In this contribution, we will present a generalized thermodynamic theory to explain how and mechanics are coupled to ionic and electronic carriers in the presence of stress field. We categorize the carriers into physically-meaningful four types, based on the signs of the charge number (i.e., polarity) and the partial molar volume (i.e., expansion coefficient). Beyond the electrostatic effects discussed in the literature, our work reveals the importance of elastic effects, as demonstrated by simulations of a composite beam bending experiment. The proposed framework not only provides a deeper understanding of stress-driven phenomena in electrochemical materials, but also suggests an unconventional approach to mechanically tune the interfacial electrical properties of mixed-conducting solids.