On Some Peculiarities of Numerical Modelling of Cement-Based Composites

Abstract:

Computational prediction of damage in cement-based composites, as steel fibre reinforced ones, under mechanical, thermal, etc. loads, manifested as creation of micro-fractured zones, followed by potential initiation and evolution of macroscopic cracks, is a rather delicatematter, due to the necessity of bridging between micro- and macro-scales. This short paper presents a relatively simple approach, using certain extension of the finite element technique, open to possible generalizations. Such model admits proper verification of its existence andconvergence results, from the physical and mathematical formulation up to software implementation of relevant algorithms. Its practical applicability is documented on computational examples.

• Periodical: Solid State Phenomena (Volume 338)
• Pages: 135-140
• DOI: https://doi.org/10.4028/p-4v4w0x
• Online since: October 2022
• Authors: Jiří Vala*, Vladislav Kozák, Michal Jedlička
• Keywords: Cement-Based Composites, Extended Finite Element Method (XFEM), Quasi-Brittle Fracture

References

[1] J. M. Melenk and I. Babuška: Comput. Meth. Appl. Mech. Eng. 39 (1996), 289–314.

[2] T. Strouboulis, K. Copps and I. Babuška: Comput. Meth. Appl. Mech. Eng. 190 (2001), 4081–4193.

[3] T. Belytchko and T. Black: Int. J. Numer. Meth. Engrg. 45 (1999), 601–620.

[4] N. Moës, J. Dolbow and T. Belytschko: Int. J. Numer. Meth. Engrg. 46 (1999), 131–150.

[5] N. Sukumar, N. Moës, B. Moran and T. Belytschko: Int. J. Numer. Meth. Engrg. 48 (2000), 1549–1570.

[6] M. Stolarska, D. D. Chopp, N. Moës and T. Belyschko: Int. J. Numer. Meth. Engrg. 51 (2001), 943–960.

[7] G. J. Wagner, N. Moës, W. K. Liu and T. Belytschko: Int. J. Numer. Meth. Engrg. 51 (2001), 293–313.

[8] T. Elguedj, A. Gravouil and A. Combescure: Comput. Meth. Appl. Mech. Eng. 195 (2006), 501–515.

[9] M. G. Pike and C. Oskay: Finite Elem. Anal. Des. 106 (2005), 16–31.

[10] T.-P. Fries and T. Belytchko: Int. J. Numer. Meth. Engrg. 68 (2006), 1358–1385.

[11] E. Gordeliy and A. Peirce: Comput. Meth. Appl. Mech. Engrg. 283 (2015) 474–502.

[12] J. P. Wolf and Ch. Song: Comput. Meth. Appl. Mech. Engrg. 190 (2001), 5551–5568.

[13] J. P. Doherty and A. J. Deeks: Comput. Geotech. 32 (2005), 436–444.

[14] Y. D. Ha and F. Bobaru: Eng. Fract. Mech. 78 (2011), 1159–1168.

[15] Z. P. Bažant and M. Jirásek: J. Eng. Mech. 128 (2002), 1119–1149.

[16] P. Havlásek, P. Grassl and M. Jirásek: Eng. Fract. Mech. 157 (2016), 72–85.

[17] Z. Gao, L. Zhang and W. Yu: Eng. Fract. Mech. 189 (2018), 481–500.

[18] A. Evgrafov and J. C. Belido: Math. Mech. Solids 24 (2019), 1935–(1953).

[19] H. Li, J. Li and H. Yuan: Theor. Appl. Fract. Mech. 97 (2018), 236–249.

[20] Y. Sun, M. G. Edwards, B. Chen and Ch. Li: Eng. Fract. Mech. 257 (2021), 108036 / 1–33.

[21] J. Vala and V. Kozák: Theor. Appl. Fract. Mech. 127 (2020), 102486 / 1–8.

[22] J. Vala and V. Kozák: Appl. Math. 66 (2021), 815–836.

[23] C. Giry, F. Dufour and J. Mazars: Int. J. Solids and Struct. 48 (2011), 3431–3443.