Element-based peridynamic axisymmetric model

Peridynamic models have achieved remarkable success in simulating solid fracture problems. However, as non-local theories, they suffer from enormous computational costs. Axisymmetric solid structures are widely applied in engineering. It simplifies three-dimensional (3D) problems into axisymmetric problems through reasonable assumptions and it can significantly reduce the computational load of the models. In this study, an element-based peridynamic (EBPD) axisymmetric model is proposed for both isotropic and anisotropic materials. The model reduces 3D problem to a two-dimensional (2D) r-z half-plane case by using the geometric and stress symmetry, which effectively lowers the computational complexity while maintaining high calculation accuracy. An element stiffness density matrix containing a constitutive matrix is constructed. The micromodulus coefficient and surface correction coefficient are derived from the strain energy equivalence. The static equilibrium equation and dynamic motion equation are established by using the variational principle and Euler-Lagrange equation. In addition, the application schemes for initial conditions, boundary conditions and load conditions also provided. A critical strain energy density failure criterion for axisymmetric problems is proposed, which can conveniently characterize crack initiation and propagation without presupposing the crack path. The Gaussian elimination method and central difference method are employed to solve static and dynamic problems, respectively. In contrast to conventional peridynamic (PD) models, the EBPD model developed herein circumvents numerical instability and removes the constraint imposed on Poisson's ratio. In addition, it can also conveniently characterize non-local stress and non-local strain. When characterizing anisotropic materials, the material parameters can vary continuously with the angle.