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Homogenization-based coarse graining framework for the analysis of reinforced concrete structural elements

In this study a coarse graining framework based on the mathematical homogenization theory is developed for the Lattice Discrete Particle Model (LDPM), a meso-scale model for concrete extensively calibrated and validated under a large variety of loading conditions [1,2]. Recent work by the second and the last authors has demonstrated that, through homogenization, LDPM gives rise to a Cosserat-type constitutive model in which the stress vs, strain and couple-stress vs curvature equations are fully coupled in the nonlinear regime [3].

In the present study, the coarse-grained system is obtained by increasing the particle size artificially with a scaling factor k. The coarse-scale material parameters are optimized by matching the macroscopic, homogenized stress vs strain and couple-stress vs curvature curves obtained by subjecting representative volume elements (RVEs) of both the fine-scale and coarse-grained models to various loading conditions. The least-square method is used to minimize the discrepancy between coarse-grained and fine-scale responses.

In this presentation, the effect on the optimization procedure of RVE size and number of RVEs with different internal structure is discussed. The effectiveness of the proposed coarse graining technique is verified by comparing full fine-scale solutions and coarse-grained solutions for reinforced concrete structural elements.

Author(s):

Erol Lale    
Istanbul Technical University
Turkey

Roozbeh Rezakhani    
Northwestern University
United States

Mohammed Alnaggar    
Northwestern University
United States

Gianluca Cusatis    
Northwestern University
United States