Influence of internal dilation on the fracture behaviour of multi-phase materials E. Schlangen * , E.A.B. Koenders, K. van Breugel Delft University of Technology, Faculty of Civil Engineering and GeoSciences, Microlab, P.O. Box 5048, 2600 GA DELFT, The Netherlands Available online 10 March 2006 Abstract Numerical modelling on the micro- and meso-level of concrete is presented. The formation of the microstructure, including the matrix and the interfacial transition zones between aggregate particles is modelled explicitly on the micro- level. The outcome of these simulations are used in a meso-level model (lattice model) to study the formation of (micro-)cracking in concrete consisting of particles embedded in a matrix. The different matrix and interface properties as well as the level of restraining of deformations is included in these simulations. Three concrete mixes with different water–cement ratio are investigated. A lower w/c shows more autogenous shrinkage, higher eigenstresses and thus a higher tendency for cracking. From the simulations it is found that eigenstresses caused by autogenous shrinkage reduce the ten- sile strength of the concrete. However, it is also concluded that the local material properties are very important and influ- ence the outcome of the simulations to a large extent. Furthermore, the influence of microcracking or weak zones on the ductility of multi-phase materials is investigated. It is found that the ratio between the strengths of the components in a material determines the width of the fracture process zone and also the ductility of the material. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Fracture simulation; Autogenous shrinkage; Lattice model; Multi-scale modelling; Eigenstress; Ductility; Microcracks; Concrete 1. Introduction Concrete is a multi-phase material and is the most used building material for civil engineering structures. It is relatively cheap, made of natural ingredients and shows a good performance. Most structures made of con- crete should last for hundred years or more. During the lifetime the structure faces a broad range of loadings, varying from mechanical load, environmental changes to internal reactions. The components of the heteroge- neous material have different properties. The way they react on loading varies too. Variation in stiffness and strength of the components has influence on the global stiffness and fracture behaviour of the material. Different thermal expansion coefficients of the components result in internal stresses (eigenstresses) in the 0013-7944/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfracmech.2006.01.033 * Corresponding author. Tel.: +31 15 27 86535; fax: +31 15 27 86383. E-mail address: E.Schlangen@citg.tudelft.nl (E. Schlangen). Engineering Fracture Mechanics 74 (2007) 18–33 www.elsevier.com/locate/engfracmech