where $Hx$ denotes a neighborhood of $x$, $u$ is the displacement vector field, $b$ is a prescribed body force density field, $\rho $ is the mass density in the reference configuration, and $f$ is a paired function whose value is the force density per unit volume that the particle located at $x\u2032$ (in the reference configuration) exerts on the particle located at point $x$ (also in reference configuration). The relative position $\xi $ of these two particles in the reference configuration is given by $\xi =x\u2032\u2212x$ and their relative displacement $\eta $ by $\eta =u(x\u2032,t)\u2212u(x,t)$. Note that $\eta +\xi $ is the relative position vector between two particles in the deformed configuration. The interaction force between two particles is called a bond. A degree of nonlocality was defined for nonlocal interaction between particles in peridynamic model based on the concept of horizon
Display Formula

(2)$f(\eta ,\xi )=0\u2200\eta \u2003whenever\u2003|\xi |>\delta $