| Abstract: |
| In the mathematical modeling of the mechanical behavior of the skin, it is common to assume that it has a viscoelastic behavior. That is, an elastic material with memory. Some models consider an instantaneous memory term while other deal with a longe-range memory term.
Our aim is to deduce such behavior via homogenization theory from a simple model where the cells are represented by fluid-filled sacs immersed in an elastic medium that represents what in Biology is known as the extracellular matrix. Assuming that the behavior of the fluid is given by the Stokes system and the one of the solid part by the linear elasticity system we obtain
a macrostructure model where the skin behaves as a viscoelastic material with a long-range memory term which decreases exponentially to zero. We also show that the model has some good properties permitting to prove the existence and uniqueness of solution and the energy conservation. These properties can be characterized in terms of the Laplace transform of the corresponding operator and can be used for more general models that are not necessarily the one obtained in the work. |
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