Crack propagation modelling using XFEM, building materials applications
Article Sidebar
Published
Sep 21, 2024
Main Article Content
Abstract
The paper shows some results of a computational modelling focused on the occurrence of damage in heterogeneous materials, mainly with brittle matrix, especially on the issue of modelling crack formation and propagation. The attention is paid to the application of the finite element method to the buildings materials in order to find critical parameters determining behaviour of materials at damage process with reference to the history of several approaches to solving this problem. The applications of damage mechanics and possible approaches to model the origin of a crack propagation through modifications in FEM systems are presented and some practical applications are tested. Main effort is devoted to cement fibre composites and the search for new methods for their more accurate modelling, especially ahead of the crack tip. Modified XFEM method and its suggested modifications as to proper modelling of the real stress distribution close to crack tip are shown.
Article Details
How to Cite
Kozák, V.
(2024).
Crack propagation modelling using XFEM, building materials applications.
Proceedings Of The Conference Algoritmy, , 235 -244.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/2182/1045
Section
Articles
References
[1] A. Afshar, A. Daneshyar, S. Mohammadi, XFEM analysis of fiber bridging in mixed-mode crack propagation in composites Compos. Struct., 125 (2015), pp. 314–327.
[2] P. M. A. Areias, T. Belytschko, Two-scale shear band evolution by local partition of unity Int. J. Numer. Methods Eng., 66 (2006), pp. 878–910.
[3] I. Babuška, J. M. Melenk, The partition of unity method Int. J. Numer. Methods Eng., 40 (1997), pp. 727–758.
[4] I. Babuška and J. T. Oden, Verification and validation in computational engineering and science: basic concepts, Comput. Methods Appl. Mech. Eng., 193 (2004), pp. 4057–4066.
[5] Q. R. Barani, A. R. Khoei, M. Mofid, Modelling of cohesive crack growth in partially saturated porous media: A study on the permeability of cohesive fracture Int. J. Fract., 167 (2011), pp. 15–31.
[6] G. I. Barenblatt, The mathematical theory of equilibrium of cracks in brittle fracture, Adv. Appl. Mech., 7 (1962), pp. 55–129.
[7] Z. P. Bazant, Y.-N. Li, Cohesive crack model with rate-dependent opening and viscoelasticity: I. Mathematical model and scaling Int. J. Fract., 86 (1997), pp. 247–265.
[8] T. Belytschko, R. Gracie and G. Ventura, A review of extended / generalized finite element methods for material modelling,. Modeling Simul. Mater. Sci. Eng., 17 (2009), pp. 043001 / 1–24.
[9] L. Bouhala, A. Makradi, S. Belouettar, H. Kiefer-Kamal, 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.
[10] T. Q. Bui, H. T. Tran, X. Hu and Ch.-T. Wu, Simulation of dynamic brittle and quasi-brittle fracture: a revisited local damage approach, Int. J. Fract., 236 (2022), pp. 59–85.
[11] R. Brighenti, D. Scorza, Numerical modelling of the fracture behaviour of brittle materials reinforced with unidirectional or randomly distributed fibres Mechanics of Materials, 52 (2012), pp. 12–27.
[12] M. Cervera, G. B. Barbat, M. Chiumenti, J. Y. Wu, A comparative review of XFEM, mixed FEM and phase field models for quasi-brittle cracking, Arch. Comput. Methods Eng., 29 (2022), pp. 1009–1083.
[13] J. de Vree, W. Brekelmans and M. van Gils, Comparison of nonlocal approaches in continuum damage mechanics, Comput. Struct., 55 (1995), pp. 581–588.
[14] A. Evgrafov and J. C. Bellido, From non-local Eringen’s model to fractional elasticity, Math. Mech. Solids, 24 (2019), pp. 1935–1953.
[15] S. H. Ebrahimi, Singularity analysis of cracks in hybrid CNT reinforced carbon fiber composites using finite element asymptotic expansion and XFEM Int. J. Solids Struct., 214-215 (2021), pp. 1–17.
[16] A. C. Eringen, Theory of Nonlocal Elasticity and Some Applications, Princeton University, technical report 62, 1984.
[17] A. C. Eringen, Nonlocal Continuum Field Theories, Springer, Berlin, 2002.
