Study On The Coupling Method Of Peridynamics And Finite Element

The economic losses caused by material fracture and destruction are getting more and more serious.There is an urgent need for an efficient and accurate method to study fracture failure,so as to reduce economic losses.The traditional continuum mechanics method involves the spatial differential equation of displacement,and the derivative of this differential equation is not defined at the discontinuity of displacement,causing singularity.The emerging peridynamic method is based on the non-local idea by solving the spatial differential equation.Because it does not involve the spatial integration of displacement,it is still defined at the discontinuity and there is no singularity.Because the peridynamic method is a non-local action,this method will cause low calculation efficiency,low calculation accuracy,significant boundary effects,especially the stress boundary cannot be applied,and other difficulties seriously restrict the application of the peridynamic method in engineering.Therefore,the peridynamic method is combined with the traditional continuum mechanical method(such as the finite element),and the peridynamic method is applied in the problem concerned area,and the continuum mechanics method is applied in the other areas,so that on the one hand,peridynamics can be used relevant theories of continuum mechanics,on the other hand,can improve calculation efficiency.This paper adopts the finite element discretizion of peridynamic theory,combines it with traditional finite element,and solves it under the framework of finite element method,which provides the possibility of the application of peridynamics in engineering.The mechanism provides a powerful solution.This paper first studies the bond-based peridynamic theory,proposes a finite-element method for bond-based peridynamics,and calculates the twodimensional flat plate under pure tensile and pure shear conditions and the calculation of the initial crack.The example verifies the correctness of the state-based peridynamics coupling algorithm.Because the bond-based peridynamic method has the limitation of Poisson's ratio: 1/3 in two dimensional case;1/4 in three dimensional case,and the state-based peridynamic method is studied for its shortcomings.The "bond" constitutive force depends on the coordination of all bonds in the near-field domain of the end point,which makes the calculation simulation time-consuming.Coupling the state-based peridynamic method with finite element will solve this problem to a certain extent.The computational consumption of the peridynamics is huge for the fracture problem in the global area.In this paper,an adaptive coupled local / non-local model method is used to simulate the fracture problem,and the "bond" damaged elements are replaced by discontinuous Galerkin elements.Through continuous modification of the coupling function of the crack tip motion,the application area of the peridynamic model is adaptively adjusted to continuously simulate crack propagation.