碳纤维增强塑料(CFRP)相比，碳纤维增强碳基复合材料(C/Cs)往往表现出明显不同的力学特征。本文采用鲁棒多尺度有限元方法研究了三维正交编织C/Cs (3DOWC/Cs)锚杆杆的剪切破坏特征，并进行了实验验证，系统评估了结构承载性能的离轴取向敏感性和损伤机理。考虑到织物内部结构的复杂性，通过微观、中观和宏观尺度的分层数值模拟得到了预测结果。利用孔隙和纤维的随机分布来精确捕捉材料的性能，同时利用基于Hashin和Puck准则的纱线初始损伤判断、基于碳基体的多线性规则和基于界面的三线性内聚区模型(CZM)的本构律来描述材料行为的耦合影响。此外，将宏观尺度模拟提取的整体荷载-位移曲线和局部渐进破坏形态分别与实验数据进行对比，验证了模型的准确性，揭示了不同离轴角度下试件的损伤机理。本研究的贡献在于通过改进的随机算法对微观层面的不确定性进行精确量化，并采用适合的本构框架对各材料构件分别进行匹配，描绘出3DOWC/Cs.i的独特力学特性Fabricating sandwich composite tubes using a new thermal expansion technique: materials preparation and energy absorption characteristicsJinzhi Li, Maojun Li, Yunfei Peng, Xujing Yangdoi:10.1016/j.tws.2024.112512利用热膨胀新技术制备夹层复合材料管:材料制备和能量吸收特性The extensive application of hollow composite structures in engineering increasingly demands innovations in highly efficient and economical manufacturing processes as well as materials to achieve lightweighting and enhance mechanical performance. To address the limitations of traditional molding processes in fabricating hollow composite structures with intricate geometries, this study proposes a novel thermal expansion molding technique. This method eliminates the need to remove the mandrel after molding, making it exceptionally suitable for the molding of foam sandwich composite structures. Leveraging this new technique, lightweight sandwich composite tubes filled with polymethacrylimide (PMI) foam and thermal expansion foam were successfully fabricated. Considering the importance of crashworthiness for automotive applications, detailed experimental studies were conducted to investigate the crushing performance of the sandwich composite tubes prepared using this technology. Experimental results reveal that the synergistic effect between the multi-component materials within the sandwich composite tubes confers surprising energy absorption characteristics and crushing stability to the structure. The sandwich composite tubes prepared by this innovative thermal expansion process exhibit promising prospects as crashworthy structures for automotive lightweighting applications, and this method provides critical inspiration for the fabrication of composite structures with complex shapes.随着空心复合材料结构在工程中的广泛应用，对其制造工艺和材料的创新提出了更高的要求，以实现轻量化和提高机械性能。为了解决传统成型工艺在制造具有复杂几何形状的中空复合材料结构方面的局限性，本研究提出了一种新的热膨胀成型技术。这种方法不需要在成型后去除芯棒，使其特别适合泡沫夹层复合材料结构的成型。利用这种新技术，轻质夹层复合材料管填充了聚甲基丙烯酰亚胺(PMI)泡沫和热膨胀泡沫成功制成。考虑到耐撞性对汽车应用的重要性，对采用该技术制备的夹层复合材料管的抗撞性能进行了详细的实验研究。实验结果表明，夹层复合管材内部多组分材料之间的协同作用使结构具有惊人的能量吸收特性和破碎稳定性。通过这种创新的热膨胀工艺制备的夹层复合材料管在汽车轻量化应用中具有良好的耐碰撞结构前景，并为复杂形状复合材料结构的制造提供了重要的灵感。Effect of beam oscillating amplitude on forming quality, microstructure, and mechanical performance of Al-Mg-Sc alloy fabricated by laser-arc hybrid additive manufacturingShengchong Ma, Xi Chen, Meng Jiang, Tianyi Han, Jinzhu Wang, Yi Yan, Zhenglong Lei, Peng He, Yanbin Chendoi:10.1016/j.tws.2024.112513光束振荡振幅对激光-电弧复合增材制造Al-Mg-Sc合金成形质量、显微组织和力学性能的影响The oscillating laser-arc hybrid additive manufacturing was applied to fabricate Al-Mg-Sc alloy and the effect of beam oscillating amplitude on macro/micro-morphology and the mechanical properties were investigated in this study. With the oscillating amplitude increased from 0 to 6 mm, the stirring effect of laser beam on molten pool was firstly enhanced due to the expanded active region and then weakened because the laser spot located at the edge of pool. As a result, the improved forming quality, the reduced porosity and the refined microstructures were achieved when the amplitude reached 4 mm, and then negative effect occurred when the amplitude was 6 mm. Eventually, the optimal mechanical performance was achieved at the amplitude of 4 mm and the as-deposited tensile properties reached 353 MPa and 24 % for UTS, and EL in vertical direction, respectively, which were 13.5 % and 50 % higher than that of 0 mm.