[18] F. Erdogan, G. C. Sih, On the crack extension in plates under plane loading and transverse shear J. Basic Eng., 85 (1963), pp. 519–527..
[19] T.-P. Fries and T. Belytschko, The intrinsic XFEM: a method for arbitrary discontinuities without additional unknowns, Int. J. Numer. Methods Eng., 68 (2006), pp. 1358–1385.
[20] A. A. Griffith, The phenomena of rupture and flow in solids, Philos. Trans. R. Soc. A, 221 (1920), pp. 163–198.
[21] P. Havlásek, P. Grassl and M. Jirásek, Analysis of size effect on strength of quasi-brittle materials using integral-type nonlocal models, Eng. Fract. Mech., 157 (2016), pp. 72–85.
[22] C. Imbert and A. Mellet, Existence of solutions for a higher order non-local equation appearing in crack dynamics, Nonlinearity, 24 (2011), pp. 3487–2514.
[23] M. Jirásek, Non-local damage mechanics with application to concrete, Revue française de génie civil, 8 (2004), pp. 683–707.
[24] J. W. Ju, Isotropic and anisotropic damage variables in continuum damage, J. Eng. Mech., 116 (1990), pp. 2764–2770.
[25] I. Kachanov, Effective elastic properties of cracked solids: critical review of some basic concepts, Appl. Mech. Rev., 45 (1992), pp. 304–335.
[26] A. R. Khoei, Extended Finite Element Method: Theory and Applications, J. Wiley & Sons, Hoboken, 2015.
[27] O. Kolednik, R. Schöngrundner, F. D. Fischer, A new view on J-integrals in elastic–plastic materials, Int. J. Fract., 187 (2014), pp. 77–107.
[28] V. Kozák and Z. Chlup, Modelling of fibre-matrix interface of brittle matrix long fibre composite by application of cohesive zone method, Key Eng. Mater., 465 (2011), pp. 231–234.
[29] V. Kozák, Z. Chlup, P. Padělek, I. Dlouhý, Prediction of traction separation law of ceramics using iterative finite element method Solid State Phenom., 258 (2017), pp. 186–189.
[30] X. Li, W. Gao and W. Liu, A mesh objective continuum damage model for quasi-brittle crack modelling and finite element implementation, Int. J. Damage Mech., 28 (2019), pp. 1299–1322.
[31] J. Mazars and G. Pijaudier-Cabot, Continuum damage theory – application to concrete, J. Eng. Mech., 115 (1989), pp. 345–365.
[32] J. Mazars, F. Hamon and S. Grange, A new 3D damage model for concrete under monotonic, cyclic and dynamic loadings, Mater. Struct., 48 (2015), pp. 3779–3793.
[33] N. Moës and T. Belytschko, Extended finite element method for cohesive crack growth, Eng. Fract. Mech., 69 (2002), pp. 813–833.
[34] I. Němec, J. Vala, H. Štekbauer, M. Jedlička and D. Burkart, New methods in collision of bodies analysis, 21st Programs and Algorithms of Numerical Mathematics (PANM) in Jablonec n. N. (2022), Institute of Mathematics CAS, Prague, 2023, pp. 133–148.
[35] N. Ottosen, A failure criterion for concrete, J. Eng. Mech., 103 (1977), pp. 527–535.
[36] M. Ortis, Y. Leroy, A. Needleman, A finite element method for localized failure analysis Comput. Methods Appl. Mech. Eng., 61 (1987), pp. 189–214.
[37] V. B. Panday, I. V. Singh, B. K. Mishra, A new creep-fatigue interaction damage model and CDM-XFEM framework for creep-fatigue crack growth simulations Theor. Appl. Fract. Mech., 124 (2023), pp. 1–13.
[38] Ch. Papenfuß, Continuum Thermodynamics and Constitutive Theory, Springer, Berlin, 2020.
[39] K. Park, G. H. Paulino and J. R. Roesler, Cohesive fracture model for functionally graded fiber reinforced concrete, Cem. Concr. Res., 40 (2010), pp. 956–965.
[40] M. G. Pike and C. Oskay, XFEM modeling of short microfiber reinforced composites with cohesive interfaces, Finite Elem. Anal. Des., 106 (2005), pp. 16–31.
