Research On Numerical Simulation Of Anisotropic Elastoplastic Deformation With SPH Method

Smoothed Particle Hydrodynamics(SPH)method is a kind of typical meshless method.In the calculation,the continuous medium is discretized into a series of particles with field variables.Then the field function and its derivatives are obtained by kernel function approximation and particle approximation algorithm.Because the calculation of SPH method is based on nodes or particles and gets rid of the constraints of the grid,SPH method is particularly suitable for calculating problems which are difficulty to deal with by finite element method and finite difference methods,such as crack propagation,large deformation of material,high-speed impact,etc.It has become one of the numerical simulation techniques which have developed very fast and been widely used.However,with the development and application of SPH method,its existing problems and defects have gradually emerged.One is the problem of completeness,and the other is the defect of tensile instability,leading the accuracy and stability of the traditional SPH method unable to be guaranteed.Elastoplastic deformation is the basis of various complex deformation problems,such as fracture and crack propagation,metal plastic forming,impact collision,etc.,which include elastoplastic deformation.Therefore,numerical modeling of the elastoplastic deformation problem is a prerequisite for simulating such complex deformation problems,and how to establish a correct elastoplastic constitutive relationship is the key to it.In addition,in engineering practice,most of the materials have undergone processing,heat treatment,or compounding,resulting in the different physical or chemical properties in each direction and showing anisotropic characteristics.Consequently,it is more realistic to simulate and analyze the elastoplastic deformation of anisotropic materials.However,most part of the calculation methods used in the numerical simulation of anisotropic problems is finite element technology,and the application and research of meshless methods in anisotropic problems are still inadequate.This paper aims to apply the meshless SPH method to the numerical simulation of anisotropic elastoplastic deformation,expand the application of SPH method to anisotropic elastoplastic deformation problem,and provide guidance to theoretical research and practical application of SPH method and anisotropic problem.In view of the above problems,this paper has done a series of work:adopting the method of symmetry processing,and using Moving Least Squares(MLS)approximation algorithm to improve SPH method to be Moving Least Squares Particle Hydrodynamics(MLSPH)method,to ensure the completeness of approximate function and its derivatives,which has improved the calculation accuracy of SPH method;through discussing the influence of the kernel function and smoothing length on the improved SPH method,the best type of kernel function and the ratio range of the smoothing length to particle spacing have been obtained,and the high accuracy of the improved SPH method has been verified by solving the Burgers equation;using Total-Lagrangian SPH method to eliminate tensile instability and greatly improve the calculation efficiency,and combing with artificial viscosity,hourglass control algorithm and Leap-Frog time integration method to make the calculation stable;using the J2 flow theory radial return algorithm to build the isotropic constitutive relationship based on the von Mises yield criterion,and using mapping return algorithm to build the anisotropic constitutive relationship based on the Hill48 yield criterion and Swift isotropically strengthened material model;applying the elastoplastic program of SPH method to simulate several deformation examples of isotropic and anisotropic materials and comparing the numerical results with the calculation results of ABAQUS finite element software or other people,verifying the correctness,stability and feasibility of the isotropic/anisotropic elastoplastic program of SPH method.In this paper,based on the Total-Lagrangian format of the improved SPH method,a reliable and stable elastoplastic deformation program for isotropic material or anisotropic material has been established,which can accurately and effectively describe the elastoplastic mechanical behavior and predict the flow law of materials in different directions,laying the foundation for the theoretical research and practical application of SPH method in anisotropic problem.