Variational updates for general thermo–chemo–mechanical processes of inelastic solids

The variational formulation of coupled mechanical problems has many advantages from the theoretical point of view and also guides the design of numerical methods that have attractive features such as symmetric tangents. In the current work we propose a novel variational principle for three-field, strongly coupled problems involving (inelastic, finite strain) mechanics, thermal transport, and mass diffusion. To obtain this result, it is key to redefine dissipative phenomena as driven by the free entropy thermodynamic potential. Such a reformulation provides a theoretical explanation of existing variational methods and paves the way for the formulation of variational updates applicable to nonlinear multi-field problems. Representative simulations are shown to illustrate the versatility and favorable features of the resulting methods in finite strain thermoplasticity, stress–diffusion, and thermo–chemo–mechanics. •A variational statement is provided for the rate problem of thermo–chemo–mechanics.•A justification is given for the role of temperature in previous variational updates.•Variational updates are proposed for three-field coupled mechanics in mechanics.•Simulations are presented for complex two- and three-field coupled problems.•Resulting implicit methods show substantial computational savings.