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[1] Barenblatt, G.I., The mathematical theory of equilibrium cracks in brittle fracture. Advances in Applied Mechanics, 7, pp. 55–129, 1962. [Crossref]
[2] Hillerborg, A., Modeer, M. & Petersson, P.E., Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cements Concrete Research, 6, pp. 773–782, 1976. [Crossref]
[3] Petersson, P.E., Crack growth and development of fracture zone in plain concrete and similar materials, Report Nº TVBM-1006, Division of Building Materials, Lund Insti-tute of Technology, Lund Sweden, 1981.
[4] Carpinteri, A., Post-peak and post-bifurcation analysis of cohesive crack propagation. Engineering Fracture Mechanics, 32, pp. 265–278, 1989. [Crossref]
[5] Rots, J.G., Computational modeling of concrete fracture. Ph.D. Thesis, Delft University of Technology, 1988.
[6] Hong, H. & Chen, J., Derivations of integral equations of elasticity. Journal of Engi-neering Mechanics ASCE, 114, pp. 1028–1044, 1988. [Crossref]
[7] Kupradze, V.D., Gegelia, T.G., Basheleishvili, M.O., Burchuladze, T.V. & Sternberg, E., Three-dimensional problems of the mathematical theory of elasticity and thermo-elasticity. Journal of Applied Mechanics, 47, p. 222, 1979. [Crossref]
[8] Sladek, J. & Sladek, V., Three-dimensional curved crack in an elastic body. Interna-tional Journal of Solids and Structures, 19, pp. 425–436, 1983. [Crossref]
[9] Bonnet, M., Boundary Integral Equation Methods for Solids and Fluids, John Wiley & Sons Ltd, 1999.
[10] Palermo, Jr., L., Almeida, L.P.C.P.F. & Gonçalves, P.C., The use of the tangential differ-ential operator in the dual boundary element equation. Structural Durability & Health Monitoring, 2(2), pp.123–130, 2006.
[11] Palermo, Jr., L. & Almeida, L.P.C.P.F., On the use of the tangential differential opera-tor in the traction boundary integral equation of the dual boundary element method for three dimensional problems. ICCES, 7(2), pp. 83–87, 2008. [Crossref]
[12] Palermo, Jr., L., The tangential differential operator applied to a stress boundary in-tegral equation for plate bending including the shear deformation effect. Engineering Analysis with Boundary Elements, 36(8), pp. 1213–1225, 2012.
[13] Almeida, L.P.C.P.F. & Palermo, Jr., L., On the implementation of the two dimensional dual boundary element method for crack problems. 5th International Conference on Boundary Elements Techniques, Lisboa, Portugal, 2004.
[14] Palermo, Jr., L, Gonçalves, P.C. & Figueiredo, L.G., A simple implementation of the dual boundary element method using the tangential differential operator for plane prob-lems. XXXII Boundary Elements and Other Reduction Methods, Southampton: WIT Press, pp. 75–84, 2010.
[15] Yang, B. & Ravi-Chandar, K.A., Single-domain dual-boundary-element formulation incorporating a cohesive zone model for elastostatic cracks. International Journal of Fracture V, 93, pp. 115–144, 1998. [Crossref]
[16] Gonçalves, P.C., Aplicação do método dos elementos de contorno no estudo da propa-gação de fissura discreta para modelos coesivos (PhD thesis, written in Portuguese), Faculdade de Engenharia Civil, Arquitetura e Urbanismo, Universidade Estadual de Campinas, p. 136, 2015.
[17] Gonçalves, P.C., Figueiredo, L.G., Palermo Jr., L. & Proença, S.P.B., The Dual-bound-ary-element formulation using the tangential differential operator and incorporating a cohesive zone model for elastostatic cracks. 12th International Conference Boundary Element and Meshless Techniques, Brasília, 2011.
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Open Access
Research article

A Boundary Element Formulation for Crack Analyses Incorporating a Cohesive Zone Model

p.c. gonçalves1,
l. palermo jr.2,
s.p.b. proença3
1
Natural Resources Institute, Federal University of Itajubá, Brazil
2
School Civ. Eng. Arch. Urban Design, University of Campinas, Brazil
3
São Carlos School of Engineering, University of São Paulo, Brazil
International Journal of Computational Methods and Experimental Measurements
|
Volume 5, Issue 3, 2017
|
Pages 231-240
Received: N/A,
Revised: N/A,
Accepted: N/A,
Available online: N/A
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Abstract:

A formulation is presented to perform crack propagation analyses in cohesive materials with the dual boundary element method (DBEM) using the tangential differential operator in the traction boundary-integral equations. The cohesive law is introduced in the system of equations to directly compute the cohesive forces at each loading step. A single edge crack is analyzed with the linear function to describe the material softening law in the cohesive zone, and the results are compared with those from the literature.

