  This work presents an extended ordinary state-based peridynamics (XOSBPD)
model for the non-spherical horizons. Based on the OSBPD, we derive the XOSBPD
by introducing the Lagrange multipliers to guarantee the non-local dilatation
and non-local strain energy density (SED) are equal to local dilatation and
local SED, respectively. In this formulation, the XOSBPD removes the limitation
of spherical horizons and is suitable for arbitrary horizon shapes. In
addition, the presented XOSBPD does not need volume and surface correction and
allows non-uniform discretization implementation with various horizon sizes.
Three classic examples demonstrate the accuracy and capability for complex
dynamical fracture analysis. The proposed method provides an efficient tool and
in-depth insight into the failure mechanism of structure components and solid
materials.
