Improved Bond-based Peridynamic Model Of Composite Material Unidirectional Plate

Composite materials have been widely used in aviation,aerospace,automobile and other fields,Therefore,accurate analysis of the crack propagation path and the final failure mode is of vital importance to engineering practice.The traditional continuum theory often has great difficulties in solving discontinuous problems.In 2000,Silling proposed a peridynamic theory suitable for describing crack damage propagation,using integral equations that can be applied at discontinuous displacements to replace differential equations used in traditional mechanics,to avoid problems with undefined derivatives when solving discontinuous displacements.Compared with the traditional finite element method which needs to assume the continuity of displacement,this theory avoids this problem.It is not only suitable for describing the continuity change of displacement,but also can simulate the damage propagation process of cracks at discontinuous displacement.The classical bond-based peridynamic model is limited with a fixed Poisson's ratio.In this paper,an improved bond-based peridynamic beam model of orthotropic unidirectional plate is proposed,which removes the limitation of Poisson's ratio and can be used to analyze the deformation and crack propagation of orthotropic unidirectional plate.In the improved bondbased peridynamic model,each bond is subjected to axial and transverse pairwise forces,and the additional rotation of particles can eliminate the additional bending momentum caused by transverse forces,thus ensuring that the model satisfies the balance of angular momentum.Therefore,the bond in the model in this paper not only has axial displacement,but also transverse displacement and particles rotation,which overcomes the problem that the Poisson's ratio of the classical bond-based peridynamic is limited.In this paper,the basic theory of peridynamic is firstly elaborated.Then,for the problem of the limited Poisson's ratio that exists in the simulation of progressive damage of composite materials using bond-based peridynamic model.A bond-based peridynamic model considering the rotation of particles and effect of shear deformation is proposed.The composite unidirectional plate treats as a two-dimensional plate.Set only a single layer of particles in the thickness direction.The composite unidirectional plate is divided into the fiber direction and the matrix direction in the plane.The bonds in the plane are divided into: the bond along the fiber tensile direction,the bond along the fiber shear direction,the bond along the matrix tensile direction and the bond along the matrix shear direction.By equalizing the obtained strain energy density of the peridynamic and the obtained strain energy density of the classical continuous medium mechanics,the four material parameters of the peridynamic are obtained,which correspond to the four macroscopic material constants of the composite material,thus eliminating the Poisson's ratio limit.Finally,the numerical methods,implicit solution and explicit solution are proposed.The conservation of linear and angular momentum of the proposed model is proved.Based on the proposed bond-based peridynamic beam model,the tensile simulation of carbon fiber composite unidirectional plates without central crack in different fiber directions is carried out.The simulation results obtained were compared with the finite element simulation results.The simulation results verified the validity of the model.The progressive damage simulation of carbon fiber composite unidirectional plates with central cracks in different fiber directions was carried out,and the crack damage propagation path of carbon fiber composite unidirectional plates under tensile load was obtained,which was compared with the experimental results to verify the accuracy and effectiveness of the model,and demonstrate its ability to predict deformation and crack growth.