Finite element modeling of bone tissue stress adaptation

The design or architecture of bone is quite complex and diverse, ranging from a very porous cellular solid (trabecular bone) to a very dense solid (cortical bone). Significant adaptations to cortical and trabecular bone mass and architecture have been observed in response to changes in stresses acting on the tissue. The purpose of this paper is to examine bone stress-adaptation schemes, including so- called self-optimization theories of bone, within two- dimensional (2D) and three-dimensional (3D) finite element modeling (FEM) domains. Stress-adaptive FEM simulations are implemented using Matlab and involve analysis of stresses and strains, followed by successive iterations with the goal to globally minimize stress-strain objective functions (strain energy density, von Mises, maximum shear) without imposing constraints other than bounds on the relative density. Both isotropic and anisotropic material properties are considered while applying time-independent loading conditions for simple geometry domains with isoparametric elements. Application of a uniform tension/shear loading to 2D rectangular domains produced heterogeneous material, complex lattice structures that were qualitatively similar to trabecular bone. Three-dimensional cantilever beam analyses using isotropic and anisotropic material properties produced density-optimized, but not necessarily stiffness and strength optimized, structures. Finite element analysis simulations can assist in understanding complex adaptive structures, including bone.