Growth and remodelling from the perspective of Noether's theorem.

• Variational formulation of growth mechanics and study of the inhomogeneities and conservation laws of a growing body. • Determination of a thermodynamically inspired, intrinsic time scale associated with growth, termed 'internal time'. • Solution of a proof of concept to determine the 'internal time' of an idealised growing tumour. 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. [ABSTRACT FROM AUTHOR]