Damage Model Strategies to Forecast Concrete Structure Behaviors Under Static and Dynamic Loadings Jacky Mazars and Stephane Grange Contents Introduction ....................................................................................... 2 Modelling Aspects ................................................................................ 4 Constitutive Equations ........................................................................ 4 Damage Evolutions ........................................................................... 4 Model Responses .............................................................................. 5 1D Version of the Model ...................................................................... 7 Strain Rate Effects (Mazars and Grange 2017) .............................................. 7 2D FE Description for Structural Applications .................................................. 9 Experimental Program on a Beam Under Cyclic Loading ................................... 10 Finite Element Description ................................................................... 11 Simplified Modelling for Structural Applications ............................................... 13 Cyclic Behavior ............................................................................... 14 Results Obtained with These Enhancements ................................................. 18 Low- and Medium-Velocity Loading on Reinforced Concrete Structures ...................... 19 Impact on a RC Beam (Mazars and Grange 2017) .......................................... 19 2D-1D Coupling for RC Beam-Column Substructure ....................................... 21 Summary/Conclusions ............................................................................ 28 References ........................................................................................ 28 Abstract Cementitious matrix damage conditions the behavior of concrete and concrete structures under static and dynamic loading. For this purpose, we present here a strategy to deal with the problem in real structures, which requires a combination of an efficient behavior model, the μ damage model, and a description of the structures based on a simplified finite element modeling using multifiber beams J. Mazars (*) Institute of Engineering Univ. Grenoble-Alpes, CNRS, 3SR, Grenoble, France e-mail: jacky.mazars@3sr-grenoble.fr S. Grange Universite Lyon, INSA-Lyon, GEOMAS, Villeurbanne cedex, France e-mail: stephane.grange@insa-lyon.fr © Springer Science+Business Media, LLC, part of Springer Nature 2021 G. Z. Voyiadjis (ed.), Handbook of Damage Mechanics, https://doi.org/10.1007/978-1-4614-8968-9_77-1 1