采用振荡激光-电弧复合增材制造技术制备了Al-Mg-Sc合金，研究了光束振荡振幅对合金宏微观形貌和力学性能的影响。当振荡幅值从0增大到6 mm时，激光束对熔池的搅拌作用先因活跃区扩大而增强，后因激光光斑位于熔池边缘而减弱。结果表明，当振幅为4 mm时，成形质量得到改善，孔隙率降低，组织细化;当振幅为6 mm时，成形质量下降;最终，在振幅为4 mm时，合金的力学性能达到最佳，纵向拉伸性能达到353 MPa，纵向拉伸性能达到24%，分别比振幅为0 mm时提高了13.5%和50%。Interfacial construction and interlayer properties of fiber metal laminates-based bionic micro–nano composite structure inspired by the toe-end morphology of tree frogsYao Wang, Da Cheng, Xiaokai Ye, Kang Liu, Jiajun Yang, Chao Yang, Libin Zhao, Ning Hudoi:10.1016/j.tws.2024.112515受树蛙趾端形态启发的金属纤维层合仿生微纳复合材料的界面结构及层间性能Fiber metal laminates (FMLs) are ultra-hybrid composites that exhibit superior fatigue resistance and damage tolerance and have great potential for application to critical thin-walled components in large aircraft. However, due to the significant performance disparities between the FMLs layers and their insufficient interfacial bonding capacity, their widespread application is limited by delamination. This study takes inspiration from the unique, highly viscous three-dimensional microstructure found in the toe-ends of tree frogs. Utilizing a combination of laser processing and phosphoric acid anodizing techniques, a bionic micro–nano composite structure exhibiting enhanced interfacial bonding capacity was successfully constructed. In this study, a geometrical model of the bionic microstructure was constructed, and an investigation into the wettability model of the bionic micro–nano composite structure was conducted. The contact angle variation for different carving sizes, speeds, and metal surface treatments was investigated. Furthermore, FMLs with a bionic micro–nano composite structure were prepared, and the number of adhesive layers was optimized. Finally, the interlayer properties of the new laminates were investigated. The results show that for the 2/1 laminates, the bionic micro–nano composite structure increases the peel strength by 29.8% compared with that of phosphoric acid anodized laminates, and the shear strength is increased by 16.01% with respect to that of sanded-only laminates. For the 3/2 laminates, the bionic micro–nano composite structure results in a 21.87% increase in shear strength compared with that of sanded-only laminates, This work provides a new pathway as well as a theoretical foundation for interfacial studies of FMLs, which will enhance their comprehensive performance and broaden their applications.金属纤维层压板(FMLs)是一种超混合复合材料，具有优异的抗疲劳性能和损伤容限，在大型飞机的关键薄壁部件上具有很大的应用潜力。然而，由于FMLs各层之间的性能差异较大，且其界面结合能力不足，其广泛应用受到脱层的限制。这项研究的灵感来自树蛙趾端发现的独特的、高粘性的三维微观结构。利用激光加工和磷酸阳极氧化技术相结合，成功构建了具有增强界面结合能力的仿生微纳复合材料结构。本研究构建了仿生微观结构的几何模型，并对仿生微纳复合结构的润湿性模型进行了研究。研究了不同雕刻尺寸、速度和金属表面处理对接触角的影响。制备了具有仿生微纳复合结构的FMLs，并对其粘接层数进行了优化。最后，对复合材料的层间性能进行了研究。结果表明:对于2/1复合材料，仿生微纳复合材料的剥离强度比磷酸阳极氧化复合材料提高29.8%，抗剪强度比纯砂复合材料提高16.01%;对于3/2复合材料，仿生微纳复合材料的抗剪强度比纯砂复合材料提高了21.87%，为FMLs的界面研究提供了新的途径和理论基础，提高了FMLs的综合性能，拓宽了其应用领域。来源：复合材料力学仿真Composites FEM
