A new type of peridynamics: Element-based peridynamics

Abstract

The general peridynamic theories are constructed using the interactions of particles in a horizon. The interactions of particles can be connected by using spring, rod and beam, etc. Element-based peridynamics (EBPD) is proposed in the present study, in which the interactions of particles are expressed by using elements in a horizon, and the basic element concepts in the continuum mechanics are reserved exactly. The force density of EBPD is described using 2-node rod elements for one-dimensional (1D) problems, 3-node triangle elements for two-dimensional (2D) problems and 4-node tetrahedron elements for three-dimensional (3D) problems. The EBPD equations are derived from the principle of the minimum potential energy. The treatments of surface effects, boundary conditions, failure criterion and solving process of the EBPD are provided in detail. The examples of the 1D singular bar, 2D stationary crack near-tip solution, 2D plate crack propagation and 3D cubic demonstrate the effectivity of the proposed EBPD. The proposed EBPD model is used for elasticity, and defined new nonlocal stress and strain expressions. In addition, no restriction of Poisson’s ratio and no zero energy modes are included in EBPD. Furthermore, EBPD has the potential to study the nonuniform discretization, varying horizons, plasticity, thermodynamic and anisotropic material. It is also convenient to couple with FEM to reduce the computational burden.