# Modelling of micro- and macro-fracture in cementitious composites

## Main Article Content

## Abstract

Frequent utilization of composites with a cementitious matrix, reinforced by fibres of different origin, as constructive parts in civil engineering motivates the reliable computational prediction of their mechanical properties, namely of the risk of initiation and development of micro- and macro-fracture. This paper demonstrates the possibility of deterministic prediction of such physical process, applying the dynamical approach with the modified Kelvin viscoelastic model and cohesive contacts together with the method of discretization in time, using 3 types of Rothe sequences, and the extended finite element method (XFEM).

## Article Details

How to Cite

Vala, J.
(2020).
Modelling of micro- and macro-fracture in cementitious composites.

*Proceedings Of The Conference Algoritmy,*, 181 - 190. Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/1594/843
Section

Articles

## References

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[13] V. Kozák and Z. Chlup, Modelling of fibre-matrix interface of brittle matrix long fibre composite by application of cohesive zone method, Key Engineering Materials 465 (2011), pp. 231–234.

[14] V. Kozák, Z. Chlup, P. Padělek and I. Dlouhý, Prediction of the traction separation law of ceramics using iterative finite element modelling, Solid State Phenomena 258 (2017), pp. 186–189.

[15] X. Li and J. Chen, An extensive cohesive damage model for simulation arbitrary damage propagation in engineering materials, Computer Methods in Applied Mechanics and Engineering 315 (2017), pp. 744–759.

[16] X. Li, W. Gao and W. Liu, A mesh objective continuum damage model for quasi-brittle crack modelling and finite element implementation, International Journal of Damage Mechanics 28 (2019), pp. 1299–1322.

[17] Z. Majdišová and V. Skala, Radial basis function approximations: comparison and applications, Applied Mathematical Modelling 51 (2017), pp. 728–743.

[18] M. Moradi, A. R. Begherieh and M. R. Esfahani, Constitutive modeling of steel fiberreinforced concrete, International Journal of Damage Mechanics 29 (2020), pp. 388–412.

[19] M. G. Pike and C. Oskay, XFEM modeling of short microfiber reinforced composites with cohesive interfaces, Finite Elements in Analysis and Design 106 (2005), pp. 16–31.

[20] Yu. Z. Povstenko, The nonlocal theory of elasticity and its application to the description of defects in solid bodies. Journal of Mathematical Sciences 97 (1999), pp. 3840–3845.

[21] K. Rektorys, The Method of Discretization in Time and Partial Differential Equations, Springer, 1982.

[22] T. Roubı́ček, Nonlinear Partial Differential Equations with Applications. Birkhäuser, 2013.

[23] X. T. Su, Z. J. Yang and G. H. Liu, Monte Carlo simulation of complex cohesive fracture in random heterogeneous quasi-brittle materials: a 3D study, International Journal of Solids and Structures 47 (2010), pp. 2336–2345.

[24] Y. Sumi, Mathematical and Computational Analyses of Cracking Formation, Springer, 2014.

[25] R. F. Swati, L. H. Wen, H. Elahi, A. A. Khan and S. Shad, Extended finite element method (XFEM) analysis of fiber reinforced composites for prediction of micro-crack propagation and delaminations in progressive damage: a review, Microsystem Technologies 25 (2019), pp. 747–763.

[26] J. Vala, Remarks to the computational analysis of semilinear direct and inverse problems of heat transfer, Thermophysics – 24th International Conference in Smolenice (2019), AIP Conference Proceedings 2170, 2019, pp. 020023/1–6.

[27] J. Vala, Structure identification of metal fibre reinforced cementitious composites, Algoritmy – 20th Conference on Scientific Computing in Podbanské (2016), Proceedings, STU Bratislava, 2016, pp. 244–253.

[28] J. Vala, P. Jarošová and V. Kozák, On the computational analysis of quasi-brittle fracture using integral-type nonlocal models, International Journal of Applied Physics 4 (2019), pp. 8–13.

[29] J. Vala and V. Kozák, Computational analysis of quasi-brittle fracture in fibre reinforced cementitious composites, Theoretical and Applied Fracture Mechanics 107 (2020), pp. 102486/1–8.

[2] T. Belytchko and T. Black, Elastic crack growth in finite elements with minimal remeshing, International Journal for Numerical Methods in Engineering 45 (1999), pp. 601–620.

[3] L. Bouhala, A. Makradi, S. Belouettar, H. Kiefer-Kamal and P. Fréres, Modelling of failure in long fibres reinforced composites by X-FEM and cohesive zone model, Composites Part B 55 (2013), pp. 352–361.

[4] A. Cianchi and V. Mazýa, Sobolev inequalities in arbitrary domains Advances in Mathematics 293 (2016), pp. 644–696.

