Research On The Coupling Algorithm Of Isogeometric Analysis And Bond Based Peridynamics For Elastic Plane Problem

Material failure and structural damage raise important issues that have always plagued the automobile industrial community.FEM is based on the theory of continuum mechanics and requires a continuous displacement field.But it is difficult to deal with discontinuity problems.Isogeometric analysis(IGA)unites CAD and CAE with the advantages of geometric accuracy,high precision,fast convergence,etc.Since IGA is also a method based on continuum mechanics and requires continuous displacement field,it cannot effectively solve the discontinuity problems such as crack propagation and damage.XIGA or XFEM is a method of adding local additional functions to describe crack.It cannot be achieved in simulating the branching and crossing of cracks.Therefore,an effective algorithm for simulating crack growth is still needed to solve the discontinuity problems such as fracture.Peridynamics(PD)is based on the non-local theory of integral equations.PD can effectively solve the problems of broken crack propagation and bifurcation.The fracture problem is a dynamic iterative process generally and it requires accurate simulation results.On the other hand,it also needs to take the calculation efficiency into account.The computation efficiency of PD is low and boundary effect exists.In order to improve the computational efficiency of PD and remove boundary effects,it is necessary to combine the two theories.In this paper,a coupled model of IGA and bond-based PD for the elastic plane problem is proposed,which provides a solution algorithm for the crack problem of the elastic plane domain.The method is simple and effective.The work of this article is listed as follows:(1)IGA-PD coupling algorithm based on the force balance is proposed.The coupling algorithm combines the PD theory into the IGA,and cracks are introduced into the IGA model.The IGA-PD algorithm first uses IGA control net to discretize PD material points,and uses PD for the fractured areas that may appear.IGA is set as the model boundary,which can reduce the amount of calculation and avoid boundary effects.Then the static and dynamic solution are introduced.The force balance of the IGA-PD algorithm is verified through the patch test.(2)An algorithm for calculating the volume of control points is proposed.On the basis of the coupling algorithm,the volume division method of control points and the search range correction,integral domain correction,centroid correction method of PD are proposed to expand the application of the coupling algorithm.The coupling algorithm can effectively deal with arbitrary net.(3)The coupling algorithm is applied to engineering simulation.The fracture propagation of concrete,automobile window glass and electronic devices are analyzed,and the practical value of IGA-PD coupling algorithm is verified.This algorithm is proposed under the framework of continuum mechanics theory,which has the advantages of omitting meshing and high efficiency,and can solve discontinuous problems such as crack propagation.