Keywords: concrete, multi-scale, homogenization, interfacial transition zone, fibre reinforced concrete.

At the beginning of the 21st century, civil engineers face the often-contradictory demands of designing larger, safer, and more durable structures at lower costs and shorter time scales. To adhere to this challenge, it is necessary to employ novel materials together with new structural concepts and construction methods. High performance cement-based composites can be named as a typical representative of these modern materials. With the help of micro-mechanical models and optimization techniques it is now possible to design concrete structures to meet requirements for both feasible production and superior failure behaviour. A review of homogenization methods, developed by the author’s research group, to obtain the macroscopic behaviour of the concrete, based on its micro-structure, is presented. The heterogeneous material is replaced by an equivalent homogeneous continuum based on a statistically representative sample of material, referred to as a representative volume element or a material unit cell. Numerous theories have been developed to predict the behaviour of composite materials. In this paper, we emphasize the finite element method (FEM) as one of the most efficient numerical methods, whereby the macroscopic responses can be obtained by volumetric averaging numerical solutions of concrete unit cells. Also presented are the developments of concrete unit cells. The concrete unit cells are developed by using generic information for the concrete paste e.g., percentage of aggregate in the concrete, aggregate distribution and percentage of the fibres. The above topics related to computational methods for the homogenization and multi-scale analysis of concrete structure are presented. These approaches have been developed in order to establish a realistic, computationally effective, approachable, adaptive multi-scale computational frame work for concrete structures.

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