Multi-scale methods in material mechanics

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• volume fraction2 Vol% unhydrated clinker84 Vol% hydration products14 Vol% pores• elastic propertiesAcker [2001]; Constantinides, Ulm [2004]• finite-element representation• principal stress64 µm64 µm64³ hexahedron elements820 000 DOFssolution time 5minHomogenizationnumerical SimulationHomogenizationGoal: Material parameters of effective material12
Elastic Behaviour„Natural“ b.c. (window-method)- RVE is embedded in a matrix of averaged stiffness- Discretization 3dHomogenization- correlation between mean values- volume average RVE- bounds for displacement and stress b.c.can also be obtained for f.e. simulations [Zohdi & Wriggers (2001)]Numerical homogenization- 3D isotropic material
Page 1 and 2: Characterization of Heterogeneous M
Page 3 and 4: Modelling of Microstructure/Homogen
Page 8 and 9: • 3D isotropic material• 2D iso
Page 10 and 11: Upscaling: Micro- and homogenised s
Page 12 and 13: Simulation of water permeabilityDeg
Page 14 and 15: Statistical tests of 64 RVEs (wh=0.
Page 16 and 17: Multi-Scale AnalysisMulti-Scale Ana
Page 18 and 19: Material Map ApproachInterpolationM
Page 20 and 21: Multi-scale analysis★ perform mic
Page 22 and 23: Adaptive multi-scale analysisAdapti

Multi-scale methods in material mechanics

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