The Effect Of Accurate Volume Correction On The Accuracy Of The Peridynamic Model

In 2000,Silling proposed the peridynamic theory based on the idea of non-local action.The peridynamic theory uses the integral form of motion equation to avoid the problem of the nonexistence of derivatives in the traditional mechanical theory when solving discontinuous displacements.It can be used to solve both continuous and non-continuous problems.Since only a part of the volume of the matter point at the boundary of the horizon lies in the horizon.The rough approximation of this part of the volume will affect the accuracy of the peridynamic method.And because most structural models are irregular(containing pores,cracks,etc.),the mesh obtained when discretization is also non-uniform.At present,there is no volume correction algorithm that can accurately calculate the volume of the intersection area and can be applied to the non-uniform discrete mesh.To solve the above problems,this paper proposes a new volume correction algorithm.Taking the two-dimensional case as an example,the algorithm divides an arbitrary polygon mesh into several triangle meshes.Each triangle mesh is classified according to the number of nodes in the horizon,and the precise area calculation method for each type is given.And the matter points at the boundary of the horizon are corrected,the centroids of the intersection areas are calculated to replace the original matter points.The method can not only accurately calculate the area of the intersection area but also be applied to non-uniform discrete mesh.Combining strain energy density analysis and numerical examples,the following research results are obtained: The volume correction algorithm proposed in this paper calculates the area of the intersection area more accurately than other algorithms,and the obtained integral domain is exactly the same size as the horizon.Compared with other algorithms,it is more accurate in calculating strain energy density and has higher accuracy and convergence when using the cubic term influence function.Through the uniaxial stretching and shear simulation of the plate with preset central circular hole,the displacement cloud diagram shows that the volume correction algorithm proposed in this paper is basically consistent with the finite element simulation,the displacement of the measuring point is also more accurate than other algorithms.For different mesh sizes,the errors with the finite element are all within 2%.Therefore,the effectiveness and accuracy of the volume correction algorithm proposed in this paper for non-uniform discrete mesh are fully verified.