[41] J. R. Rice, A path independent integral and the approximate analysis of strain concentration by notches and cracks, J. Appl. Mech., 35 (1968), pp. 379–386.
[42] J. Scheel, A. Schlosser, A. Ricoeur, The J-integral for mixed-mode loaded cracks with cohesive zones, Int. J. Fract., 227 (2021), pp. 79–94.
[43] G. C. Sih, Strain-energy density factor applied to mixed mode crack problems, Int. J. Fract., 10 (1974), pp. 304–321.
[44] S. Taira, R. Ohtani and T. Kitamura, Application of J-integral to high-temperature crack propagation, Part I – Creep crack propagation, J. Eng. Mater. Technol., 101 (1979), pp. 154–161.
[45] C. Xiao, L. Wen, R. Tian, Arbitrary 3D crack propagation with improved XFEM: accurate and efficient crack geometries Comput. Methods Appl. Mech. Eng., 377 (2021), pp. 1–32.
[46] J. Vala, Numerical approaches to the modelling of quasi-brittle crack propagation, Arch. Math., 56 (2023), pp. 295–303.
[47] J. Vala, L. Hobst and V. Kozák, Detection of metal fibres in cementitious composites based on signal and image processing approaches, WSEAS Trans. Appl. Theor. Mech., 10 (2015), pp. 39–46.
[48] J. Vala and V. Kozák, Computational analysis of quasi-brittle fracture in fibre reinforced cementitious composites, Theor. Appl. Fract. Mech., 107 (2020), pp. 102486 / 1–8.
[49] J. Vala and V. Kozák, Nonlocal damage modelling of quasi-brittle composites, Appl. Math., 66 (2021), pp. 815–836.
[50] J. Vala, Computational smeared damage in macroscopic analysis of quasi-brittle materials and structures, 22nd Algoritmy in Podbanské (2024), STU Bratislava, to appear.
[51] J. Vilppo, R. Kouhia, J. Hartikainen, K. Kolari, A. Fedoroff and K. Calonius, Anisotropic damage model for concrete and other quasi-brittle materials, Int. J. Solids Struct., 225 (2021), pp. 111048 / 1–13.
[52] Ch. D. Vuong, X. Hu and T. Q. Bui, A dynamic description of the smoothing gradient damage model for quasi-brittle failure, Finite Elem. Anal. Des., 230 (2024), pp. 104084 / 1–25.
[53] C. Ye, J. Shi, G. J. Cheng, An extended finite element method (XFEM) study on the effect of reinforcing particles on the crack propagation behaviour in a metal-matrix composite Int. J. Fatigue, 44 (2012), pp. 151–156.
[54] T. T. Yu, Z. W. Gong, Numerical simulation of temperature field in heterogeneous material with the XFEM Archives of Civil and Mechanical Engineering, 13 (2013), pp. 199–208.
[2] P. M. A. Areias, T. Belytschko, Two-scale shear band evolution by local partition of unity Int. J. Numer. Methods Eng., 66 (2006), pp. 878–910.
[3] I. Babuška, J. M. Melenk, The partition of unity method Int. J. Numer. Methods Eng., 40 (1997), pp. 727–758.
[4] I. Babuška and J. T. Oden, Verification and validation in computational engineering and science: basic concepts, Comput. Methods Appl. Mech. Eng., 193 (2004), pp. 4057–4066.
[5] Q. R. Barani, A. R. Khoei, M. Mofid, Modelling of cohesive crack growth in partially saturated porous media: A study on the permeability of cohesive fracture Int. J. Fract., 167 (2011), pp. 15–31.
[6] G. I. Barenblatt, The mathematical theory of equilibrium of cracks in brittle fracture, Adv. Appl. Mech., 7 (1962), pp. 55–129.
[7] Z. P. Bazant, Y.-N. Li, Cohesive crack model with rate-dependent opening and viscoelasticity: I. Mathematical model and scaling Int. J. Fract., 86 (1997), pp. 247–265.
[8] T. Belytschko, R. Gracie and G. Ventura, A review of extended / generalized finite element methods for material modelling,. Modeling Simul. Mater. Sci. Eng., 17 (2009), pp. 043001 / 1–24.
[9] L. Bouhala, A. Makradi, S. Belouettar, H. Kiefer-Kamal, 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.
