×

Internal springs distribution for quasi-brittle fracture via symmetric boundary element method. (English) Zbl 1156.74368

Summary: The symmetric boundary element formulation is applied to the fracture mechanics problems for quasi brittle materials. The basic aim of the present work is the development and implementation of two discrete cohesive zone models using Symmetric Galerkin multi-zone Boundary Elements Method. The non-linearity at the process zone of the crack will be simulated through a discrete distribution of nodal springs whose generalized (or weighted) stiffnesses are obtainable by the cohesive forces and relative displacements modelling. This goal is reached coherently with the constitutive relation \(\sigma - \Delta u\) that describes the interaction between mechanical and kinematical quantities along the process zone.The cracked body is considered as a solid having a “particular” geometry whose analysis is obtainable through the displacement approach employed by T. Panzeca and M. Salerno [Comput. Mech. 26, No. 5, 437–446 (2000; Zbl 0993.74078); T. Panzeca, F. Cucco and S. Terravecchia [Comput. Methods Appl. Mech. Eng. 191, No. 31, 3347–3367 (2002; Zbl 1101.74370)] by some of the present authors in the ambit of the Symmetric Galerkin Boundary Elements Method (SGBEM). In this approach the crack edge nodes are considered distinct and the analysis is performed by evaluating all the equation system coefficients in closed form [M. Guiggiani, Numerical techniques for boundary element methods, Proc. 7th GAMM-Semin., Kiel/Ger. 1991, Notes Numer. Fluid Mech. 33, 23–34 (1992; Zbl 0743.65013); T. Panzeca, H. Fujita-Yashima and M. .; Salerno, Eur. J. Mech., A, Solids 20, No. 2, 277–298 (2001; Zbl 0983.74079); S. Terravecchia, Closed form in the Symmetric Boundary Element Approach. Eng. Anal. Bound. Elem. Meth. 30, 479–488 (2006)]. Some examples show the goodness of the methodology proposed through a comparison with other formulations [G. I. Barenblatt, The mathematical theory of equilibrium cracks in brittle fracture, in: Advances in Appl. Mechanics, Vol. VII, 55-129 (1962); A. L. Saleh, M. H. Aliabadi, Crack growth analysis in concrete using Boundary Element Method. Eng. Fract. Mech. 51, 533–545 (1995); M. H. Aliabadi, A. L. Saleh, Fracture mechanics analysis of cracking in plain and reinforced concrete using boundary element method. Eng. Fract. Mech. 69, 267–280 (2002)]. In these examples the applied loads and the length of the process zone are a priori given and kept fixed during the analysis in order to check the constitutive behavior along the process zone.

MSC:

