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An extended cohesive damage model for simulating arbitrary damage propagation in engineering materials. (English) Zbl 1439.74334
Summary: This paper introduces the extended cohesive damage model (ECDM) for simulating arbitrary damage propagation in engineering materials. By embedding the micromechanical cohesive damage model (CDM) into the eXtended Finite Element Method (XFEM) and eliminating the enriched degree of freedoms (DoFs), the ECDM defines the cohesive crack path at a low scale in the condensed equilibrium equations and enables the local enrichments of approximation spaces without enriched DoFs. In this developed ECDM, a new equivalent damage scalar as a function of strain field is introduced to avoid the appearance of enriched DoFs, and to substitute the conventional characterization in the approximation of displacement jump. The embedment of CDM is no longer required by the ECDM, which allows discontinuities to exist within a finite element rather than the element boundaries. This feature enables the ECDM to simulate the reality of arbitrary cracks. Initial applications of the ECDM in simulation of arbitrary cracks shows that the developed ECDM works very well when compared to experiment work and XFEM analysis.

MSC:
74R05 Brittle damage
74-10 Mathematical modeling or simulation for problems pertaining to mechanics of deformable solids
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[1] Zienkiewicz, O. C.; Zhu, J. Z., A simple error estimator and adaptive procedure for practical engineering analysis, Internat. J. Numer. Methods Engrg., 24, 2, 337-357 (1987)
[2] Murthy, K. S.R. K.; Mukhopadhyay, M., Adaptive finite element analysis of mixed - mode crack problems with automatic mesh generator, Internat. J. Numer. Methods Engrg., 49, 8, 1087-1100 (2000)
[3] Khoei, A. R.; Azadi, H.; Moslemi, H., Modeling of crack propagation via an automatic adaptive mesh refinement based on modified superconvergent patch recovery technique, Eng. Fract. Mech., 75, 10, 2921-2945 (2008)
[4] Melenk, J. M.; Babuška, I., The partition of unity finite element method: basic theory and applications, Comput. Methods Appl. Mech. Engrg., 139, 1, 289-314 (1996)
[5] Babuška, I.; Melenk, J. M., The partition of unity method, Internat. J. Numer. Methods Engrg., 40, 727-758 (1997)
[6] Belytschko, T.; Black, T., Elastic crack growth in finite elements with minimal remeshing, Internat. J. Numer. Methods Engrg., 45, 601-620 (1999)
[7] Duarte, C. A.; Hamzeh, O. N.; Liszka, T. J.; Tworzydlo, W. W., A generalized finite element method for the simulation of three-dimensional dynamic crack propagation, Comput. Methods Appl. Mech. Engrg., 190, 15, 2227-2262 (2001)
[8] Oden, J. T.; Duarte, C. A.M.; Zienkiewicz, O. C., A new cloud-based hp finite element method, Comput. Methods Appl. Mech. Engrg., 153, 1, 117-126 (1998)
[9] Glowinski, R.; He, J.; Rappaz, J.; Wagner, J., Approximation of multi-scale elliptic problems using patches of finite elements, C. R. Math., 337, 10, 679-684 (2003)
[10] Strouboulis, T.; Babuška, I.; Hidajat, R., The generalized finite element method for Helmholtz equation: theory, computation, and open problems, Comput. Methods Appl. Mech. Engrg., 195, 37, 4711-4731 (2006)
[11] Mos, N.; Dolbow, J.; Belytschko, T., A finite element method for crack growth without remeshing, Internat. J. Numer. Methods Engrg., 46, 1, 131-150 (1999)
[12] Belytschko, T.; Gracie, R.; Ventura, G., A review of extended/generalized finite element methods for material modeling, Modelling Simul. Mater. Sci. Eng., 17, 4, Article 043001 pp. (2009)
[13] Moës, N.; Belytschko, T., Extended finite element method for cohesive crack growth, Eng. Fract. Mech., 69, 7, 813-833 (2002)
[14] Mergheim, J.; Kuhl, E.; Steinmann, P., A finite element method for the computational modelling of cohesive cracks, Internat. J. Numer. Methods Engrg., 63, 2, 276-289 (2005)
[15] Benvenuti, E., A regularized XFEM framework for embedded cohesive interfaces, Comput. Methods Appl. Mech. Engrg., 197, 49, 4367-4378 (2008)
[16] Unger, J. F.; Eckardt, S.; Könke, C., Modelling of cohesive crack growth in concrete structures with the extended finite element method, Comput. Methods Appl. Mech. Engrg., 196, 41, 4087-4100 (2007)
