On Some Problems in Determining Tensile Parameters of Concrete Model from Size Effect Tests

1. Bažant Z.P.: Concrete fracture modelling: testing and practice. Engineering Fracture Mechanics 2002; 69:165-206.10.1016/S0013-7944(01)00084-4Search in Google Scholar

2. Bažant Z.P., Le J.-L., Hoover C.G.: Nonlocal boundary layer (NBL) model: overcoming boundary condition problems in strength statistics and fracture analysis of quasibrittle materials. Proceedings of the 7th International Conference on Fracture Mechanics of Concrete and Concrete Structures 2010; 135–143.Search in Google Scholar

3. Beda P.B.: Dynamical Systems Approach of Internal Length in Fractional Calculus. Engineering Transactions 2017, 65:209-215.Search in Google Scholar

4. Błaszczyk T.: Analytical and numerical solution of the fractional Euler–Bernoulli beam equation. Journal of Mechanics of Materials and Structures 2017; 12:23:34.10.2140/jomms.2017.12.23Search in Google Scholar

5. Bobiński J., Tejchman J.. A coupled constitutive model for fracture in plain concrete based on continuum theory with non-local softening and eXtended Finite Element Method. Finite Elements in Analysis and Design 2016; 114:1-21.10.1016/j.finel.2016.02.001Search in Google Scholar

6. Brinkgreve R.B.J.: Geomaterial models and numerical analysis of softening. PhD Thesis, TU Delft 1994.Search in Google Scholar

7. Çağlar Y., Şener S.: Size effect tests of different notch depth specimens with support rotation measurements. Engineering Fracture Mechanics 2016; 157:43–55.10.1016/j.engfracmech.2016.02.028Search in Google Scholar

8. Cox J.V.: An extended finite element method with analytical enrichment for cohesive crack modelling. International Journal for Numerical Methods in Engineering 2009; 78:48-83.10.1002/nme.2475Search in Google Scholar

9. Giry C., Dufour F., Mazars J.: Stress-based nonlocal damage model. International Journal of Solids and Structures 2011; 48:3431–3443.10.1016/j.ijsolstr.2011.08.012Search in Google Scholar

10. Glema A., Łodygowski T., Perzyna P.: Interaction of deformation waves and localization phenomena in inelastic solids. Computer Methods in Applied Mechanics and Engineering 2000; 183:123-140.10.1016/S0045-7825(99)00215-7Search in Google Scholar

11. Grassl P., Xenos D., Jirásek M., Horák M.: Evaluation of nonlocal approaches for modelling fracture near nonconvex boundaries. International Journal of Solids and Structures 2014; 51:3239–3251.10.1016/j.ijsolstr.2014.05.023Search in Google Scholar

12. Grégoire D., Rojas-Solano L., Pijaudier-Cabot G.: Failure and size effect for notched and unnotched concrete beams. International Journal for Numerical and Analytical Methods in Geomechanics 2013; 37:1434–1452.10.1002/nag.2180Search in Google Scholar

13. Havlásek P., Grassl P., Jirásek M.: Analysis of size effect on strength of quasi-brittle materials using integral-type nonlocal models. Engineering Fracture Mechanics 2016; 157:72–85.10.1016/j.engfracmech.2016.02.029Search in Google Scholar

14. Hordijk D.A.: Local approach to fatigue of concrete. PhD Thesis, TU Delft 1991.Search in Google Scholar

15. Hoover C.G., Bažant Z.P., Vorel J., Wendner R., Hubler M.H.: Comprehensive concrete fracture tests: Description and results. Engineering Fracture Mechanics 2013; 114:92–103.10.1016/j.engfracmech.2013.08.007Search in Google Scholar

16. Hoover C.G., Bažant Z.P.: Cohesive crack, size effect, crack band and work-of-fracture models compared to comprehensive concrete fracture tests. International Journal of Fracture 2014; 187:133–143.10.1007/s10704-013-9926-0Search in Google Scholar

17. Lazopoulos K.A., Lazopoulos A.K.: Fractional vector calculus and fluid mechanics. Journal of the Mechanical Behavior of Materials 2017; 26:43-54.10.1515/jmbm-2017-0012Search in Google Scholar

18. Marzec I., Skarżyński Ł., Bobiński J., Tejchman J.: Modelling reinforced concrete beams under mixed shear-tension failure with different continuous FE approaches. Computers and Concrete 2013; 12:585-612.10.12989/cac.2013.12.5.585Search in Google Scholar

19. Marzec I., Tejchman J., Winnicki A.: Computational simulations of concrete behaviour under dynamic conditions using elasto-visco-plastic model with non-local softening. Computers and Concrete 2015; 15(4):515-545.10.12989/cac.2015.15.4.515Search in Google Scholar

20. Mazars J., Hamon F., Grange S.: A new 3d damage model for concrete under monotonic, cyclic and dynamic load. Materials and Structures 2015; 48:3779–3793.10.1617/s11527-014-0439-8Search in Google Scholar

21. Melenk J.M., Babuška I.: The partition of unity finite element method: basic theory and applications. Computer Methods in Applied Mechanics and Engineering 1996; 139:289-314.10.1016/S0045-7825(96)01087-0Search in Google Scholar

22. Simone A., Wells G.N., Sluys L.J.: From continuous to discontinuous failure in a gradient-enhanced continuum damage model. Computer Methods in Applied Mechanics and Engineering 2003; 192:4581-4607.10.1016/S0045-7825(03)00428-6Search in Google Scholar

23. Simone A., Sluys L.J.: The use of displacement discontinuities in a rate-dependent medium. Computer Methods in Applied Mechanics and Engineering 2004; 193:3015-3033.10.1016/j.cma.2003.08.006Search in Google Scholar

24. Sumelka W.: Non-local Kirchhoff–Love plates in terms of fractional calculus. Archives of Civil and Mechanical Engineering 2015; 15:231-242.10.1016/j.acme.2014.03.006Search in Google Scholar

25. Sumelka W., Błaszczyk T., Liebold C.: Fractional Euler–Bernoulli beams: Theory, numerical study and experimental validation. European Journal of Mechanics - A/Solids 2015; 54:243-251.10.1016/j.euromechsol.2015.07.002Search in Google Scholar

26. Unger J.F., Eckardt S., Könke C.: Modelling of cohesive crack growth in concrete structures with the extended finite element method. Computer Methods in Applied Mechanics and Engineering 2007; 196:4087–4100.10.1016/j.cma.2007.03.023Search in Google Scholar

27. Wang W.M., Sluys L.J., de Borst R.: Viscoplasticity for instabilities due to strain softening and strain-rate softening. International Journal for Numerical Methods in Engineering 1997; 40:3839-3864.10.1002/(SICI)1097-0207(19971030)40:20<3839::AID-NME245>3.0.CO;2-6Search in Google Scholar

28. Wells G.N., Sluys L.J.: A new method for modelling cohesive cracks using finite elements. International Journal for Numerical Methods in Engineering 2001; 50:2667-2682.10.1002/nme.143Search in Google Scholar

29. Winnicki A., Pearce C.J., Bićanić N.: Viscoplastic Hoffman consistency model for concrete. Computers & Structures 2001; 79:7-19.10.1016/S0045-7949(00)00110-3Search in Google Scholar

30. Zi G., Belytschko T.: New crack-tip elements for XFEM and applications to cohesive cracks. International Journal for Numerical Methods in Engineering 2003; 57:2221-2240.10.1002/nme.849Search in Google Scholar