On the modeling of activation in biological transversely isotropic materials

Abstract

Many biological materials exhibit the ability to activate, essentially due to the action of muscle cells. While the mathematical description of passive materials is well-established, even for large deformations, this is not the case for activation, since capturing its complexities poses significant challenges. This paper focuses on the mathematical modeling of activation of biological materials, guided by the important example of skeletal muscle tissue. We will consider an incompressible and transversely isotropic material within a hyperelastic framework. Our goal is to design constitutive relations that agree with uniaxial experimental data whenever possible. Finally, we propose a novel model based on a coercive and polyconvex elastic energy density for a fiber-reinforced material; in this model, activation occurs solely through a change in the reference configuration of the fibers, following the mixture active strain approach. This model assumes constant activation, preserving the good mathematical features of the original model while still capturing the essential aspects of activation observed in experiments. Mathematics Subject Classification (2020) 74B20 · 74L15