Anti Plane Problem Of Nanofiber Composites Based On Periodic Model

Nanocomposites have strong size dependence effect,and it is of great significance to research their microscomic stress field and macroscopic effective properties,which has become a hot issue in current research.Periodic model is a common modeling method of composite materials,and modern material preparation technology has been able to complete the periodic arrangement of inclusion phases.In this paper,the interface phase model and the zero-thickness interface model are used to research the antiplane problem of nanofiber composites with periodic structure.The main work of this thesis is as follows:(1)Based on Eshelby’s idea of equivalent inclusion and combining with complex variables function method and doubly quasi-periodic Riemann boundary value problem theory,an analytical analysis method is developed for the antiplane problem of three-phase(fiber/interface phase/matrix)fiber composites with periodic structure,and the full-field elastic solution is obtained.(2)The size dependence of the stress field and the effective antiplane modulus is investigated by using the solution of the three-phase model and the mean field theory.The effects of the properties of interface phase,thickness and fiber arrangement on the effective stiffness coefficient of the antiplane are discussed.The comparison with the finite element results proves the correctness of the proposed method.(3)In the three-phase model,the ratio of the zero-thickness interface modulus to the thickness of the interface layer is taken as the phase modulus.It is proved that when the thickness of the interface phase tends to zero,the solution of the three-phase model can be reduced to that of the zero-thickness interface model.(4)The zero thickness interface model is used to study the stress field and effective antiplane modulus.The results show that when the interface modulus of zero thickness is negative and the fiber radius is less than a certain value,the oscillation and instability of the stress field appear,and the oscillation and instability are related to the fiber arrangement.The calculation of the effective antiplane modulus shows that although the stress field oscillates and is unstable,the effective antiplane modulus does not show any oscillation and instability.In this paper,it is proved that the solution of the zero-thickness interface model can be obtained from the solution of the interface phase model.This study provides a new idea for solving the mechanical problems of nanocomposites by using the zero-thickness interface model.The conclusions obtained in this paper can provide valuable reference for the microstructure design and performance evaluation of nanocomposites.