On some problems in determining tensile parameters of concrete modl from size effect tests

• Autorzy: Marzec I. , Bobinski J.
• Języki publikacji: EN

Abstrakty

EN

The paper presents results of numerical simulations of size effect phenomenon in concrete specimens. The behaviour of in-plane geometrically similar notched and unnotched beams under three-point bending is investigated. In total 18 beams are analysed. Concrete beams of four different sizes and five different notch to depth ratios are simulated. Two methods are applied to describe cracks. First, an elasto-plastic constitutive law with a Rankine criterion and an associated flow rule is defined. In order to obtain mesh independent results, an integral non-local theory is used as a regularisation method in the softening regime. Alternatively, cracks are described in a discrete way within Extended Finite Element Method (XFEM). Two softening relationships in the softening regime are studied: a bilinear and an exponential curve. Obtained numerical results are compared with experimental outcomes recently reported in literature. Calculated maximum forces (nominal strengths) are quantitatively verified against experimental values, but the force – displacement curves are also examined. It is shown that both approaches give results consistent with experiments. Moreover, both softening curves with different initial fracture energies can produce similar force-displacement curves

• Wydawca: -
• Czasopismo: Polish Maritime Research
• Rocznik: 2019
• Tom: 26
• Numer: 2
• Opis fizyczny: p.115-125,fig.,ref.

Twórcy

autor

Marzec I.

• Gdansk University of Technology, Narutowicza 11/12, 80-233 Gdansk, Poland

autor

Bobinski J.

• Gdansk University of Technology, Narutowicza 11/12, 80-233 Gdansk, Poland

Bibliografia

• 1. Bažant Z.P.: Concrete fracture modelling: testing and practice. Engineering Fracture Mechanics 2002; 69:165-206.
• 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.
• 3. Beda P.B.: Dynamical Systems Approach of Internal Length in Fractional Calculus. Engineering Transactions 2017, 65:209-215.
• 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.
• 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.
• 6. Brinkgreve R.B.J.: Geomaterial models and numerical analysis of softening. PhD Thesis, TU Delft 1994.
• 7. Çağlar Y., Şener S.: Size effect tests of different notch depth specimens with support rotation measurements. Engineering Fracture Mechanics 2016; 157:43–55.
• 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.
• 9. Giry C., Dufour F., Mazars J.: Stress-based nonlocal damage model. International Journal of Solids and Structures 2011; 48:3431–3443.
• 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.
• 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.
• 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.
• 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.
• 14 . Hordijk D.A.: Local approach to fatigue of concrete. PhD Thesis, TU Delft 1991.
• 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.
• 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.
• 17. Lazopoulos K.A., Lazopoulos A.K.: Fractional vector calculus and fluid mechanics. Journal of the Mechanical Behavior of Materials 2017; 26:43-54.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• 24. Sumelka W.: Non-local Kirchhoff–Love plates in terms of fractional calculus. Archives of Civil and Mechanical Engineering 2015; 15:231-242.
• 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.
• 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.
• 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.
• 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.
• 29. Winnicki A., Pearce C.J., Bićanić N.: Viscoplastic Hoffman consistency model for concrete. Computers & Structures 2001; 79:7-19.
• 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.

Identyfikatory

DOI

10.2478/pomr-2019-0031