Numerical simulations are performed to characterize the micro- and macro-scale aspects of the electro-chemo-mechanical coupling behavior of a positive-electrolyte-negative (PEN) structure under SOFC operation. The mathematical homogenization method is applied to evaluate the macroscopic material properties of porous electrodes by performing the corresponding microscopic analyses. In particular, the potential transfer conditions at pore surfaces and triple-phase boundaries are homogenized to be source terms in the macroscopic electron-ion coupled transport problem. A case study is conducted to identify the major source of generation and evolution of cracks running through a disc-shaped cell. In this context, we are concerned especially with the effects of the radius of the cell, the thickness of the electrolyte and the profile of temperature's in-plane distribution on the macroscopic tensile circumferential stress distributions.