Error Estimation and Mesh Optimization for Finite Element Analysis of Short Fiber Reinforced Composite Materials

Abstract

Abstract Knowledge of internal stress fields in fiber or whisker reinforced composites is crucial to the design, manufacturing and applications of composites. Finite element analysis (FEA) presents the only rigorous approach to a solution of this problem. However, the application of FEA to composites requires careful attention to the geometry of the optimum mesh used in the analysis. Standard energy analysis and mesh refinement procedures have yet to be generalized or extended to the special case of fiber or whisker reinforced non-homogeneous composites. Current automatic mesh generation codes do not provide the optimum mesh for composites. This paper is concerned with the development of a generalized approach for optimal mesh refinement in a short fiber reinforced composite. Optimization procedures are based on the calculation of the error in energy norm for global convergence and the traction differential approach at the fiber/matrix interface for local convergence whereas the mesh refinement strategy is based on the use of elongated elements at the fiber/matrix interface. An isoparametric finite element model that has a periodic hexagonal array of elastic fibers surrounded by an elastic matrix was used in the investigation. It is shown that this approach provides the optimum mesh with a much more rapid convergence than conventional meshes. In this manner converged local solutions can be obtained with significantly lower degrees of freedom than by conventional mesh refinement methods.