1. Continuum finite element modeling of concrete structural components - Nilanjan Mitra

2. Crack modeling for concrete Discrete crack model Advanced remeshing (Ingraffea & Saouma, Cervenka) Adaptive boundary/fem (Carter, Spievak) Advanced fem Meshfree fem (Belytschko) X fem (Sukumar, Moes, Dolbow) Lattice methods (van Mier, Bolander) Smeared crack model Enriched continua Empirical global (Vecchio & Collins, Hsu) Phenomenological (Rots, de Borst, Willam, Crisfield, Blaauwendraad) Fixed crack Coaxial rotating Multi-directional fixed Damage Plasticity (de Borst, Simo, Lubliner, Desai, Fenves, Govindjee) Microplane models (Bazant, Prat, Ozbolt, Caner) Cosserat continua (Cosserat, Green, Rivlin, Mindlin, Vardoulakis, Muhlhaus, de Borst, Willam, Sluys, Etse) Higher order gradient (Aifantis, Vardoulakis, de Borst, Pamin, Voyiadjis) Embedded discontinuity (Jirasek, Lotfi, Shing, Spencer, Belytschko, Sluys, Larsson, Simo, Oliver, Armero, Olofsson) KOS SOS SKON

3. Models done with TNO DIANA

4. Constitutive models for continuum FEM Compressive model for concrete: Yield surface – Drucker-Prager Flow rule -- Associative Compression Hardening/Softening function -- calibrated to match Popovics relation Plastic strain is zero till 30% of the strength is achieved Suitable for biaxial loading -- 16% increase in strength Tensile model for concrete: Linear tension cut-off Hordijk model for tension softening Model for reinforcement steel: Associated Von-Mises plasticity with strain hardening Model for bond in between reinforcement and concrete: Elastic radial response Transverse response is calibrated to match the Eligehausen model for bond

5. Benchmark analysis using DIANA Fracture energy tests at UW: Deflected shape Cracks Martin, J., Stanton, J., Mitra, N., and Lowes, L. N.(2007), ACI Materials Journal, 104, 575-584

6. Parametric study for fracture energy test Variation with f t Variation with E c

7. Parametric study for fracture energy test Variation with G f Variation with shear retention, Different crack models

8. Parametric study for fracture energy test Different element types Variation with threshold angle Q4 (2*2) Q8 (2*2) Q8 (3*3)

9. Benchmark analysis using DIANA Beam flexure tests: Without bond-slip  Perfect bond With bond-slip Without bond-slip  Perfect bond

10. Benchmark analysis using DIANA Flexural bending mechanism bond test Anchorage mechanism bond test Bond tests:

11. Compressive Stress distribution within the joint Joint region Top reinforcement bar steel stress Four noded quad elements for concrete Drucker Prager associated plasticity for compression Phenomenological Multi-directional fixed crack model for tension Linear tension cut-off & Hordijk tension softening curve Truss element for reinforcement steel in the connection region Von-mises plasticity for reinforcement steel Interface elements to model bond – Radial response : Elastic Transverse response: Nonlinear calibrated to Eligehausen uniaxial bond model Elastic elements with cracked stiffness to model the beams and columns Model Highlights Joint Analysis Crack development

12. Studies carried out with ABAQUS

13. Model material properties Compression stress-strain curve : Popovics equation[1973]. Tension behavior : Mitra [2008]. Linear response : 30% of maximum compressive strength. Concrete model: Concrete Damage Plasticity.

14. Beam-column Joint Model Beam and column as line element Connection region Monotonic increasing lateral load Constant axial load Simulated Joint with loading and boundary condition. Transfer of force/moment to joint : ‘Distributing coupling’.

15. Beam-column Joint Model Cont. Column as line element Reinforcements (24/12 ɸ for column and 16/12 ɸ for beam) Joint region Beam as line element

16. Beam-column Joint Model Cont. Studies made up to 2% drift. Nature of loading :

17. Behavior of the Beam-Column Joint Under Lateral Loading Cont. Bending stress at 2% drift Shear stress concentration at joint face

18. Behavior of the Beam-Column Joint Under Lateral Loading Cont.

19. More work pending for 3d continuum simulation for joints: Looking for students to complete the work Any interested student with some prior expertise in FE modeling, preferably with concrete modeling can contact me in my email add.