Smoothed finite element method for analysis of multi-layered systems – Applications in biomaterials

• Smoothed finite element methods (SFEM) are formulated and used for multi-layered bio-material system.
• The selective ES/NS-FEM model overcomes volumetric locking in multi-layered bio-material system.
• ES-FEM are more accurate than conventional FEM and NS-FEM in compressible multi-layered bio-material systems.

In general, the biologic system can be rather sophisticated and commonly present in hierarchical layers. Hence, the quadrilateral or brick elements are very difficult to precisely capture the anatomic details for mechanobiologic modeling. Further, the conventional finite element method (FEM) could possibly give poor solutions using triangular or tetrahedral elements due to its overly-stiff property. In addition, the biologic soft tissues are often considered as ‘incompressible’ materials, where conventional FEM could suffer from volumetric locking in numerical solution. For these reasons, smoothed finite element methods (SFEM) are proposed here to solve the multi-layered bio-systems for softening conventional FEM models.