CONCRETE FRACTURE ANALYSIS USING THE CONTINUUM STRONG DISCONTINUITY APPROACH AND THE BOUNDARY ELEMENT METHOD
DOI:
https://doi.org/10.26512/ripe.v2i6.21600Keywords:
Concrete fracture. Damage constitutive models. Continuum Strong Discontinuity Approach. Boundary Element Method.Abstract
The implicit formulation of the boundary element method is applied to bi-dimensional problems of material failure involving, sequentially, inelastic dissipation with softening in continuous media, bifurcation and transition between weak and strong discontinuities. The bifurcation condition is defined by the singularity of the localization tensor, also known, for historical reasons, as acoustic tensor. The weak discontinuities are related to strain localization bands of finite width, which become increasingly narrow until to collapse in a surface with discontinuous displacement field, called strong discontinuity surface. To associate such steps to the fracture process in concrete specimens, an isotropic damage (continuum) constitutive model is used to represent the material behaviour in all of them, taking into account the adaptations that come
from the strong discontinuity analysis for the post-bifurcation phases. The crack propagation across the domain is done by an automatic cells generation algorithm and, in this context, the fracture process zone in the crack tip became totally represented by the cells in the continuum damage regime and the cells with weak discontinuities.
Downloads
References
Aliabadi, M. H., 2002. The boundary element method: volume 2 - applications in solids and structures. John Wiley & Sons, Chichester.
Arrea, M. & Ingraffea, A. R., 1982. Mixed-mode crack propagation in mortar and concrete.
Technical report, 81-13, Department of Structural Engineering, Cornell University, Ithaca, USA.
Benallal, A., Botta, A. S., & Venturini, W. S., 2006. On the description of localization and failure phenomena by the boundary element method. Computer Methods in Applied Mechanics and Engineering, vol. 195, pp. 5833”“5856.
Benallal, A., Fudoli, C. A., & Venturini, W. S., 2002. An implicit BEM formulation for gradient plasticity and localization phenomena. International Journal for Numerical Methods in Engineering, vol. 53, pp. 1853”“1869.
Botta, A. S., Venturini,W. S., & Benallal, A., 2005. BEM applied to damage models emphasizing localization and associated regularization techniques. Engineering Analysis with Boundary Elements, vol. 29, pp. 814”“827.
Bui, H. D., 1978. Some remarks about the formulation of three-dimensional thermoelastoplastic problems by integral equations. International Journal of Solids and Structures, vol. 14, pp. 935”“939.
G´alvez, J. C., Elices, M., Guinea, G. V., & Planas, J., 1998. Mixed mode fracture of concrete under proportional and nonproportional loading. International Journal of Fracture, vol. 94, pp. 267”“284.
Gao, X.-W. & Davies, T. G., 2002. Boundary Element Programming in Mechanics. Cambridge University Press, Cambridge.
Garc´Ä±a, R., Fl´orez-L´opez, J., & Cerrolaza, M., 1999. A boundary element formulation for a class of non-local damage models. International Journal of Solids and Structures, vol. 36, pp. 3617”“3638.
Herding, U. & Kuhn, G., 1996. A field boundary element formulation for damage mechanics. Engineering Analysis with Boundary Elements, vol. 18, pp. 137”“147.
Lin, F.-B., Yan, G., Baˇzant, Z. P., & Ding, F., 2002. Non-local strain softening model of quasi-brittle materials using boundary element method. Engineering Analysis with Boundary Elements, vol. 26, pp. 417”“424.
Manzoli, O. L., Pedrini, R. A., & Venturini, W. S., 2009. Strong discontinuity analysis in solid mechanics using boundary element method. In Spountzakis, E. J. & Aliabadi, M. H., eds, Avances in Boundary Element Techniques X, pp. 323”“329, Atenas, Grcia.
Manzoli, O. L. & Venturini, W. S., 2004. Uma formulao do MEC para simulao numrica de descontinuidades fortes. Revista Internacional de Mtodos Numricos para Clculo y Diseo en Ingeniera, vol. 20, n. 3, pp. 215”“234.
Manzoli, O. L. & Venturini, W. S., 2007. An implicit BEM formulation to model strong discontinuities. Computational Mechanics, vol. 40, pp. 901”“909.
Mendelson, A., 1973. Boundary integral methods in elasticity and plasticity. Technical report, NASA TN D-7418, USA.
