Modelling the active and passive behavior of fiber reinforced biological tissues
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We introduce a class of material models able to describe the passive-active behavior of biological tissues stiffened by collagen fibrils. The tiny fibrils are characterized by a dispersion of their spatial orientation, defined by a probability density function, which introduce anisotropy. Anisotropy affects both passive and active behaviors, producing complex responses of the material. Unlike most anisotropic models usually adopted for biological tissues [1], here we assume that the passive behavior is monolithic and no splitting between volumetric and isochoric strain energy density is made. The model wants to reproduce observed experimental behaviors, where volumetric deformation induce shear stresses and angle changes induce isotropic pressure. The active behavior is described by an active strain, including a volumetric and an isochoric contributions modelled in independent ways, in line with our previous models [2]. The non-correlation of the active deformations, which can be justified by the different mechanical functions of the material constituents that generate them, results in a coupled anisotropic behavior due to the passive response. The model is developed to address the typical behaviors of muscles of the human eye, attendant the focusing of the light into the cornea, specifically the iris and the ocular muscles.