Abstract
The accurate and efficient prediction of the interaction of microcracks with macrocracks has been a challenge for many years. In this paper a discretization error controlled adaptive multiscale technique for the accurate simulation of microstructural effects within a macroscopic component is presented. The simulation of cracks is achieved using the corrected XFEM. The error estimation procedure is based on the well known Zienkiewicz and Zhu method extended to the XFEM for cracks such that physically meaningful stress irregularities and non-smoothnesses are accurately reflected. The incorporation of microstructural features such as microcracks is achieved by means of the multiscale projection method. In this context an error controlled adaptive mesh refinement is performed on the fine scale where microstructural effects may lead to highly complex mechanical behavior. The presented method is applied to a few examples showing its validity and applicability to arbitrary problems within fracture mechanics.
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Loehnert, S., Prange, C. & Wriggers, P. Error controlled adaptive multiscale XFEM simulation of cracks. Int J Fract 178, 147–156 (2012). https://doi.org/10.1007/s10704-012-9777-0
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DOI: https://doi.org/10.1007/s10704-012-9777-0