A general three dimensional continuum theory for growth and elastic deformation modelling of polymer materials, plant and animal tissues is presented.
It can be used to better understand the development of human organs, such as lungs, kidneys, guts, brains, etc. It can also be used to model the damage to brain or other vital human body parts inflicted by impact, during surgery or in other hazardous situations.
The mechanical model derived in this work is based on the theory of finite strains. It can be used to model visco-hyperelastic phenomena during tissue growth, deformation, relaxation and its intrinsic energy dissipation.
The model follows the laws of continuum mechanics and is thermodynamically correct. The solution of partial differential equations of the model is obtained with the use of finite element method, incorporated in FEniCS library.
To verify the developed continuum model, a simplified analytical model based on typical examples from the literature is derived.