Chapter 8 - BEM in Biomechanics: Modeling Advances and Limitations

In this chapter, authors provide a description of boundary element method (BEM) applications in biomechanics, with a focus on advantages and limitations of BEM versus other numerical methods such as finite element method, finite difference method, and meshless methods. In addition to a general overview, the chapter focus on how the BEM approach can be advantageous in those biomechanical problems involving fracture mechanics and contact modeling. To this aim, its preprocessing flexibility to tackle sharp geometric changes and complex remeshing is highlighted. The comparison among BEM and other numerical approaches proceeds through the evaluation of inherent accuracy, preprocessing and postprocessing efforts, and run times. Bio-CAD models with complex shapes are usually created from medical images acquisition, computer tomography or magnetic resonance scan, with different modeling techniques, which result in different accuracy and usability of the generated tessellated or surface computer-aided design (CAD) geometry. Special attention must be drawn to the mathematical reconstruction of bio-CAD model to facilitate the meshing process in the BEM environment and reduce the geometrical imperfections generated during the CAD to computer-aided engineering translation phase. BEM is best suited to reproduce accurately high surface stress gradients that are generally a modeling issue (e.g., in bone–implant contact simulations). Working with 3D models, the mesh refinement in the neighboring areas where high stress gradients are expected is much facilitated when using BEM, also because it is possible to use discontinuous elements and circumvent the constraint of a continuous mesh. BEM approach is certainly more accurate for linear analysis but, on the other hand, less versatile in some areas like those of highly nonlinear material behavior. A short description of some case studies showing the described advantages of BEM approach is reported.