Concrete fracture behavior is predicted by one of multi-scaling methods, called the virtual internal bond (VIB) model. The VIB model describes the microscopic interactions between the cement pastes and aggregates using the concept of homogenization. The microscopic behavior is connected to macroscopic behavior by the Cauchy-Born rule, which results in the strain energy function. From the macroscopic strain energy function, the VIB model represents both elastic and fracture behavior within the framework of continuum mechanics. In this study, a modified Morse functional potential is introduced for material particles interactions so that the potential is independent of the length scale lattice parameter. The other parameters in the potential function are determined on the basis of macroscopic fracture parameters, i.e. the fracture energy and the cohesive strength. Moreover, the fracture energy is evaluated in conjunction with the J-integral. Finally, the VIB model with the modified Morse potential is verified by the double cantilever beam test and validated by three-point bending tests.