An adaptive three-dimensional finite element algorithm for the orthogonal cutting of composite materials

Abstract

In order to analyze the mechanism of cutting a fiber-reinforced composite using the finite element method (FEM) an appropriate meshing for the matrix, the fibers and their interfaces is essential. In a two-dimensional FEM analysis, the uniform increase of elements remains an attractive way with reasonable cost. However, this is not true in three-dimensional cases as the degrees of freedom rise dramatically. This paper aims at an efficient way to achieve smooth material removal in three-dimensional cuttings of fiber-reinforced composites. An adaptive algorithm was developed to control the solution steps and input data and to handle the remeshing of the selected elements using the criterion of the maximum shear stress. Different sets of three-dimensional elements were used to account for the fiber and matrix materials. At each solution step, the algorithm examined all sets of elements, determined those with the maximum shear stress and replaced them with refined meshes such that interconnectivity of the new elements satisfies the compatibility conditions. The solution of the previous time step was then mapped to the new mesh as the initial conditions. The chip formation was realized by the technique of element death. It was found that although the use of an algorithm increases the computational time, it offers a more cost-effective finite element mesh than the conventional method of refinement. In addition, the algorithm can accommodate the behavior of a fiber-reinforced composite under general cutting conditions. The numerical result shows a close agreement with the relevant experimental results.