Growth of shell-like soft biological tissues under mechanical loading

Abstract

Application of mechanical loading to soft biological tissues plays a central role in tissue engineering. Mechanical stimuli convert into intracellular biochemical activity, referred to as mechanotransduction, and lead to the growth of tissues. In most practical applications, the mechanotransduction phenomenon has been examined on thin tissues in two- or three-dimensional space. Accordingly, a phenomenological finite growth formulation for shell-like soft tissues under mechanical loading is presented in this work. The basic kinematic and kinetic quantities besides the constitutive response are formulated. The unconditionally stable implicit Euler-backward scheme is employed to solve the evolution equation of the growth parameter. Moreover, a nonlinear finite element formulation is developed, which can provide numerical solutions under arbitrary geometry, loading, and boundary conditions. Several examples are presented that demonstrate the applicability and performance of the formulation. The results indicate that finite growth as well as finite deformation of thin tissues under mechanical input can be successfully predicted by the present formulation.