Mukherjee, S., 1977. Corrected boundary-integral equations in planar thermoelastoplasticity. International Journal of Solids and Structures, vol. 13, pp. 331”“335.
Oliver, J., 1996. Modelling strong discontinuities in solid mechanics via strain softening constitutive equations. Part 1: Fundamentals. International Journal for Numerical Methods in Engineering, vol. 39, pp. 3575”“3600.
Oliver, J., 2000. On the discrete constitutive models induced by strong discontinuity kinematics and continuum constitutive equations. International Journal of Solids and Structures, vol. 37, pp. 7207”“7229.
Oliver, J., Huespe, A. E., Blanco, S., & Linero, D. L., 2006. Stability and robustness issues in numerical modeling of material failure with the strong discontinuity approach. Computer Methods in Applied Mechanics and Engineering, vol. 195, pp. 7093”“7114.
Peixoto, R. G., 2016. An´alise de degradac¸ ˜ao material, bifurcac¸ ˜ao e transic¸ ˜ao entre descontinuidades fracas e fortes atrav´es do m´etodo dos elementos de contorno. PhD thesis, Universidade Federal de Minas Gerais, Belo Horizonte.
Peixoto, R. G., Ribeiro, G. O., Pitangueira, R. L. S., & Penna, S. S., 2015. Strain localization in the boundary element method: the strong discontinuity approach as a limit case. In Dumont, N. A., ed, Proceedings of the XXXVI Iberian Latin-American Congress on Computational Methods in Engineering - CILAMCE, Rio de Janeiro, RJ, Brazil.
Rajgelj, S., Amadio, C., & Nappi, A., 1992. Application of damage mechanics concepts to the boundary element method. In Brebbia, C. A. & Ingber, M. S., eds, Seventh International Conference on Boundary Element Technology, pp. 617”“634.
Riccardella, P. C., 1973. An implementation of the boundary integral technique for planar problems in elasticity and elastoplasticity. Technical report, SM-73-10, Carnegie Mellon University, Pittsburgh, USA.
Rice, J. R. & Rudnicki, J. W., 1980. A note on some features of the theory of localization of deformation. International Journal of Solids and Structures, vol. 16, pp. 597”“605.
Simo, J. C., Oliver, J., & Armero, F., 1993. An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids. Computational Mechanics, vol. 12, pp. 277”“296.
Sl´adek, J., Sl´adek, V., & Baˇzant, Z. P., 2003. Non-local boundary integral formulation for softening damage. International Journal for Numerical Methods in Engineering, vol. 57, pp. 103”“116.
Swedlow, J. L. & Cruse, T. A., 1971. Formulation of boundary integral equations for three dimensional elastoplastic flow. Journal of Solids and Structures, vol. 7, pp. 1673”“1683.
Telles, J. C. F., 1983. Boundary Element Method applied to inelastic problems. Springer-Verlag, Berlin.
Telles, J. C. F. & Brebbia, C. A., 1979. On the application of the boundary element method to plasticity. Applied Mathematical Modelling, vol. 3, n. 4, pp. 466”“470.
Telles, J. C. F. & Carrer, J. A. M., 1991. Implicit procedures for the solution of elastoplastic problems by the boundary element method. Mathematical and Computer Modelling, vol. 15, pp. 303”“311.
van der Giessen, E. & de Borst, R., 1998. Introduction to material instabilities in solids. In de Borst, R. & van der Giessen, E., eds, Material instabilities in solids, chapter 1. John Wiley & Sons, Chichester.
Downloads
Published
How to Cite
Issue
Section
License
Given the public access policy of the journal, the use of the published texts is free, with the obligation of recognizing the original authorship and the first publication in this journal. The authors of the published contributions are entirely and exclusively responsible for their contents.
1. The authors authorize the publication of the article in this journal.
2. The authors guarantee that the contribution is original, and take full responsibility for its content in case of impugnation by third parties.
3. The authors guarantee that the contribution is not under evaluation in another journal.
4. The authors keep the copyright and convey to the journal the right of first publication, the work being licensed under a Creative Commons Attribution License-BY.
5. The authors are allowed and stimulated to publicize and distribute their work on-line after the publication in the journal.
6. The authors of the approved works authorize the journal to distribute their content, after publication, for reproduction in content indexes, virtual libraries and similars.
7. The editors reserve the right to make adjustments to the text and to adequate the article to the editorial rules of the journal.