74R10 Brittle fracture
74S15 Boundary element methods applied to problems in solid mechanics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Aliabadi, M. H.; Saleh, A. L., Fracture mechanics analysis of cracking in plain and reinforced concrete using boundary element method, Eng. Fract. Mech., 69, 267-280 (2002)
[2] Barenblatt, G. I., Mathematical theory of equilibrium cracks in brittle fracture, Adv. Appl. Mech., 7, 55-129 (1962)
[3] Bazant, Z. P.; Li, Y. N., Cohesive crack with rate-dependent opening and viscoelasticity: I. Mathematical model and scaling, Int. J. Fract., 86, 247-265 (1997)
[4] Bazant, Z. P.; Yu, Q.; Zi, G., Choice of standard fracture test for concrete and its statistical evaluation, Int. J. Fract., 118, 303-337 (2002)
[5] Blandford, G. E.; Ingraffea, A. R.; Liggett, J. A., Two-Dimensional stress intensity factor computation using the Boundary Element Method, Int. J. Numer. Methods Engrg., 17, 387-404 (1981) · Zbl 0463.73082
[6] Carini, A.; Diligenti, M.; Maranesi, P.; Zannella, M., Analytical integrations for two-dimensional elastic analysis by the symmetric Galerkin boundary element methods, Comp. Mech., 23, 308-323 (1999) · Zbl 0949.74075
[7] Carpinteri, A.; Cornetti, P.; Barpi, F.; Valente, S., Cohesive crack model description of ductile to brittle size-scale transition: dimensional analysis vs. Renormalized group theory, Eng. Fract. Mech., 70, 1809-1839 (2003)
[8] Chen, T.; Wang, B.; Cen, Z.; Wu, Z., A symmetric Galerkin multi-zone boundary element method for cohesive crack growth, Eng. Fract. Mech., 63, 591-609 (1999)
[9] Cocchetti, G., 1998. Failure analysis of Quasi-Brittle and poroplastic structures with particular reference to gravity dams. PhD thesis, Polytecnique of Milan; Cocchetti, G., 1998. Failure analysis of Quasi-Brittle and poroplastic structures with particular reference to gravity dams. PhD thesis, Polytecnique of Milan
[10] Elices, M.; Guinea, G. V.; Gòmez, J.; Planas, J., The cohesive zone model: advantages, limitations and challenges, Eng. Fract. Mech., 69, 137-163 (2002)
[11] Frangi, A., Fracture propagation in 3D by the symmetric Galerkin boundary element method, Int. J. Fract., 116, 313-330 (2002)
[12] Gdoutos, E. E., Fracture Mechanics (1993), Kluwer Academic Publishers: Kluwer Academic Publishers Xanthi, Greece · Zbl 0834.73056
[13] Gray, L. J.; Balakrishna, C.; Kane, J. H., Symmetric Galerkin fracture analysis, Eng. Anal. Bound. Elem. Meth., 15, 103-109 (1993)
[14] Gray, L. J., Evaluation of singular and hypersingular Galerkin boundary integrals: direct limits and symbolic computation, (Sladek, J.; Sladek, V., Singular Integrals in Boundary Element Methods (1998), Computational Mechanics Publications: Computational Mechanics Publications Southampton)
[15] Guiggiani, M., 1991. Direct Evaluation of hypersingular integrals in 2D BEM. In: Proceedings of the 7th GAMM Seminar on Numerical Techniques for Boundary Element Methods. Kiel, Germany; Guiggiani, M., 1991. Direct Evaluation of hypersingular integrals in 2D BEM. In: Proceedings of the 7th GAMM Seminar on Numerical Techniques for Boundary Element Methods. Kiel, Germany · Zbl 0743.65013
[16] Li, S.; Mear, M. E.; Xiao, L., Symmetric weak-form integral equation method for three-dimensional fracture analysis, Comput. Meth. Appl. Mech. Engrg., 151, 435-459 (1998) · Zbl 0906.73074
[17] Maier, G.; Novati, G.; Cen, Z., Symmetric Galerkin BEM for quasi-brittle fracture and frictional contact problems, Comp. Mech., 13, 74-89 (1993) · Zbl 0786.73080
[18] Maier, G.; Polizzotto, C., A Galerkin approach to boundary element elastoplastic analysis, Comput. Meth. Appl. Mech. Engrg., 60, 175-194 (1987) · Zbl 0602.73081
[19] Mi, Y.; Aliabadi, M. H., Three-dimensional crack-growth simulation using BEM, Computers & Structures, 52, 871-878 (1994) · Zbl 0900.73900
[20] Panzeca, T.; Salerno, M., Macro-elements in the mixed boundary value problems, Comp. Mech., 26, 437-446 (2000) · Zbl 0993.74078
[21] Panzeca, T., Cucco, F., Terravecchia, S., 2002a. Karnak.sGbem. Release 1.0., www.bemsoft.it; Panzeca, T., Cucco, F., Terravecchia, S., 2002a. Karnak.sGbem. Release 1.0., www.bemsoft.it
[22] Panzeca, T.; Cucco, F.; Terravecchia, S., Symmetric Boundary Element Method versus Finite Element Method, Comput. Meth. Appl. Mech. Engrg., 191, 3347-3367 (2002) · Zbl 1101.74370
[23] Panzeca, T., Cucco, F., Milana, V., Terravecchia, S., 2004. Multidomain approach for thermoelasticity in the SGBEM, In: 5th International Conference on Boundary Element Techniques, Beteq. Madeira, Portugal; Panzeca, T., Cucco, F., Milana, V., Terravecchia, S., 2004. Multidomain approach for thermoelasticity in the SGBEM, In: 5th International Conference on Boundary Element Techniques, Beteq. Madeira, Portugal
[24] Panzeca, T.; Fujita Yashima, H.; Salerno, M., Direct stiffness matrices of BEs in the Galerkin BEM formulation, Eur. J. Mech. A/Solids, 20, 277-298 (2001) · Zbl 0983.74079
[25] Phan, A. V.; Gray, L. J., Symmetric-Galerkin BEM simulation of fracture with frictional contact, Int. J. Numer. Methods Engrg., 57, 835-851 (2003) · Zbl 1062.74641
[26] Polizzotto, C., An energy approach to the boundary element method: Part I, Comput. Meth. Appl. Mech. Engrg., 69, 167-184 (1988) · Zbl 0629.73069
[27] Portela, A.; Aliabadi, M. H.; Rooke, D. P., Dual Boundary Element Method: effective implementation for crack problem, Int. J. Numer. Methods Engrg., 33, 1269-1287 (1992) · Zbl 0825.73908
[28] Rice, J. R., A path-independent integral and approximate analysis of strain concentration by notches and cracks, J. Appl. Mech., 35, 379-386 (1968)
[29] Saleh, A. L.; Aliabadi, M. H., Crack growth analysis in concrete using Boundary Element Method, Eng. Fract. Mech., 51, 533-545 (1995)
[30] Salvadori, A., A symmetric boundary integral formulation for cohesive interface problems, Comp. Mech., 32, 381-391 (2003) · Zbl 1038.74668
[31] Sladek, J.; Sladek, V.; Bazant, P. Z., Non-local boundary integral formulation for softening damage, Int. J. Numer. Methods Engrg., 57, 103-116 (2003) · Zbl 1062.74644
[32] Terravecchia, S., Closed form in the Symmetric Boundary Element Approach, Eng. Anal. Bound. Elem. Meth., 30, 479-488 (2006) · Zbl 1195.74263
[33] Ueda, S.; Biwa, S.; Watanabe, K.; Heuer, R.; Pecorari, C., On the stiffness of spring model for closed crack, Int. J. Engrg. Sci., 74, 874-888 (2006) · Zbl 1213.74272
[34] Williams, R. C.; Phan, A. V.; Tippur, H. V.; Kaplan, T.; Gray, L. J., SGBEM analysis of crack-particle(s) due to elastic constants mismatch, Engrg. Fract. Mech., 44, 314-331 (2006)
[35] Xie, D.; Biggers, J. B.S., Progressive crack growth analysis using interface element based on the virtual crack closure technique, Finite Elem. Anal. Design., 42, 977-984 (2006)
[36] Yang, B.; Ravi-Chandar, K., A single-domain dual-boundary-element formulation incorporating a cohesive zone model for elestostatic cracks, Int. J. Fract., 93, 115-144 (1998)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.