不同铺层厚度复合材料的低速冲击特性与损伤模式研究

复合材料凭借其轻质、高强的特性逐渐在工程材料界占据重要地位,对于复合材料的冲击损伤的研究也一直吸引着诸多研究学者的关注.为表征不同铺层厚度复合材料层合板的抗冲击性能,利用自由落体冲击设备,进行了复合材料层合板的冲击实验研究.给出了不同冲击能量下的损伤模式,并利用位移、速度、接触力以及能量的时间变化曲线,深入分析了侵入和穿透两种损伤模式的特点.研究发现,随着铺层厚度的增加,复合材料在冲击过程中吸收的能量也随之增加.引入能量平衡法,基于体系的能量守恒定律,利用Newton-Raphson数值方法求解了侵入损伤模式下的接触力大小,通过实验结果给定挠度求解了对应的速率变化情况,并将理论结果与实验结果进行比较.     

复合材料层合板低速冲击后压缩的损伤累积模型

为了分析复合材料层合板低速冲击后的压缩性能,首先用三维动态有限元素法对两种层合板进行了低速冲击损伤模拟计算,以此作为冲击后压缩（CAI）层合板的初始损伤,然后用三维静态有限元对含损伤的层合板进行压缩破坏模拟和剩余强度计算,从而实现了层合板从冲击损伤到压缩破坏损伤全过程的模拟．结果表明,损伤投影面积和CAI强度的计算值与试验结果有较好的一致性．     

碳纤维-不锈钢层板热载条件下冲击动态响应及层间损伤仿真研究

为了研究碳纤维不锈钢层板的冲击动态响应以及热载荷条件下的冲击性能,采用ABAQUS/Explicit,编写基于复合材料渐进损伤用户子程序VUMAT;引入Johnson-Cook模型,仿真计算了碳纤维增强环氧树脂基复合材料-SS304不锈钢层板热载条件下冲击动态响应过程;分析了其冲击动态响应及渐进损伤,着重讨论了热载荷条件对碳纤维金属层板的冲击能量吸收、接触力等抗冲击性能及失效模式的影响.结果显示,高速冲击载荷作用下,纤维层的脆性断裂、金属层的塑性变形以及纤维层与金属层之间的脱层是碳纤维不锈钢层板的主要失效形式.热载荷的存在直接影响了冲头的接触力,随环境温度升高,接触力总体上降低,子弹的速度衰减越慢,剩余速度增大.结果表明,热载荷降低了纤维金属板的冲击动能吸收特性,弱化了碳纤维金属板的抗冲击性能.无论是纤维金属层板的整体破坏,还是纤维失效、基体失效和脱层失效,热载荷都产生了重要影响.     

基于辛对偶体系的层合板自由边缘效应的分析解

在原变量——位移和其对偶变量——应力组成的辛几何空间,建立了Pipes-Pagano模型的复合材料层合板问题的辛对偶求解体系．与传统的单类变量不同,辛对偶变量有利于同时描述层间位移连续性条件和应力平衡条件．进入辛对偶体系以后,就可以应用辛对偶体系的统一解析求解方法,如分离变量和辛本征展开的方法对层合板问题进行解析分析和求解．对层合板自由边缘效应的分析求解,验证了辛对偶体系的方法对层合板问题的分析求解是十分有效的．     

含分层损伤复合材料加筋层合板的分层扩展研究

建立了复合材料加筋结构的后屈曲和分层损伤扩展行为的数值模拟方法．基于Mindlin一阶剪切理论和von-Karman大挠度理论的层合板和层合梁单元，提出了含分层损伤复合材料加筋层合板分层扩展行为的有限元分析方法；利用虚裂纹闭合技术计算分层前缘的总能量释放率，并采用总能量释放率准则分层扩展判据，结合自适应网格移动技术，对在压缩载荷作用下的具有不同加筋形式，不同初始分层面积和形状的加筋板结构分层扩展行为进行了数值模拟研究，在分析中还考虑了加筋刚度、位置和分布，分层形状和大小、边界支撑强弱和分层前缘的接触效应对结构分层扩展行为的影响．本所提出的研究方法对工程界关于复合材料结构的设计具有重要意义．     

带裂纹层合板能量释放率分析

为了进一步了解裂纹尖端应力场的特性,本文对复合材料层合板的界面裂纹作了分析.文中强调了能量释放率分量存在的条件,并给出能量释放率分量和应力强度因子间的关系式.结合经典板理论的分析结果,根据外荷作用及某些几何参数和材料多数,导出了一般复合材料层合板的应力强度因子的封闭形式解.为了得到在一般荷载条件下能量释放率的分量,必须分别确定模型混合参数Ω,文中讨论了确定参数Ω的方法,最后,应用本文方法于几种不同种类的复合材料层合板,证明其结果可应用于工程实践.     

