摘要
本文基于细观力学单胞法和Gurtin-Murdoch表面弹性理论,研究了周期纳米多涂层纤维复合材料在纵向剪切载荷作用时的弹性场和有效弹性性能.利用周期微结构的单胞泛函变分方法和特征函数展开法,给出了周期纳米涂层复合材料有纵向剪切有效模量的解析解.所得解答与已有结果比较的一致性说明了本文方法的有效性.通过改变多涂层的微结构参数,可以调控周期纳米纤维复合材料材料的宏观有效性能.算例中讨论了涂层力学性能、涂层几何参数、表面性能和纤维体积分数对复合材料有效性能的影响.本文提出的方法和所得结果为周期纳米涂层纤维复合材料力学性能的预测和调控提供了理论依据.
The microstructure distribution forms within composite materials are diverse,and periodic microstructure is one of the typical distribution patterns.Periodic structures have basic cells that are repeatedly distributed,representing the situation where the inclusion arrangement within a material changes from completely disordered to strictly ordered.Modern composite material design,especially computer-aided material design,usually refers to the design of periodically distributed cells.Multi-coating refers to a new type of coating in which the geometric parameters are proportional on the thickness coordinate.Multi-coating can achieve gradient changes in material parameters,allowing for gradient changes in the mechanical properties of the coating and thereby enabling the design and control of material properties such as strength,toughness,and stiffness.Nanocomposites possess unique mechanical properties.When the structural size of the reinforcing phase reaches the nanoscale,the surface effect cannot be ignored.The macroscopic mechanical properties of nanocomposites are different from those of traditional composites.In this work,based on the unit cell method of micromechanics and the Gurtin-Murdoch theory of surface elasticity,the elastic field and effective property of periodic coated-fiber nanocomposites subjected to longitudinal shear loads are studied.The analytical solution of the longitudinal shear effective modulus of periodic nanocoated composites is obtained by using the unit cell functional variational method and the eigenfunction expansion method.The consistency between the obtained solution and the existing results indicates the validity of the proposed method.The macroscopic effective property of periodic nanocomposites can be controlled by changing the microstructure parameters of the multi-coating.The effects of coating mechanical properties,coating geometric parameters,surface properties and fiber volume fraction on the effective properties of the composite are discussed.The analytical method proposed in this paper and the obtained results provide a theoretical basis for the design of periodic nanocoated fiber composites and the regulation of their mechanical properties.
作者
肖俊华
郑欣
信玉岩
Junhua Xiao;Xin Zheng;Yuyan Xin(Department of Engineering Mechanics,Yanshan University,Qinhuangdao,066004;Hebei Key Laboratory of Mechanical Reliability for Heavy Equipments and Large Structures,Yanshan University,Qinhuangdao,066004;Department of Engineering Mechanics,Hohai University,Nanjing,211100)
出处
《固体力学学报》
北大核心
2025年第5期598-609,共12页
Chinese Journal of Solid Mechanics
基金
河北省自然科学基金项目(A2022203025)资助。
关键词
周期纳米复合材料
表面效应
多涂层纤维
特征函数展开法
变分法
Periodic nanocomposites
surface effect
multi-coated fiber
eigenfunction expansion method
variational method
