Poroelastic finite element analysis of a bone specimen under cyclic loading

It had been suggested that the fluid embodied in bone lacunar-canalicular porosity may play an important role in bone remodelling [Weinbaum et al., 1994. Journal of Biomechanics 27, 339-360]. In this paper a finite element model of a poroelastic prismatic solid of rectangular cross-section is considered to simulate bone behaviour, precisely as in the previous work by Zhang and Cowin [Zhang and Cowin, 1994. Journal of Mechanical Physics of Solids 42, 1575-1599]. This solid is subject to combined cyclic axial and bending loads at its end. The objectives of the study are: (1) to verify the accuracy of the simplifying hypotheses underlying the analytical solutions established by the above authors; (2) to provide further insight into the behaviour of that solid; (3) to test the advantages in generality and versatility and the computing costs of general-purpose finite element codes in poroelastic analysis. The study is parametric with respect to the fluid leakage coefficient, to the ratio of the bending moment and axial load, and to the ratio of the characteristic relaxation time of the pore pressure over the excitation period. Results show that, for all the cases considered, the pore pressure distribution along the section height of the poroelastic beam exhibits a very good matching with previous analytical results. Stresses transversal with respect to the beam axis (assumed as constant or zero in previous analytical solutions) are evaluated. The analysis pointed out that: (1) the effects due to end-loads with zero resultants practically extinguish within a distance from the beam end almost equal to a typical length of the cross-section; (2) cross-sections remain plane above that distance; (3) the transversal total stresses are three orders of magnitude lower than axial stress.