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.

从理论的角度来看，耦合力学问题的变分公式具有许多优点，并且还指导了具有吸引人特征（例如对称切线）的数值方法的设计。在目前的工作中，我们为涉及（非弹性、有限应变）力学、热传输和质量扩散的三场强耦合问题提出了一种新的变分原理。为了获得这一结果，关键是重新定义由自由熵热力学势驱动的耗散现象。这种重新表述为现有变分方法提供了理论解释，并为适用于非线性多场问题的变分更新的制定铺平了道路。