Study On The Theory And Application Of Bond-Peridynamics

Theory of Peridynamics(Peridynamics PD)is a new type of mechanical theory which develops rapidly in recent years.Based on the thought of nonlocal action,the theory describes the mechanical behavior of matter with the integral form of the state quantity of matter point,and further develops the method of describing the mechanical behavior.It avoids the defect that the differential equation is meaningless when face the discontinuity problem in the traditional mechanical theory.In recent years,many scholars' research on this theory makes this theory applied to discontinuous multi-scale problems,and has attracted more and more attention in the field of structural damage simulation.In the theory of Peridynamics,the interaction between material points is expressed as a state quantity related to time.In special cases,the model is changed into a bond based Peridynamics model;in the theory of bond based Peridynamics,the interaction between material point pairs is changed into a force with opposite direction and acting on the same line.Composite materials are widely used in aviation,shipbuilding and other high-tech fields are due to their strong designability and mechanical properties,but their anisotropy and complex failure mode are the difficulties in the research and application of composite materials.The theory of Peridynamics has also made a unique contribution to the study of composite properties.In the theory of Peridynamics,the classical theoretical model of composite materials assumes that there are only matrix bonds and fiber bonds in the monolayer plane,and only the action bonds along the fiber direction are the fiber bonds,while the action bonds in other directions are all the matrix bonds.At the same time,normal bond and shear bond are introduced to represent the failure mode of lamination and sliding.Although the general PD model reduces the calculation amount and establishes the Peridynamics model of composite materials on the premise of ensuring the overall calculation accuracy to some extent,it cannot completely describe the material characteristics of the anisotropy of composite materials,which will inevitably lead to errors in the simulation of the direction of complex fibers.At the beginning of this paper,the basic theory and numerical methods of the Peridynamics theory in recent years are introduced briefly,and the establishment of the core theory is derived briefly.In the later research,a functional model is proposed to associate the bond function with the fiber direction,and the damage of fiber-reinforced composite laminates is analyzed by using this method.According to the bond Peridynamics method and the general composite material PD model,the bond stiffness changing with the angle is introduced to make the mechanical properties of the composite materials which have a strong correlation with the direction of the fiber,which and makes the model more close to the mechanical properties of the composite material in the practical sense and more appropriate to describe its mechanical properties.According to the established model,the corresponding calculation program was written with Fortran language.The calculated data of each time step could be obtained by running on the VS platform,and the damage and failure forms at different time points could be revealed by post-processing software.Based on PD theory,this paper introduces and analyzes the research and development of bond basis PD theory and its theoretical system with the help of examples.The damage process of composite laminates under different initial damage and defect forms was analyzed.Firstly,the mechanical behavior of the composite monolayer was analyzed.Secondly,the crack propagation of the unidirectional composite laminate was simulated.Finally,the damage forms of the composite laminate with different defect layers were simulated.The validity of the model was verified by comparing with the experimental results in literature.This method further reveals the damage mechanism and cracks propagation process of composite materials.The superiority of the Peridynamics theory in dealing with discontinuous problems is demonstrated again.