Research On Coupling Of Mirco-beam Bond-based Peridynamics And Finite Element Method In Beam Modeling

Frame structures are widely used in daily life.When a frame structure is under load,the local structure will deform,damage or even break,which will lead to the destruction of the entire structure.Therefore,understanding the mechanical response characteristics and damage rules of beams under external forces is of great significance for the safety protection of frame structures.Classical continuum mechanics assumes that the deformation of an object is continuous,so it cannot accurately describe discontinuities such as cracks.The peridynamic(PD)theory adopts the form of spatial integral equation to describe the motion,which ensures that the discontinuity of the displacement is still meaningful,and the damage of the material is also part of the constitutive equation,thereby allowing cracks to expand in any direction.This feature makes PD widely used in the prediction of material damage.Based on the micro-beam bond-based PD beam model,this paper proposes to use the discontinuous Galerkin finite element method to solve the problem,and successfully realizes the coupling of the PD beam model and the finite element beam model.First,a micro-beam bond-based PD beam model is introduced.In this model,a bond is regarded as a beam element,and the end of each bond has three translational and three rotational degrees of freedom,which can simultaneously consider axial,torsional and bending deformations.This model can be used to study the deformation of the beam under complex loading conditions.Second,the discontinuous Galerkin finite element method for the PD beam model is proposed,the numerical solution process and the corresponding volume correction algorithm are derived,and the energy based failure criterion is used to simulate structural fracture in detail.The static implicit solution flow of the process.By introducing the Heaviside function in the transition zone,the PD model and the finite element model are added to obtain the coupled model,and the program is written under the C++ framework.Finally,some numerical examples for static problem are calculated,including a straight beam,a frame consisting of two straight beams and a spatial beam structure subjected to lateral loads.By comparing the calculation results by the coupling model with by the finite element one,the feasibility of the proposed method is verified.Then,the fracture analysis of the straight beam and the frame beam structure subjected to concentrated load is carried out to verify the effectiveness of the method for the fracture analysis of spatial beam structures.The proposed method can be used for damage prediction of complex spatial beams.