Heterogeneous Finite Element Methods for Micro-Stress Analysis of Composites

摘要

The "heterogeneous element approach" is a new concept developed for micro-stress analysis of composite materials with a complex micro-geometry. The major underlying idea of the concept is that an element can consist of more than one material. As such, it is not necessary to match element boundaries to the fiber (or yarn)-matrix interface. This simplifies the mesh generation process immensely. Secondly, heterogeneous formulations enforce both displacement continuity and stress equilibrium conditions. As a result, the convergent rate of the heterogeneous element approach is much faster than either conventional iso-parametrical or conventional mixed form element approaches. Numerical examples show that less than 10% of elements are required in the vicinity of the interface if the heterogeneous element approach is employed. Two types of heterogeneous elements are formulated: displacement based and mixed form. For the former, displacement continuity along the interface is guaranteed. Further, stress equilibrium along the interface is satisfied in a weak form. For the latter, both displacement continuity and the equilibrium conditions along the interface are guaranteed. Several numerical examples are presented to verify the effectiveness of the new approach