Porous muscles: Variational methods for active porous media
Many biological organisms are comprised of deformable porous media, with additional complexity of an embedded muscle. Using geometric variational methods, we derive the equations of motion of a for the dynamics of such an 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, with no need to guess the balance of forces and torques. We then 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.
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