Generalized reconfigurations and growth mechanics of biological structures considering regular and irregular features: A computational study

Many soft biological structures have natural features of viscoelastic and hyperelastic materials. Research focused on the growth biomechanics of these structures is challenging from theoretical and experimental points of view, especially when irregular forms/defects of biological objects should be considered. To this aim, an effort is made in this paper to develop a general nonlinear finite element model for the growth of biological soft structures such as arteries, skin or different tissues. The non-Newtonian fluid is considered for viscoelastic branches. The effect of variation in thickness growth and irregular geometry as well as defects of biostructure is taken into account for the first time. The general nonlinear formulations are obtained for isotropic as well as anisotropic material properties. Furthermore, to resolve evolution equations resulting of internal variables for growth as well as viscoelastic branches, two effective implicit trapezoidal time integration schemes are employed. To study the applicability of the proposed model, the obtained results are compared with results from clinical studies for skin growth, available in the literature. The results demonstrate that the present model enables to capture of the experimental observations with very good accuracy. Additionally, the presented model enables to study of different shapes of biostructure, and variation in thickness growth, including regular and irregular defects, which have never been investigated previously.