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Dispersive models in biomechanics

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USMW02 - Mathematical mechanical biology: old school and new school, methods and applications

Due to their intrinsic complexity, it is not easy to modelthe mechanical behaviour of biomaterials. Despite thedifficulties encountered, some scholars have successfullyintroduced mathematical models to describe some aspectsof the mechanical response of soft tissues. However, noneof these models accounts for material dispersion. Sincemost of materials of biological interest are compositemade of different constituents reinforced by collagen and/orelastin fibers, material dispersion and anisotropy are nonnegligible.Within the theory of elasticity, several modelsfor anisotropic materials have been developed. The samecannot be said for anisotropic dispersive materials. Theexisting models accounting for material dispersion havebeen introduced only for isotropic materials. The aim ofthis manuscript is to introduce the most general model foranisotropic dispersion in transversely isotropic materials.Our model has the potentiality to represent a first steptoward a better understanding of the mechanical responseof fiber-reinforced soft materials

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