Keywords: Cohesive model, Crack analysis, Dual boundary element model, Plane problems, Tangential differential operator

1. Introduction

2. Dual Boundary Integral Equations

3. Cohesive Zone Model

4. Numerical Implementation

5. Numerical Example

6. Conclusions

Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

References
[1] Barenblatt, G.I., The mathematical theory of equilibrium cracks in brittle fracture. Advances in Applied Mechanics, 7, pp. 55–129, 1962. [Crossref]
[2] Hillerborg, A., Modeer, M. & Petersson, P.E., Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cements Concrete Research, 6, pp. 773–782, 1976. [Crossref]
[3] Petersson, P.E., Crack growth and development of fracture zone in plain concrete and similar materials, Report Nº TVBM-1006, Division of Building Materials, Lund Insti-tute of Technology, Lund Sweden, 1981.
[4] Carpinteri, A., Post-peak and post-bifurcation analysis of cohesive crack propagation. Engineering Fracture Mechanics, 32, pp. 265–278, 1989. [Crossref]
[5] Rots, J.G., Computational modeling of concrete fracture. Ph.D. Thesis, Delft University of Technology, 1988.
[6] Hong, H. & Chen, J., Derivations of integral equations of elasticity. Journal of Engi-neering Mechanics ASCE, 114, pp. 1028–1044, 1988. [Crossref]
[7] Kupradze, V.D., Gegelia, T.G., Basheleishvili, M.O., Burchuladze, T.V. & Sternberg, E., Three-dimensional problems of the mathematical theory of elasticity and thermo-elasticity. Journal of Applied Mechanics, 47, p. 222, 1979. [Crossref]
[8] Sladek, J. & Sladek, V., Three-dimensional curved crack in an elastic body. Interna-tional Journal of Solids and Structures, 19, pp. 425–436, 1983. [Crossref]
[9] Bonnet, M., Boundary Integral Equation Methods for Solids and Fluids, John Wiley & Sons Ltd, 1999.
[10] Palermo, Jr., L., Almeida, L.P.C.P.F. & Gonçalves, P.C., The use of the tangential differ-ential operator in the dual boundary element equation. Structural Durability & Health Monitoring, 2(2), pp.123–130, 2006.
[11] Palermo, Jr., L. & Almeida, L.P.C.P.F., On the use of the tangential differential opera-tor in the traction boundary integral equation of the dual boundary element method for three dimensional problems. ICCES, 7(2), pp. 83–87, 2008. [Crossref]
[12] Palermo, Jr., L., The tangential differential operator applied to a stress boundary in-tegral equation for plate bending including the shear deformation effect. Engineering Analysis with Boundary Elements, 36(8), pp. 1213–1225, 2012.
[13] Almeida, L.P.C.P.F. & Palermo, Jr., L., On the implementation of the two dimensional dual boundary element method for crack problems. 5th International Conference on Boundary Elements Techniques, Lisboa, Portugal, 2004.
[14] Palermo, Jr., L, Gonçalves, P.C. & Figueiredo, L.G., A simple implementation of the dual boundary element method using the tangential differential operator for plane prob-lems. XXXII Boundary Elements and Other Reduction Methods, Southampton: WIT Press, pp. 75–84, 2010.
[15] Yang, B. & Ravi-Chandar, K.A., Single-domain dual-boundary-element formulation incorporating a cohesive zone model for elastostatic cracks. International Journal of Fracture V, 93, pp. 115–144, 1998. [Crossref]
[16] Gonçalves, P.C., Aplicação do método dos elementos de contorno no estudo da propa-gação de fissura discreta para modelos coesivos (PhD thesis, written in Portuguese), Faculdade de Engenharia Civil, Arquitetura e Urbanismo, Universidade Estadual de Campinas, p. 136, 2015.
[17] Gonçalves, P.C., Figueiredo, L.G., Palermo Jr., L. & Proença, S.P.B., The Dual-bound-ary-element formulation using the tangential differential operator and incorporating a cohesive zone model for elastostatic cracks. 12th International Conference Boundary Element and Meshless Techniques, Brasília, 2011.
Cite this:
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Gonçalves, P., Jr., L. P., & Proença, S. (2017). A Boundary Element Formulation for Crack Analyses Incorporating a Cohesive Zone Model. Int. J. Comput. Methods Exp. Meas., 5(3), 231-240. https://doi.org/10.2495/CMEM-V5-N3-231-240
P. Gonçalves, L. P. Jr., and S. Proença, "A Boundary Element Formulation for Crack Analyses Incorporating a Cohesive Zone Model," Int. J. Comput. Methods Exp. Meas., vol. 5, no. 3, pp. 231-240, 2017. https://doi.org/10.2495/CMEM-V5-N3-231-240
@research-article{Gonçalves2017ABE,
title={A Boundary Element Formulation for Crack Analyses Incorporating a Cohesive Zone Model},
author={P.C. GonçAlves and L. Palermo Jr. and S.P.B. ProençA},
journal={International Journal of Computational Methods and Experimental Measurements},
year={2017},
page={231-240},
doi={https://doi.org/10.2495/CMEM-V5-N3-231-240}
}
P.C. GonçAlves, et al. "A Boundary Element Formulation for Crack Analyses Incorporating a Cohesive Zone Model." International Journal of Computational Methods and Experimental Measurements, v 5, pp 231-240. doi: https://doi.org/10.2495/CMEM-V5-N3-231-240
P.C. GonçAlves, L. Palermo Jr. and S.P.B. ProençA. "A Boundary Element Formulation for Crack Analyses Incorporating a Cohesive Zone Model." International Journal of Computational Methods and Experimental Measurements, 5, (2017): 231-240. doi: https://doi.org/10.2495/CMEM-V5-N3-231-240
GONÇALVES PC， PALERMO JR. L， PROENÇA SPB. A Boundary Element Formulation for Crack Analyses Incorporating a Cohesive Zone Model[J]. International Journal of Computational Methods and Experimental Measurements， 2017， 5(3)： 231-240. https://doi.org/10.2495/CMEM-V5-N3-231-240