Growth in biphasic tissue

Abstract

Continuum mechanical models for growth and remodelling of biological tissue are well suited for the description of physiological and pathological processes, such as bone remodelling, muscle adaption or the progression of a tumour. An overview of four selected growth models from the literature is given and fundamental kinematic and multiphasic approaches for open and closed systems are outlined. Beyond that, a biphasic model using the Theory of Porous Media is enhanced by the kinematic split of the deformation gradient for the study of a growing cylinder. Based on the analytical solution of the specific case without outflow, a novel growth approach is developed allowing a gradual consideration of the kinematic split. Subsequently, this approach is applied to the extended case with outflow and evaluated numerically. Herein, consolidating characteristics of growth that are driven by the interaction of fluid pressure and solid stress are identified. Finally, a numerical example of a growing body embedded in surrounding tissue shows that residual compressive stresses arise due to incompatible deformation.