European Congress on Computational Methods in Applied Sciences and Engineering ECCOMAS 2004 P. Neittaanm¨ aki, T. Rossi, K. Majava, and O. Pironneau (eds.) O. Nevanlinna and R. Rannacher (assoc. eds.) Jyv¨ askyl¨ a, 24–28 July 2004 A MULTIGRID FINITE ELEMENT METHOD FOR THE MESOSCALE ANALYSIS OF CONCRETE Stefan H¨ afner and Carsten K¨onke Institute of Structural Mechanics, Bauhaus-University Weimar Marienstraße 15, 99423 Weimar, Germany e-mail: stefan.haefner@bauing.uni-weimar.de , carsten.koenke@bauing.uni-weimar.de Key words: Concrete, Heterogeneous Material, Finite Element Method, Mesoscale Analysis, Multigrid Method. Abstract. In classical engineering models concrete structures are described by ho- mogenized values of material properties such as elastic modulus and ultimate stresses. However, as concrete mainly consists of natural aggregates and mortar matrix, it is a heterogeneous material with significant physical differences among its components. For most realistic simulation, we propose to process a mechanical analysis of concrete on the mesoscale. The first important aspect is the geometrical modeling of the heterogeneous material. Besides the possibility of digital image processing, other methods are introduced for generating inclusion–matrix models of concrete. As any real-size concrete specimen includes numerous particles, the geometrical complexity becomes critical for creating an adequate finite element mesh of inclusion surfaces. Instead of that, uniform element grids are used to model the structure and the material properties are assigned at the elements according to the corresponding position of the geometrical model. The resulting, potentially high number of unknowns raised the need of an efficient solver. Various iterative solvers are evaluated and a corresponding multigrid solver is introduced. The algorithms includes mesh adaptivity and cyclic coarse grid correction. Different error influences are consid- ered and assessed for achieving best overall efficiency. Some examples are presented to examine the proposed methods regarding algorithmic aspects, accuracy and computational costs. 1