Bridging the Length Scales in Models for Crack Predictions in Hardening Concrete Structures
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Bridging the Length Scales in Models for Crack Predictions in Hardening Concrete Structures Eddy A.B. Koenders1 and Klaas van Breugel2 1 Structural and Building Engineering 2 Micromechanical Laboratory Delft University of Technology Faculty of Civil Engineering, Stevinweg 1, 2628 CN Delft, The Netherlands
ABSTRACT With models being developed at different levels of observation, length scales become an issue. In particular for simulation models that have to line-up and be compatible, this issue requires due attention. Different approaches can be adopted to bridge these length scales, each with their own pros and cons. In this contribution, two different approaches to deal with the scale differences in models for hardening concrete structures will be presented. Based on the parameters involved in the stress calculation of hardening concrete (macro)structures, the approaches are clarified. The first approach is based on the “bridging” concept whereas the second approach follows the Ribbon concept. Both concepts are discussed in terms of length scale bridging and its consequences for the modelling results. The paper ends with a discussion about the parameter variations related to the different length scales by means of a probabilistic approach.
INTRODUCTION The production of a durable high quality building material, like concrete, is demanding for a clear and fundamental understanding of all its (internal) properties. Depending on the level of observation, different constituents can be identified, which implicitly illuminates the scale-level for the numerical model. From this, the multi-scale modelling approach has been born comprising three levels of observation, viz. macro, meso and micro level (see figure 1). However, recent developments on the nano-scale level have confirmed the nano-level as an independent level at which material behaviour can also be simulated. For the modelling world, this implicitly introduced a new scale difference that has to be bridged in modelling material properties. With respect to simulation of these properties that associate with these particular levels, emphasis is on the level on which these models run and how to let them ‘communicate’. In order to make these models compatible – data exchange between the different scale levels, these different length-scales have to be bridged. When considering concrete as a building material, simulation models are available for predicting different kinds of material properties. Each model is build around a certain level of observation that coincides with the particular modelling level. Models used for simulation of the microstructural development, expressed in terms of the degree of hydration, mainly run on the nano- and the micro-scale level. The output results of these hydration models are used as input for stress-calculation models, which run on the higher macro-scale level. However, internally, these stress-calculation models that predict the sensitivity of concrete towards thermal and
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