Hamilton体系下含弱粘接复合材料层合板的灵敏度分析研究

基于径向基点插值函数(RPIM),在Hamilton体系下研究了含弱粘接复合材料层合板的灵敏度分析问题．利用弹簧层模型和修正H-R(Hellinger-Reissner)变分原理,推导了可用于含弱粘接复合材料层合板响应和灵敏度分析的混合控制方程,给出了基于该混合控制方程进行灵敏度分析的解析法(AM)、半解析法(SA)和有限差分法(FD)．该混合控制方程的主要优点是可以在进行灵敏度分析过程中避免卷积运算．另外,利用该混合控制方程进行灵敏度分析不仅能够同时得到响应结果和灵敏度系数,而且还考虑了层合板的层间弱粘接问题．     

对称复合材料层合板弯曲的三维数值分析

本文采用三维各向异性有限单元模拟纯弯曲载荷下的复合材料层合板，给出了应力、应变沿厚度方向的变化规律。分析结果表明，在斜交对称铺层层合板的中心区域（远离加载端和自由边的区域），板的层间粘接界面附近，有根强的应力集中现象，可称之为层间效应。层间界面处力学性质的突变导致了层间应力的产生，并使层合板处于三向应力状态。三维数值模型给出的应变分布不同于基于Ｋｉｒｃｈｈｏｆｆ－Ｌｏｖｅ直法线假设的经典层合板理论给出的应变分布。     

Hamilton体系下层合板弱粘接模型的应用

层合板的层间粘接模型对整个层合板的结构有重要影响．运用Hamilton正则方程对层合板层间的不同类型的粘接模型进行了分析．结合弹性材料修正后的Hellinger Reissner变分原理和插值函数,构建了直角坐标系下8节点层合板的每一层的线性方程;考虑到脱层板的连接界面处应力和位移的关系,改进了现有的常用弱粘接模型,建立不同粘接模型的控制方程;最后通过求解整个板的控制方程,得到层合板的层间应力和位移．数值算例验证了该模型的正确性,并研究了层间界面为线性和非线性时的问题．结果表明:应用改进后的弱粘接模型,能够更好地模拟层合板的弱界面失效过程．     

带裂纹层合板复应力强度分析

本文用经典板理论求得了复合材料层合板的界面应力强度因子.利用裂纹尖端能量释放率和复应力强度因子间的关系,给出最一般的复合材料层合板,在相应外荷载和模型混合参数下的复应力强度因子的一个封闭形式的解.然后提出确定这一模型混合参数的步骤,给出某些层合板的数值结果.并给出在相应外荷载下的小范围接触条件.特别证明了界面韧度曲线的对称性质.最后讨论振荡指数消失后,预计的断裂荷载的精确性.还通过一个实例表明β=0法的有效性和局限性.     

Impact Responses of Prismatic Lithium-Ion Battery Based on the Membrane Factor Method北大核心CSCD

Aimed at the internal short circuit problem due to large deformation of the prismatic lithium-ion battery cell under impact loadings, a simplified battery model was first established. Then the motion equations of velocity and displacement based on the membrane factor method were proposed. With the effects of the face-sheet thickness and the densification region on the normalized final deflection, impact response characteristics of prismatic battery cells were investigated in detail. The results show that, the improved motion equations involving the membrane factor can reflect the dynamic response mechanisms of the prismatic battery cell under impact loadings, and the large deflection under high-speed impact can be predicted. With the increase of the face-sheet thickness, the deflection of the battery cell’s lower part decreases obviously. However, the densification region expands with the face-sheet thickness. The deflection and the densification region of the cell’s lower part both increase with the inner core density of the battery. This proposed impact model provides a theoretical guidance for the multi-functional integrated dynamic design of prismatic battery cells. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

爆炸和冲击载荷下金属材料及结构的动态失效仿真

通过数值模拟研究爆炸冲击载荷下金属材料和结构的动态失效规律对表征爆炸冲击毁伤效应及设计新型抗冲击结构具有重要意义.强动载下金属材料失效涉及材料大变形、热力耦合、材料状态变化等多个复杂物理过程,给数值仿真带来了极大挑战,其中包括裂纹、剪切带等复杂失效模式的几何描述、动态失效准则的确定、塑性与损伤耦合演化的描述等问题.针对这些挑战性问题,基于能量变分建立描述金属动态失效过程的热弹塑性相场理论和计算模型,实现了断裂与剪切带失效模式的统一描述,并提出了其显式有限元高效求解策略.进一步将该模型应用于爆炸冲击载荷下金属脆韧失效模式转变、绝热剪切带（ASBs）自组织及冲击波作用下薄壁圆盘失效形式转变三个典型金属动态失效问题,验证了理论模型的准确性及计算模型的稳健性.该工作为后续开展基于仿真的爆炸冲击毁伤评估及防护结构设计研究奠定了基础.     

A Numerical and Experimental Study on the Impact Behavior of a Carbon-Fiber-Reinforced Thermoplastic Poly (Methyl Methacrylate) Composite

Mechanics of Composite Materials - The goal of the present study was to investigate the low-speed impact behavior and damage patterns of carbonfiber-reinforced methyl methacrylate composites. The...     

