• A novel Helmholtz-energy-based framework taking coupled deformation, mass diffusion, heat conduction, charge flow and electrochemical reaction into account is developed. • The electrochemical reaction kinetics among different phases can be explicitly expressed as a function of distinct electric potentials in different conductive phases. • A well constructive Helmholtz free energy is proposed to build a numerical model of button solid oxide fuel cell, and the thermo-electro-chemo-mechanically coupled effects in solid oxide fuel cell are analyzed. • The numerical results reveal that the chemical deformation is crucial for solid oxide fuel cell. It is necessary to take the chemical stress into consideration when calculating the stress in solid oxide fuel cell. Electrochemistry, a branch of chemistry involving chemical reactions that produce electrical currents, has found vast applications in modern industries such as batteries, fuel cells and electroplating. To analyze frequently encountered thermo-electro-chemo-mechanical problems in electrochemically active materials with two different conductive phases, ionic conductor or electronic conductor, we develop a novel Helmholtz-energy-based framework taking coupled mechanical deformation, mass diffusion, heat conduction, charge flow and electrochemical reaction into account. Different from other existing multiphysics coupled models, the electrochemical reaction kinetics among different phases can be explicitly expressed in this work as a function of those distinct electric potentials in different conductive phases. This framework can be reduced in some special cases to cover the well-known phenomena such as Soret-Dufour effect and Peltier-Seebeck effect. Taking advantage of this new description, a numerical model of button solid oxide fuel cell (SOFC) with thermo-electro-chemo-mechanically coupled effects is established in COMSOL by introducing a well constructive Helmholtz free energy. Thus, the distribution of multi-physics fields in SOFC can be numerically studied and compared with some experimental results, which shows a good agreement. The numerical results also reveal that the chemical deformation is crucial for SOFC as it can change the stress state. To calculate the stress in SOFC accurately, it is necessary to take the chemical stress into consideration. In addition, this work provides a new sparkling ideal to reduce the stress for the design of future SOFC. [ABSTRACT FROM AUTHOR]