A comparison of implicit and explicit natural element methods in large strains problems: Application to soft biological tissues modeling

The natural element method (NEM) is one of the members of the large family of meshless methods, with clear advantages over the finite element method (FEM) in problems involving large mesh distortions or complex geometries where the design of the mesh is costly. These problems are found in many applications like, for instance, simulation of biological structures involving soft tissues, such as, articular joints. One additional advantage of NEM is that it can be easily coupled with finite elements and implemented into any FE framework, including well-known commercial packages. NEM as most other spatial approximation approaches can be applied to evolution problems in two types of time (or pseudo-time) integration schemes, namely implicit and explicit. However, the NEM explicit version has neither been implemented nor sufficiently analyzed, so a comparative study of those two types of NEM time integration schemes is still missing. The main aim of this paper is to discuss issues related to NEM accuracy and stability in its explicit version, and problems related to its implementation into an explicit FE commercial code. Finally, a comparative study addressing the main properties, advantages and disadvantages of both types of NE schemes, implicit and explicit, is presented. Several examples of application are discussed including aspects where NEM is competitive with FEM including modeling of human articular joints like the knee. Explicit NEM allows achieving accurate results for high distortions and complex contact conditions although constraints on time step still are a major drawback and comparable to those known in finite elements to keep stability and accuracy despite the less NEM sensitivity to mesh distortion.