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Center for Nonlinear Studies |
Porous media presents a highly complex example of fluid-structure interactions where a deforming elastic matrix interacts with the fluid. Many biological organisms are comprised of deformable porous media, with additional complexity of a muscle acting on the matrix. Using geometric variational methods, we derive the equations of motion of a for the dynamics of both the passive and active porous media. The use of variational methods allows to incorporate both the muscle action and incompressibility of the fluid and the elastic matrix in a consistent, rigorous framework. We also derive conservation laws for the motion, perform numerical simulations and show the possibility of self-propulsion of a biological organism due to particular running wave-like application of the muscle stress. We also discuss variational derivation for equations of porous media from the point of view of variational thermodynamics, leading to conclusions about thermodynamically consistent functional forms of friction forces and stresses acting on the media. We conclude by deriving the equations for porous media that is damaged by the applied stress, and discuss possible applications and particular cases.