Interlaminar fracture and low-velocity impact of carbon/epoxy composite materials

The interlaminar fracture and the low-velocity impact behavior of carbon/epoxy composite materials have been studied using width-tapered double cantilever beam (WTDCB), end-notched flexure (ENF), and Boeing impact specimens. The objectives of this research are to determine the essential parameters governing interlaminar fracture and damage of realistic laminated composites and to characterize a correlation between the critical strain energy release rates measured by interlaminar fracture and by low-velocity impact tests. The geometry and the lay-up sequence of specimens are designed to probe various conditions such as the skewness parameter, beam volume, and test fixture. The effect of interfacial ply orientations and crack propagation directions on interlaminar fracture toughness and the effect of ply orientations and thickness on impact behavior are examined. The critical strain energy release rate was calculated from the respective tests: in the interlaminar fracture test, the compliance method and linear beam theory are used; the residual energy calculated from the impact test and the total delamination area estimated by ultrasonic inspection are used in the low-velocity impact test. Results show that the critical strain energy release rate is affected mainly by ply orientations. The critical strain energy release rate measured by the low-velocity impact test lies between the mode I and mode II critical strain energy release rates obtained by the interlaminar fracture test. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Published in Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 195–214, March–April, 2000.     

Life Prediction of FRP Composites by a Direct Method

A direct computational approach for lifetime prediction of fibre-reinforced polymer (FRP) composites is presented. The approach is based on a direct method which allows predicting the fatigue life from the stabilised damage state. The classical direct method is generalised to the case of coupled plasticity with damage mechanics of the UD-FRP composite materials [1]. The constitutive model is based on a continuous damage meso-scale approach [2]. By analysing damage variables and thermodynamical forces associated with damage at the stabilised state, fatigue life prediction law is proposed as a power law function of stabilised thermodynamic forces. The obtained numerical results have been validated by experimental test results on standard glass-fibre/epoxy angle-ply and cross-ply laminate plates. The proposed approach could serve as a useful tool for the design of FRP composites. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of Thermal Impact Welded Lightweight Structures

In the field of composites, welding of lightweight structures consisting of metal/fibre-reinforced polymers is a very seminal issue, concerning for example the automotive industry. The theoretical and numerical modelling as well as the simulation of the mentioned composites is a crucial and integrating subarea. By using various material laws in a traction-separation context, different experimental and analytical methods must be consulted to verify the mesomechanical models. In this contribution we discuss a characterisation of interfacial elasto-plasticity with Lemaitre-damage, which has been applied to model thermal impact welded single lap tensile specimens. Then, numerical and experimental results are discussed. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Structural Crack Identification Based on the Variational Mode Decomposition北大核心CSCD

In order to enrich the bridge damage detection method and further improve the accuracy of bridge damage identification, a detection method for simply supported beams with cracks under dynamic loads was proposed not based on the complete finite element model. Under the premise of not blocking traffic, the method only needs to analyze and deal with the acceleration responses of the simply supported beam span, which reduces the mounting, dismounting and maintenance of sensors in practical engineering. At the same time, based on the model, an analytical formula of the acceleration at the midspan of the simply supported cracked beam was derived. Based on the theoretical derivation, the instantaneous energy and the mean energy difference were constructed through the variational mode decomposition and the Hilbert transform, and these 2 crack identification indexes were used to effectively identify small cracks with a crack depth ratio of only 5%. Then the influences of different wheel loads, environmental noises and damage degrees on detection results were studied. The results show that: ① the instantaneous frequency has a better recognition effect for crack positions; ② the mean energy difference is sensitive to crack depth ratio δ and the wheel load magnitude; ③ this method has strong noise robustness. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

梯度增强的弹塑性损伤非局部本构模型研究

简要介绍了几种主要的梯度增强非局部模型．基于“能量耗散梯度依赖”原则,在连续介质热力学框架内推导了梯度增强损伤与塑性耦合的本构关系,同时给出了一个基于塑性的损伤模型的梯度依赖本构的具体形式．在数值计算方面,结合移动最小二乘法和泰勒级数展开方法,建立了损伤场（有限元高斯积分点上）的Laplace值的近似求解格式,分别给出了二维和三维情况下的相关公式．给出的二维的韧性断裂的梯度依赖损伤塑性的数值应用,表明了格式的有效性和实用性．还讨论了内部长度的意义及取值问题．     

基于成本效用分析的电能替代实证研究

近年来的雾霾让人们逐渐意识到环境保护的重要性,国网公司基于我国“多煤、少气、贫油”的国情,提出了以电代煤的电能替代方案。本文以在电力和煤炭的使用过程中可获得的热值作为效用,以使用过程中所需要的年费用作为成本,建立了电能替代的成本效用模型,计算出实现电力和煤炭相互替代的排污费临界值,并通过一个算例进行了实证分析。分析结果表明:电价、单位电力排污量、燃煤设备寿命对排污费临界值有正向影响;煤价、单位燃煤排污量、电力设备寿命对其有负向影响。最后,在分析的基础上给出了电能替代的政策建议。