Growth and remodelling from the perspective of Noether's theorem

Starting from the observation that the growth of a body breaks the time translation symmetry of the body’s dynamics, we determine a scalar field, called internal time, that defines an indicator of the intrinsic time scale of the growth-related body’s structural evolution. By recasting the theory of growth for monophasic media within a variational framework, we obtain the internal time as the solution of a partial differential equation descending from Noether’s Theorem. We do this by considering two approaches, one formulated in terms of internal variables and one adopting the concept of augmented kinematics.