Meshless Elasticity Model and Contact Mechanics-based Verification Technique

Mesh-based techniques are well studied and established methods for solving continuum biomechanics problems. When the problem at hand involves extreme deformations or artificial discontinuities, meshless methods provide sev-eral advantages over the mesh-based methods. This work discusses the Moving Least Square approximation-based meshless collocation method for simulating de-formable objects and presents a verification technique that is based on the Hertzian theory of non-adhesive elastic contact. The effectiveness of the Hertzian contact theory as a means for verification was first tested and proven through a well-established FEM code, FEBio. The meshless method was implemented as a reusable component for the SOFA framework, an open source software library for real-time simulations. Through experimentation, the Hertzian theory has been tested against SOFA hexahedral FEM and the meshless models within the SOFA framework. Convergence studies and L2 error curves are provided for both mod-els. Experimental results demonstrated the effectiveness of the implementation of the meshless method.