Two-dimensional double horizon peridynamics for membranes

<abstract> <p>In this study, a two-dimensional "double-horizon peridynamics" formulation was presented for membranes. According to double-horizon peridynamics, each material point has two horizons: inner and outer horizons. This new formulation can reduce the computational time by using larger horizons and smaller inner horizons. To demonstrate the capability of the proposed formulation, various different analytical and numerical solutions were presented for a rectangular plate under different boundary conditions for static and dynamic problems. A comparison of peridynamic and classical solutions was given for different inner and outer horizon size values.</p> </abstract>