A general anisotropic peridynamic plane model based on micro-beam bond

Peridynamic (PD) theory can overcome the shortcomings of classical continuum mechanics (CCM) in simulating crack initiation and propagation. In this paper, a general anisotropic PD plane model is proposed based on the micro-beam bond. First, the general anisotropic expression of the micromoduli in different directions can be expressed through a certain transformation relation, which can make the bond exhibit general anisotropy. Then, with the use of the Allman interpolation method, the deformations of the bond can be obtained, and the PD strain energy density of the general anisotropic plane model can be expressed. Finally, the general anisotropic PD parameters in the micromoduli expression can be obtained by equating the strain energy densities of PD and CCM models. Numerical examples of static uniaxial tension, static shear, dynamic fracture of the compact tension test and dynamic fracture of the three-hole plate test prove the effectiveness of the proposed model in handling static in-plane problems and dynamic in-plane fracture problems.

Automated summary

A general anisotropic Peridynamic (PD) plane model based on micro-beam bond is proposed in this paper to overcome the shortcomings of classical continuum mechanics (CCM) in simulating crack initiation and propagation. The anisotropic expression of the micromoduli in different directions is achieved through a certain transformation relation, and the deformations of the bond are obtained using the Allman interpolation method. The proposed model is validated through numerical examples of static uniaxial tension, static shear, dynamic fracture of the compact tension test, and dynamic fracture of the three-hole plate test.