[17] Comi, C.; Mariani, S.; Perego, U., An extended FE strategy for transition from continuum damage to mode I cohesive crack propagation, Int. J. Numer. Anal. Methods Geomech., 31, 2, 213-238 (2007)
[18] Simone, A.; Wells, G. N.; Sluys, L. J., From continuous to discontinuous failure in a gradient-enhanced continuum damage model, Comput. Methods Appl. Mech. Engrg., 192, 41, 4581-4607 (2003)
[19] Wang, Y.; Waisman, H., From diffuse damage to sharp cohesive cracks: A coupled XFEM framework for failure analysis of quasi-brittle materials, Comput. Methods Appl. Mech. Engrg., 299, 57-89 (2016)
[20] Hansbo, A.; Hansbo, P., A finite element method for the simulation of strong and weak discontinuities in solid mechanics, Comput. Methods Appl. Mech. Engrg., 193, 33, 3523-3540 (2004)
[21] Areias, P.; Belytschko, T., A comment on the article A finite element method for simulation of strong and weak discontinuities in solid mechanics by A. Hansbo and P. Hansbo [Comput. Methods Appl. Mech. Engrg. 193 (2004) 3523-3540], Comput. Methods Appl. Mech. Engrg., 195, 9, 1275-1276 (2006)
[22] Oliver, J.; Huespe, A. E.; Samaniego, E., A study on finite elements for capturing strong discontinuities, Internat. J. Numer. Methods Engrg., 56, 14, 2135-2161 (2003)
[23] Oliver, J.; Huespe, A. E.; Sanchez, P. J., A comparative study on finite elements for capturing strong discontinuities: E-FEM vs X-FEM, Comput. Methods Appl. Mech. Engrg., 195, 37, 4732-4752 (2006)
[24] Fang, X. J.; Yang, Q. D.; Cox, B. N.; Zhou, Z. Q., An augmented cohesive zone element for arbitrary crack coalescence and bifurcation in heterogeneous materials, Internat. J. Numer. Methods Engrg., 88, 9, 841-861 (2011)
[25] Liu, W.; Yang, Q. D.; Mohammadizadeh, S.; Su, X. Y.; Ling, D. S., An accurate and efficient augmented finite element method for arbitrary crack interactions, J. Appl. Mech., 80, 4, Article 041033 pp. (2013)
[26] Liu, W.; Yang, Q. D.; Mohammadizadeh, S.; Su, X. Y., An efficient augmented finite element method for arbitrary cracking and crack interaction in solids, Internat. J. Numer. Methods Engrg., 99, 6, 438-468 (2014)
[27] Elices, M.; Guinea, G. V.; Gomez, J.; Planas, J., The cohesive zone model: advantages, limitations and challenges, Eng. Fract. Mech., 69, 2, 137-163 (2002)
[28] Park, K.; Paulino, G. H., Cohesive zone models: a critical review of traction-separation relationships across fracture surfaces, Appl. Mech. Rev., 64, 6, Article 060802 pp. (2011)
[29] J, Chen, An extended cohesive damage model with a length scale in fracture analysis of adhesively bonded joints, Eng. Fract. Mech., 119, 202-213 (2014)
[30] Rabczuk, T.; Zi, G.; Gerstenberger, A.; Wall, W. A., A new crack tip element for the phantom - node method with arbitrary cohesive cracks, Internat. J. Numer. Methods Engrg., 75, 5, 577-599 (2008)
[31] Song, J. H.; Areias, P.; Belytschko, T., A method for dynamic crack and shear band propagation with phantom nodes, Internat. J. Numer. Methods Engrg., 67, 6, 868-893 (2006)
[32] Giner, E.; Sukumar, N.; Tarancon, J. E.; Fuenmayor, F. J., An Abaqus implementation of the extended finite element method, Eng. Fract. Mech., 76, 3, 347-368 (2009)
[33] Fries, T. P.; Baydoun, M., Crack propagation with the extended finite element method and a hybrid explicit-implicit crack description, Internat. J. Numer. Methods Engrg., 89, 12, 1527-1558 (2012)
[34] Bertsekas, D. P., Nonlinear Programming (2003), Athena Scientific: Athena Scientific Belmont, MA
[35] Wang, G.; Wei, Y.; Qiao, S.; Lin, P.; Chen, Y., Generalized Inverses: Theory and Computations, 37-75 (2004), Beijing Science Press
[36] K, Awinda; Chen, J.; Barnett, S.; Fox, D., Modelling behaviour of ultra high performance fibre reinforced concrete, Adv. Appl. Ceram., 113, 8, 502-508 (2014)
[37] Nooru-Mohamed, Mohamed Buhary, Mixed-Mode Fracture of Concrete: An Experimental Approach (1992), Delft University of Technology: Delft University of Technology TU Delft
[38] Wells, G. N.; Sluys, L. J., A new method for modelling cohesive cracks using finite elements, Internat. J. Numer. Methods Engrg., 50, 12, 2667-2682 (2001)
[39] Wu, J. Y.; Li, F. B.; Xu, S. L., Extended embedded finite elements with continuous displacement jumps for the modeling of localized failure in solids, Comput. Methods Appl. Mech. Engrg., 285, 346-378 (2015)
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