Friction is a complex phenomenon that arises from the interaction of deforming surface microasperities and adhesive forces at very small length scales. In this work, we use a computational model to understand the effects of various physical parameters on the friction response between two similar linearly elastic-perfectly plastic surfaces. The main ingredients of the computational model are a statistical model of the surface based on a Gaussian autocorrelation function (ACF), a parametric representation of the normal and shear responses of a single microasperity, and a statistical homogenization procedure to compute the overall friction response. The surfaces are assumed to be isotropic in nature. We employ this computational model to develop constitutive relationships for the friction force and coefficient of friction for Aluminum 6061 and stainless steel surfaces. We study the effects of various quantities such as surface roughness, material properties, normal load, and adhesive forces on the overall friction response. Our results show that the model is able to capture a wide variety of friction responses. Our results also suggest that the root mean squared (RMS) roughness of the surface alone is insufficient to describe the friction characteristics of a surface, and that an additional parameter is needed. We propose one such parameter, the aspect ratio, which is the ratio of the RMS roughness to the correlation length.