The aim of this course is to describe some mathematical models in Continuum Mechanics which are widely used in Biology.
Starting from a review of kinematics and a short introduction about rheology and hyperelasticity, we present both fluid and elastic models. First, we introduce some constitutive models for fluid flows and show how the Navier-Stokes equations can be generalized in order to include some biological specific behavior.
Second, we study a hyperelastic model of muscle tissue which can describe the ability of the muscle of being activated through a chemical reaction. This process, which is usually called "activation", is now widely discussed in the literature. We present the two most popular approaches: active stress and active strain.
