[hal-00816357, v1] Mechanical behavior of annulus fibrosus tissue: identification of a poro-hyper-elastic model from experimental measurements

Annulus fibrosus (AF) is the outer tissue of intervertebral disc (IVD) which is a highly specialized element of the spine that provides flexibility and dissipative capacities. When mechanical loads are transmitted along the spine, IVD mainly supports compression and bending stresses. This results in a hydrostatic excessive pressure in the central nucleus pulposus and generates circumferential tensile stresses in the surrounding AF. To hold these large circumferential strains, AF tissue is assimilated to a composite material made of oriented structures of collagen fibers embedded in a highly hydrated (60−70%) matrix [6]. This particular microstructure and biphasic composition confers to AF a non-linear and anisotropic behavior. Many experimental studies have underlined the anisotropic and non-linear mechanical behavior of AF using uniaxial tensile tests [5-7]. However, few authors have experimentally investigated the biaxial behavior [8]. Various models of the AF mechanical behavior have been proposed in the context of fiber-reinforced theory. To account for finite strains, hyper-elastic formulations have been developed which introduce some exponential strain energy functions [5,7]. Thanks to their large degrees of freedom, these models have been successfully employed to curvefit many experimental stress-strain data in different configurations: tension or compression on axial, radial or circumferential samples. Nevertheless, these descriptions fail to represent the hysteresis observed under loading cycles [1,10] that would be related to a viscous component. This behavior is classically described by a poro-elastic formulation and can account for coupling effects between macroscopic mechanical strains and viscous flow through it [9]. In this framework, the porous structure is usually described by an elastic behavior unable to capture non-linearities. This work aims to couple a poro-mechanical formulation with a hyper-elastic model to account for fluid flows and describe viscous effects.