[10] T. Q. Bui, H. T. Tran, X. Hu and Ch.-T. Wu, Simulation of dynamic brittle and quasi-brittle fracture: a revisited local damage approach, Int. J. Fract., 236 (2022), pp. 59–85.
[11] R. Brighenti, D. Scorza, Numerical modelling of the fracture behaviour of brittle materials reinforced with unidirectional or randomly distributed fibres Mechanics of Materials, 52 (2012), pp. 12–27.
[12] M. Cervera, G. B. Barbat, M. Chiumenti, J. Y. Wu, A comparative review of XFEM, mixed FEM and phase field models for quasi-brittle cracking, Arch. Comput. Methods Eng., 29 (2022), pp. 1009–1083.
[13] J. de Vree, W. Brekelmans and M. van Gils, Comparison of nonlocal approaches in continuum damage mechanics, Comput. Struct., 55 (1995), pp. 581–588.
[14] A. Evgrafov and J. C. Bellido, From non-local Eringen’s model to fractional elasticity, Math. Mech. Solids, 24 (2019), pp. 1935–1953.
[15] S. H. Ebrahimi, Singularity analysis of cracks in hybrid CNT reinforced carbon fiber composites using finite element asymptotic expansion and XFEM Int. J. Solids Struct., 214-215 (2021), pp. 1–17.
[16] A. C. Eringen, Theory of Nonlocal Elasticity and Some Applications, Princeton University, technical report 62, 1984.
[17] A. C. Eringen, Nonlocal Continuum Field Theories, Springer, Berlin, 2002.
[18] F. Erdogan, G. C. Sih, On the crack extension in plates under plane loading and transverse shear J. Basic Eng., 85 (1963), pp. 519–527..
[19] T.-P. Fries and T. Belytschko, The intrinsic XFEM: a method for arbitrary discontinuities without additional unknowns, Int. J. Numer. Methods Eng., 68 (2006), pp. 1358–1385.
[20] A. A. Griffith, The phenomena of rupture and flow in solids, Philos. Trans. R. Soc. A, 221 (1920), pp. 163–198.
[21] P. Havlásek, P. Grassl and M. Jirásek, Analysis of size effect on strength of quasi-brittle materials using integral-type nonlocal models, Eng. Fract. Mech., 157 (2016), pp. 72–85.
[22] C. Imbert and A. Mellet, Existence of solutions for a higher order non-local equation appearing in crack dynamics, Nonlinearity, 24 (2011), pp. 3487–2514.
[23] M. Jirásek, Non-local damage mechanics with application to concrete, Revue française de génie civil, 8 (2004), pp. 683–707.
[24] J. W. Ju, Isotropic and anisotropic damage variables in continuum damage, J. Eng. Mech., 116 (1990), pp. 2764–2770.
[25] I. Kachanov, Effective elastic properties of cracked solids: critical review of some basic concepts, Appl. Mech. Rev., 45 (1992), pp. 304–335.
[26] A. R. Khoei, Extended Finite Element Method: Theory and Applications, J. Wiley & Sons, Hoboken, 2015.
[27] O. Kolednik, R. Schöngrundner, F. D. Fischer, A new view on J-integrals in elastic–plastic materials, Int. J. Fract., 187 (2014), pp. 77–107.
[28] V. Kozák and Z. Chlup, Modelling of fibre-matrix interface of brittle matrix long fibre composite by application of cohesive zone method, Key Eng. Mater., 465 (2011), pp. 231–234.
[29] V. Kozák, Z. Chlup, P. Padělek, I. Dlouhý, Prediction of traction separation law of ceramics using iterative finite element method Solid State Phenom., 258 (2017), pp. 186–189.
[30] X. Li, W. Gao and W. Liu, A mesh objective continuum damage model for quasi-brittle crack modelling and finite element implementation, Int. J. Damage Mech., 28 (2019), pp. 1299–1322.
[31] J. Mazars and G. Pijaudier-Cabot, Continuum damage theory – application to concrete, J. Eng. Mech., 115 (1989), pp. 345–365.
[32] J. Mazars, F. Hamon and S. Grange, A new 3D damage model for concrete under monotonic, cyclic and dynamic loadings, Mater. Struct., 48 (2015), pp. 3779–3793.
[33] N. Moës and T. Belytschko, Extended finite element method for cohesive crack growth, Eng. Fract. Mech., 69 (2002), pp. 813–833.
