Research On Progressive Damage Simulation Of Laminates Based On Peridynamics

The Peridynamics(PD)is a non-local method that rewrites the traditional differential equation of motion into an integral form,which can effectively deal with the discontinuity problem in the material and obtain the damage path of the material under the load.Peridynamics represents the interactions between material points as state quantities,and the special form of state quantities degenerates into Bond-Based PD theory.In the Bond-Based PD,the force density vectors of the interactions between the material points are equal in magnitude,opposite in direction,and act in a straight line.Most of the calculations in the paper are based on Bond-Based PD theory.The non-local strain energy density is equivalent to the classical form of strain energy density,and the critical stretch can be obtained.When the growth ratio exceeds the critical stretch,the bonds break down and the damage begins to form.Composite laminates are anisotropic materials.The presence of reinforcing fibers makes laminates stronger in the fiber direction and weaker in the direction perpendicular to the fibers.The use of PD theory for the analysis of composite materials requires the introduction of interacting fiber bonds and matrix bonds in the plane.The fiber bonds exist only in the fiber direction,and the matrix bonds exist in all directions;at the same time,the layers need to be controlled between the layers of the laminated plates.Layering or relative sliding requires the introduction of inter-layer normal and shear bond.Isotropic materials are relatively simple and only one bond interaction is considered between the material points.Using the Fortran language to write corresponding numerical programs for specific examples,the damage forms of different time steps can be calculated,and the progressive damage process of materials can be displayed.In this paper,PD theory is used to analyze different initial defect materials.The two processes of elastic deformation and progressive damage of the model example are discussed separately.The case study of in-plane loading is a quasi-static problem.The equation of motion is established first,and then the adaptive dynamic relaxation method is used to solve the steady-state response solution.The study of composite materials firstly analyzed four kinds of unidirectional plates,and simulated the process of elastic deformation and crack propagation of unidirectional plates.The failures of laminated plates under in-plane velocity boundary conditions and impact loading conditions are simulated respectively,and the damage results of models at different times are successfully obtained.