Mathematical and numerical multiscale modelling

We discuss the role of thermodynamic consistency in multiphysics and multiscale models, and how it can be preserved among scales. The quest for consistency and adoption of thermodynamic non equilibrium models has led to remarkable results in the field of fluidsolid interaction problems such as an improved model for drying shrinkage in concrete or the possibility to model non-isothermal leaching of calcium in concrete. The problem of thermodynamical consistency in case of asymptotic homogenization is also mentioned.

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