[5] P. Drábek and J. Milota, Methods of Nonlinear Analysis, Birkhäuser, 2013.

[6] J. Eliáš, M. Vořechovský, J. Skoček and Z. P. Bažant, Stochastic discrete meso-scale simulations of concrete fracture: comparison to experimental data, Engineering Fracture Mechanics 135 (2015), pp. 1–16.

[7] A. C. Eringen, Theory of Nonlocal Elasticity and Some Applications, Princeton University Press, 1984, technical report 64.

[8] A. Evgrafov and J. C. Belido, From nonlocal Eringen's model to fractional elasticity, Mathematics and Mechanics of Solids 24 (2019), pp. 1935–1953.

[9] T.-P. Fries and T. Belytschko, The intrinsic XFEM: a method for arbitrary discontinuities without additional unknowns, International Journal for Numerical Methods in Engineering 68 (2006), pp. 1358–1385.

[10] M. Jirásek, Damage and smeared crack models, in: Numerical Modeling of Concrete Cracking (G. Hofstetter and G. Meschke, eds), Springer: CISM International Centre for Mechanical Sciences 532, 2011, 1–49.

[11] M. Kaliske, H. Dal, R. Fleischhauer, C. Jenkel and C. Netzker, Characterization of fracture processes by continuum and discrete modelling, Computational Mechanics 50 (2012), pp. 303–320.

[12] A. R. Khoei, Extended Finite Element Method: Theory and Applications. J. Wiley & Sons, 2015.

[13] V. Kozák and Z. Chlup, Modelling of fibre-matrix interface of brittle matrix long fibre composite by application of cohesive zone method, Key Engineering Materials 465 (2011), pp. 231–234.

[14] V. Kozák, Z. Chlup, P. Padělek and I. Dlouhý, Prediction of the traction separation law of ceramics using iterative finite element modelling, Solid State Phenomena 258 (2017), pp. 186–189.

[15] X. Li and J. Chen, An extensive cohesive damage model for simulation arbitrary damage propagation in engineering materials, Computer Methods in Applied Mechanics and Engineering 315 (2017), pp. 744–759.

[16] X. Li, W. Gao and W. Liu, A mesh objective continuum damage model for quasi-brittle crack modelling and finite element implementation, International Journal of Damage Mechanics 28 (2019), pp. 1299–1322.

[17] Z. Majdišová and V. Skala, Radial basis function approximations: comparison and applications, Applied Mathematical Modelling 51 (2017), pp. 728–743.

[18] M. Moradi, A. R. Begherieh and M. R. Esfahani, Constitutive modeling of steel fiberreinforced concrete, International Journal of Damage Mechanics 29 (2020), pp. 388–412.

[19] M. G. Pike and C. Oskay, XFEM modeling of short microfiber reinforced composites with cohesive interfaces, Finite Elements in Analysis and Design 106 (2005), pp. 16–31.

[20] Yu. Z. Povstenko, The nonlocal theory of elasticity and its application to the description of defects in solid bodies. Journal of Mathematical Sciences 97 (1999), pp. 3840–3845.

[21] K. Rektorys, The Method of Discretization in Time and Partial Differential Equations, Springer, 1982.

[22] T. Roubı́ček, Nonlinear Partial Differential Equations with Applications. Birkhäuser, 2013.

[23] X. T. Su, Z. J. Yang and G. H. Liu, Monte Carlo simulation of complex cohesive fracture in random heterogeneous quasi-brittle materials: a 3D study, International Journal of Solids and Structures 47 (2010), pp. 2336–2345.

[24] Y. Sumi, Mathematical and Computational Analyses of Cracking Formation, Springer, 2014.

[25] R. F. Swati, L. H. Wen, H. Elahi, A. A. Khan and S. Shad, Extended finite element method (XFEM) analysis of fiber reinforced composites for prediction of micro-crack propagation and delaminations in progressive damage: a review, Microsystem Technologies 25 (2019), pp. 747–763.

[26] J. Vala, Remarks to the computational analysis of semilinear direct and inverse problems of heat transfer, Thermophysics – 24th International Conference in Smolenice (2019), AIP Conference Proceedings 2170, 2019, pp. 020023/1–6.

[27] J. Vala, Structure identification of metal fibre reinforced cementitious composites, Algoritmy – 20th Conference on Scientific Computing in Podbanské (2016), Proceedings, STU Bratislava, 2016, pp. 244–253.

[28] J. Vala, P. Jarošová and V. Kozák, On the computational analysis of quasi-brittle fracture using integral-type nonlocal models, International Journal of Applied Physics 4 (2019), pp. 8–13.

[29] J. Vala and V. Kozák, Computational analysis of quasi-brittle fracture in fibre reinforced cementitious composites, Theoretical and Applied Fracture Mechanics 107 (2020), pp. 102486/1–8.