Two-dimensional growth of incompressible and compressible soft biological tissues

Soft tissues have the ability of growth as a response to some especial changes of their environment. The aim of this work is to develop a non-linear finite element formulation for two-dimensional growth of soft tissues. The formulation is derived in Total Lagrangian (TL) framework. Moreover, the growth variable is considered as a single-valued scalar parameter known as growth multiplier. To deal with evolution equation resulting from the growth parameter, an implicit midpoint scheme is employed. Furthermore, a method is presented for compressible hyperelastic material models, and the formulas can be applied to incompressible and compressible, isotropic and anisotropic tissues. Finally, to investigate the performance of the proposed model, some examples are provided and compared to those available in the literature.

Automated summary

The aim of this work is to develop a non-linear finite element formulation for two-dimensional growth of soft tissues, and several examples are provided to validate the proposed model.