Numerical Implementation Of The Micro-beam Bond Based Peridynamic Shell Models

With the increasing number of cars in the daily traffic,the frequency of safety accidents is also increasing year by year.Deformation,damage and fracture of auto parts in accidents will cause danger to human body.It is of great significance to study the mechanical behavior and failure rules of materials under specific conditions for the safety of automobiles.Peridynamics(PD)is a newly proposed non-local theory,which analyzes computational mechanics behavior in the form of space integral,overcomes the disadvantage that discontinuities in traditional continuum mechanics cannot be derived,and can well simulate the damage and fracture of materials.Based on the discontinuous Galerkin finite element method,the implicit and explicit numerical methods for solving the micro-beam bond based PD shell model are implemented in this paper,and the effectiveness of the algorithm is verified by a series of numerical examples.The main research work of this paper includes:(1)By summarizing the research background and status quo of near-field dynamics,the micro-beam bond basis near-field dynamics model is introduced,and its basic theory and the derivation process of PD parameters are introduced.Based on the micro-beam bond basis nearfield dynamics theory,the PD shell model is deduced.(2)Based on the discontinuous Galerkin finite element method,starting from the bond stiffness matrix composed of material points,combined with the element shape function,the single stiffness matrix between discontinuous Galerkin elements is established,and finally the implicit solution format of the micro-beam bond based PD shell model is established.Based on Hamilton principle,the mass matrix coefficients of multi-degree of freedom plate and shell elements are established,and the explicit solution scheme of PD shell model based on micro-beam bond is proposed.(3)The above algorithm was realized based on C++,and three implicit examples of uniaxial tension,pure shear,and flexural load-supported thin plates were analyzed to measure the solving accuracy of the algorithm under different grids.The crack propagation,double notched crack plate and double torsion test of preset crack were simulated based on the explicit solution algorithm.The results show that the algorithm for solving the micro-beam bond based PD shell model established by discontinuous Galerkin finite element method has high computational accuracy and good applicability to different size mesh discrete regions.