Comparison of two numerical approaches for bone remodelling.

This paper addresses the "checkerboard" phenomenon, which occurs in numerical simulation of bone remodelling. It attempts to answer the question: is an element-based approach suitable for bone remodelling? Two different numerical approaches, the element-based and the node-based finite element analyses, are implemented using ABAQUS. A comparison of the numerical results demonstrates that the checkerboard phenomenon occurs only in the element-based finite element analyses; the node-based approach eradicates the checkerboard phenomenon but requires much more computational time. This study shows that it is essential to enforce the continuity of bone density across the element boundaries. As the node-based approach requires much more computational time, the first-order Adams-Bashforth integration method is introduced to reduce computational cost. The comparisons with Euler's forward method demonstrate that the first-order Adams-Bashforth method indeed enhances accuracy and reduces computational cost. This study concludes that the node-based approach with the first-order Adams-Bashforth integration scheme is to be recommended for computational bone remodelling studies.