Modelling dissipative energy at different length scales

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Mohamed-Mourad Lafifi

Dear Pranoy Nair,

I suggest you to see links and attached files on topic.

https://www.nature.com/articles/s41598-017-03046-8

https://www.mdpi.com/2071-1050/12/13/5385

https://hal.archives-ouvertes.fr/hal-00302298/document

https://www.sciencedirect.com/topics/engineering/integral-length-scale

Article Dissipation of isotropic turbulence and length-scale measure...

Article Energy dissipation in atomic-scale friction

Article The physics of atomic-scale friction: Basic considerations a...

Article Scaling Effects on Materials Tribology: From Macro to Micro Scale

Best regards

Kerim Yunt

Maybe You would like to start with anticipating how dissipation as a phenomenon is integrated into mechanics and its principles properly.

Because this has consequences on the modelling , numerical treatment etc. especially Coulomb type friction gives rise to the consideration of differential inclusions. A dissipation based definition of the principle of Jourdain is presented for rheonomic (explicitly time dependent) mechanical systems, which evolve under the influence of convex dissipation potentials. It is shown, that the variational condition of the dissipative principle of Jourdain is the necessary condition for the maximization of the total dissipated power with respect to generalized velocities. The principle of maximum dissipation is shown to be the dual principle of the dissipative principle of Jourdain. A dissipative principle of Gauss is formulated by making use of nonsmooth analysis and potential theory and its dual principle is formulated.