Research On Discrete Solid Element Method For Strong Nonlinear Simulaiton Of Continuum Structure

In this paper,a three-dimensional discrete solid element method(DSEM)for strong nonlinear simulation of continuum structure is proposed.The mechanics theory,mathematical equations,physical models and calculation processes of the DSEM are studied.The DSEM software is developed by the Fortran language.The complex problems of extreme deformation,strong material nonlinearity,dynamic buckling,wrinkle and crack propagation of continuous media are studied,and the whole process simulation of the structure transition from continuity to discontinuity is realized.(1)A novel three-dimensional(3D)discrete solid element method(DSEM)to calculate the strong nonlinearity of continuity is proposed.The physical model of the DSEM is established,including the arrangement of the spherical elements and the setting criteria of the spring between the spherical elements,and the Poisson’s ratio effect of the continuum structure is considered.The motion equation and the contact constitutive equation are deduced.The damping calculation method,the selection of time step and the contact judgment algorithm of spatial decomposition are discussed.The calculation process of the DSEM is established,and the calculation software of the DSEM is developed by the Fortran language.(2)The research ideas and calculation flow of the DSEM to solve the geometric large deformation problem are given,and the structural geometric nonlinear calculation program is developed.The principle of energy conservation is used to strictly deduce the normal and shear spring stiffness and the relationship between spring stiffness and elastic constants is established.The elastic calculation and the extremely large deformation of the continuity by the DSEM are verified using the numerical examples.(3)The plasticity theory of the DSEM is studied,and the basic framework of structural plasticity calculation of the DSEM is established.Two elastoplastic calculation models are established: the ideal elastoplastic model and the bilinear isotropic reinforcement model.The distortion energy density coefficient is deduced by the principle of energy conservation.The DSEM yield equation expressed by the contact force is established by introducing the Mises yield condition.The Drucker’s postulate and the consistency condition are used to deduce the plastic scale factor and the flow rule.The incremental contact constitutive equation,the loading and unloading criterion are establishen.And the corresponding contact force increment in the elastic phase,plastic loading phase and plastic unloading phase are given.The numerical analysis shows that the DSEM can effectively address the problems of extremely large deformation,strong material nonlinearity,wrinkles and buckling.(4)The boundary effect of the DSEM model is analyzed,and the accuracy of the DSEM in modelling the mechanical behavior of continuity is improved.The spring stiffness of the spherical elements on the boundary edge,surface and corner of the DSEM model using the principle of energy conservation is strictly deduced and the relationship between the spring stiffness and elastic constants are established.The elastoplastic bending of the thin plate with outstanding boundary effect and the buckling of the cracked thin plate are analyzed.(5)The fracture model of the DSEM is established,and the dynamic crack propagation in continuous medium are studied.Based on the strain energy release rate criterion and the fracture energy,the fracture model of the DSEM is established,including the bilinear softening model suitable for linear elastic fracture and the trilinear softening model suitable for elastoplastic fracture.The contact force and contact displacement of each feature point in the two softening models are deduced in detail.The DSEM is used to simulate the double cantilever beam test and the dynamic propagation of the composite crack.The fracture models in the DSEM are verified and the powerful ability of the DSEM to deal with fracture problems is demonsrated.Theoretical analysis and numerical examples show that the 3D DSEM proposed in this paper is effective for analyzing the mechanical behavior of continuum structures,and provides a new research approach for the analysis of complex problems such as strong nonlinearity and fracture problems.