Multiscale Coupling through Locally Enriched Finite Elements

Abstract

AbstractMultiscale modeling helps us to focus our limited computational power into those special places where traditional models based on continuum mechanics will fail while not losing the big picture of the macro scale behavior. An hourglass shaped development can be observed in today's simulation technologies. Simulation tools in the macroscale category and that for the micro phenomenons are both relatively well developed. Many algorithms and methods have been proposed in recent years to fill the gap between them. However, rather than trying to bridging different techniques, many tend to replace them completely and become independent simulation tools. Since many single–scale models have already been widely adopted by both the industry and the academy, it would be more beneficial to concentrate just on coupling techniques which can be applied without significant modifications of the original simulation framework. In this work, we present a multiscale idea of coupling the fine–scale model with the coarse–scale model through local enrichment within the elements at the coupling boundary. Higher order shape functions have been used to ‘enrich’ the coarse–scale model, allowing softer transition of the displacement field from the fine–scale model to the coarse–scale model. A least–square process has been used to fit the displacement gradients of different models at the coupling region. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)