A fibre reorientation model for orthotropic multiplicative growth. Configurational driving stresses, kinematics-based reorientation, and algorithmic aspects

The main goal of this contribution consists in the development of a remodelling framework for orthotropic continua whereby the underlying symmetry group is incorporated via two fibre families. Special emphasis is placed on the modelling of biological tissues at finite deformations. Besides the incorporation of a referential mass source, anisotropic growth is addressed by means of a multiplicative decomposition of the overall deformation gradient into an elastic and a growth distortion. Projected quantities of a configurational growth stress tensor are advocated as driving forces for time-dependent saturation-type evolution of the principal values of the growth distortion. Moreover, the reorientation of both fibre families, which directly affects the strain energy as well as the growth distortion itself, is guided by analyzing critical energy points. In particular, a time-dependent formulation is developed which aligns the fibre directions according to the principal stretch directions. Finally, the proposed framework is embedded into a finite element context so that representative numerical examples, examining growth and resorption in volume and density together with fibre reorientation, close this study.