Continuum mechanics is based on the assumption that physical quantities such as displacement and stress at material points are continuous and differentiable, which means that the existence of individual atoms involved in a solid is ignored. For this reason, numerical methods are organized hierarchically according to the size of the problem. For example, at the micron scale, where continuum mechanics is not applicable, different methods such as dislocation dynamics are used, while at the nanoscale, first-principles analysis and molecular dynamics are used. In contrast, fracture phenomena in solids occur when defects at the atomic level aggregate to form flaws, which then cause fracture. In addition, groups of defects move, resulting in inelastic deformation. Silling [1] proposed the theory of peridynamics to integrate such hierarchical methods. In this theory, the problem is considered to be composed of discrete points of material, these points are connected by springs, and the inertial force is obtained by integrating the interaction force of each point over a given region by volume. It should be noted that the peridynamics theory is constructed within the framework of Eringen's nonlocalized continuum mechanics [2]. On the other hand, the interaction force in the equation of motion has a strange dimension of force per square of volume, and the method of determining the peridynamic constants while corresponding them to macroscopic material constants must go through a very complicated procedure. To resolve this contradiction, in this study we have attempted to reformulate the volume integral in peridynamics theory into a particle integral representation. This reformulation gives us the following advantages. It makes it easier to physically represent the interaction forces, and it clarifies the physical background of the relationship between macroscopic and microscopic spring constants.