Application of the natural element method to finite deformation inelastic problems in isotropic and fiber-reinforced biological soft tissues

Abstract

In this paper, the application of the natural element method (NEM) to solve inelastic finite deformation problems in isotropic and fiber-reinforced materials is presented. As most meshless methods, the NEM does not require an explicit connectivity definition. Consequently, it is quite adequate to simulate large strain problems with important mesh distortions, reducing the need for remeshing and projection of results which becomes extremely important in three-dimensional problems. The NEM has also important advantages over other meshless methods, such as the interpolant character of the shape functions and the ability of exactly reproducing essential boundary conditions along convex boundaries. The α-NEM extension generalizes this behavior to non-convex boundaries. A fully three-dimensional finite-strain damage model for visco-hyperelastic fibrous soft tissue has been implemented to solve different problems. In order to show the performance of the constitutive model and its algorithmic counterpart some simple examples are included, comparing the obtained results with the ones obtained with a standard finite element approach. A more complex three-dimensional numerical application to ligament mechanics is also presented. This example clearly shows the important capabilities of the NEM in this kind of applications.