Numerous experiments have shown that contractile cells like fibroblasts adapt their internal structure to their microenvironment by generating and orienting a network of stress fibers (SFs). This phenomenon has been modeled in previous studies with stability analysis through calculation of the fiber's potential or strain energy, where SFs are assigned a constant elasticity. Recent experiments have shown that the elasticity in SFs is rate dependent, resulting in a different stress fiber organization under constant or cyclic stretching. Here, a thermodynamical model that describes the anisotropic polymerization of the contractile units into SFs via the calculation of the mechanochemical potential of the two constituents is proposed. The stretch-dependent part of the SF potential is made of two terms that describe the passive and active behavior of the SF. In this paper, it is shown that the contributions of these two terms vary widely under constant or cyclic stretching as the SFs exhibit a rate-dependent elasticity and lead to two very different anisotropic SF organizations. It is further demonstrated that the substrate stiffness as well as its Poisson's ratio and anisotropy play a crucial role in the formation and organization of the SFs, consistent with what has been observed in various experiments.