[34] I. Němec, J. Vala, H. Štekbauer, M. Jedlička and D. Burkart, New methods in collision of bodies analysis, 21st Programs and Algorithms of Numerical Mathematics (PANM) in Jablonec n. N. (2022), Institute of Mathematics CAS, Prague, 2023, pp. 133–148.
[35] N. Ottosen, A failure criterion for concrete, J. Eng. Mech., 103 (1977), pp. 527–535.
[36] M. Ortis, Y. Leroy, A. Needleman, A finite element method for localized failure analysis Comput. Methods Appl. Mech. Eng., 61 (1987), pp. 189–214.
[37] V. B. Panday, I. V. Singh, B. K. Mishra, A new creep-fatigue interaction damage model and CDM-XFEM framework for creep-fatigue crack growth simulations Theor. Appl. Fract. Mech., 124 (2023), pp. 1–13.
[38] Ch. Papenfuß, Continuum Thermodynamics and Constitutive Theory, Springer, Berlin, 2020.
[39] K. Park, G. H. Paulino and J. R. Roesler, Cohesive fracture model for functionally graded fiber reinforced concrete, Cem. Concr. Res., 40 (2010), pp. 956–965.
[40] M. G. Pike and C. Oskay, XFEM modeling of short microfiber reinforced composites with cohesive interfaces, Finite Elem. Anal. Des., 106 (2005), pp. 16–31.
[41] J. R. Rice, A path independent integral and the approximate analysis of strain concentration by notches and cracks, J. Appl. Mech., 35 (1968), pp. 379–386.
[42] J. Scheel, A. Schlosser, A. Ricoeur, The J-integral for mixed-mode loaded cracks with cohesive zones, Int. J. Fract., 227 (2021), pp. 79–94.
[43] G. C. Sih, Strain-energy density factor applied to mixed mode crack problems, Int. J. Fract., 10 (1974), pp. 304–321.
[44] S. Taira, R. Ohtani and T. Kitamura, Application of J-integral to high-temperature crack propagation, Part I – Creep crack propagation, J. Eng. Mater. Technol., 101 (1979), pp. 154–161.
[45] C. Xiao, L. Wen, R. Tian, Arbitrary 3D crack propagation with improved XFEM: accurate and efficient crack geometries Comput. Methods Appl. Mech. Eng., 377 (2021), pp. 1–32.
[46] J. Vala, Numerical approaches to the modelling of quasi-brittle crack propagation, Arch. Math., 56 (2023), pp. 295–303.
[47] J. Vala, L. Hobst and V. Kozák, Detection of metal fibres in cementitious composites based on signal and image processing approaches, WSEAS Trans. Appl. Theor. Mech., 10 (2015), pp. 39–46.
[48] J. Vala and V. Kozák, Computational analysis of quasi-brittle fracture in fibre reinforced cementitious composites, Theor. Appl. Fract. Mech., 107 (2020), pp. 102486 / 1–8.
[49] J. Vala and V. Kozák, Nonlocal damage modelling of quasi-brittle composites, Appl. Math., 66 (2021), pp. 815–836.
[50] J. Vala, Computational smeared damage in macroscopic analysis of quasi-brittle materials and structures, 22nd Algoritmy in Podbanské (2024), STU Bratislava, to appear.
[51] J. Vilppo, R. Kouhia, J. Hartikainen, K. Kolari, A. Fedoroff and K. Calonius, Anisotropic damage model for concrete and other quasi-brittle materials, Int. J. Solids Struct., 225 (2021), pp. 111048 / 1–13.
[52] Ch. D. Vuong, X. Hu and T. Q. Bui, A dynamic description of the smoothing gradient damage model for quasi-brittle failure, Finite Elem. Anal. Des., 230 (2024), pp. 104084 / 1–25.
[53] C. Ye, J. Shi, G. J. Cheng, An extended finite element method (XFEM) study on the effect of reinforcing particles on the crack propagation behaviour in a metal-matrix composite Int. J. Fatigue, 44 (2012), pp. 151–156.
[54] T. T. Yu, Z. W. Gong, Numerical simulation of temperature field in heterogeneous material with the XFEM Archives of Civil and Mechanical Engineering, 13 (2013), pp. 199–208.