Amorphous swelling: A macromodel for mass and energy flow

A mathematical model is proposed to explain amorphous swelling. The model is based on nonequilibrium thermodynamics and optimization techniques. The swelling stress and strains in each amorphously swelling morphomk are calculated in terms of the absorbed water. Since each morphomaʹs swelling is controlled by the adjacent morphomaʹs activity, an optimization technique is proposed to calculate stress and strains between two (or more) neighboring swelling morphoma. By considering a penalty criterion for constraints violation, a condition is imposed in order that swelling in each morphoma is produced with a preferred mode. The premise of the model is general and may be applied to explain growth and remodeling of living tissues, foams, and growth of highly compressive cellular solids; the latter are widely used for energy absorbers.