Mathematical framework for modeling tissue growth.

A phenomenological continuum mechanics framework for modeling growth of living tissues is proposed. Tissue is considered as an open system where mass is not conserved. The momentum balance is completed with the full-scale mass balance. Constitutive equations define simple growing materials. 'Thermoelastic' formulation of a simple growing material is specified. Within this framework traction free growth of a cylinder is considered. It is shown that the theory accommodates the case where stresses are not generated in uniform volumetric growth. It is also found that surface growth corresponds to a boundary layer solution of the governing equations.