Structural computational biomechanics with advanced discretization techniques

The computational mechanics and biomechanics research community continuously seeks the best numerical approach to reproduce and simulate in-silico biological phenomena. Today, it is possible to find in the literature several advanced discretization techniques capable to simulate computationally the structural behaviour of biological structures. Consensually, the finite element method is by far the most popular numerical technique in computational biomechanics. This simple and efficient numerical technique allows to discretize the problem domain using a grid of nodes organized with a structured element mesh. Nevertheless, recently, other advanced discretization techniques started to appear in the literature. One of the most promising recently developed class of advanced discretization techniques is the class of “meshless methods”. These new numerical techniques possess several advantages over the traditional techniques. For instances, meshless methods are capable to discretize the problem domain with an unstructured nodal distribution, which allows to obtain a discrete geometrical model directly from medical images. Therefore, this meshing advantage is a true asset in computational biomechanics. There are several meshless techniques described with detail in the literature, and all of them are capable to perform accurately and efficiently a biomechanical structural analysis. As expected, since all those meshless methods are fundamentally very dissimilar, their computational performances are naturally different. In this work, it is presented a short survey on meshless methods and their advantages over traditional discretization techniques, such as the finite element method. The main goal is to show the potential and existent relevant meshless methods' state-of-the-art in biomechanics.