Abstract
In the context of cohesive fracture mechanics, a non-associated elastic-plastic based cohesive law is considered in modeling quasi-brittle materials. The structural problem is stated by means of boundary integral equations. In the framework of the symmetric Galerkin formulation, the non associated nature of the cohesive law implies unsymmetry of the relevant boundary operator. To overcome such a drawback, the problem is transformed into an extended equivalent one governed by a symmetric integral operator. It is shown that the new problem admits of a min-max characterization.
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Nooru-Mohamed, M.B. and van Mier, J.G.M., Fracture of concrete under Mixed Mode Loading, in Fracture of concrete and rock, recent development, S.P. Shah, S.E. Schwartz and B. Barr eds., Elsevier, Amsterdam, 458–467 (1989).
Guo, Z.K., Kobayashi, A.S. and Hawkins, N.M., Mixed Modes I and II Concrete Fracture: An experimental analysis, J. Appl. Mech., ASME, 61, 815–821 (1994).
Amadei, B., Sture, S., Saeb, S. and Atkinson, R.H., An evaluation of masonry joint shear strength in existing buildings, report to NSF, Department of Civil, Environmental and Architectural Engineering, University of Colorado, Boulder, 1989.
Lotfi, H. and Shing, P., Interface model applied to fracture of masonry structures, J. Struct Engrg., ASCE, 120(1), 63–80 (1994).
Carol, I., Prat, P.C. and Lopez, CM., Normal/shear cracking model: application to discrete crack analysis, J. Engrg. Mech., ASCE, 123(8), 1–9 (1997).
Maugin, G.A., The thermomechanics of plasticity and fracture, Cambridge University Press, New York, 1992.
Carini, A., De Donato, O., Fundamental solutions for linear vis-coelastic continua, Int. J. Solids Structures, 29, 2989–3009 (1992).
Cruse, T.A., Boundary Element Analysis in Computational Fracture Mechanics, Kluwer Academic, Dordrecht, The Netherlands, 1988.
Cen, Z., and Maier, G., Bifurcations and instabilities in fracture of cohesive-softening structures: a boundary element analysis, Fatigue Fract. Engng. Mater. Struct, 15, 911–928 (1992).
Sirtori, S., Maier, G., Novati, G., and Miccoli, S., A Galerkin symmetric boundary-element method in elasticity: formulation and implementation, Int. J. Numer. Methods Eng., 35, 255–282 (1992).
Maier, G., and Hueckel, T. Non associated and coupled flow rules of elastoplasticity for rock-like materials, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 16, 77–92,(1979)
Salvadori A. Quasi Brittle Fracture Mechanics by Cohesive Crack Models and Symmetric Galerkin Boundary Element Method, PhD Thesis, Politecnico di Milano, Milano, (1999)
Carini, A. and Genna, F., Variational formulations in the non-associated flow theory of plasticity, (submitted).
Comi, C. and Perego, U., A unified approach for variationally consistent finite elements in elastoplasticity, Comp. Meth. in Appl. Mech. and Engng., 121, 323–344 (1995).
Pandolfi, A. and Carini, A., Some extremum properties of finite-step solutions in elastoplasticity, Int. J. Solids and Structures, 36, 185–218 (1999).
Bramble, J.H. and Pasciak, J.E., A preconditioning technique for indefinite systems resulting from mixed approximations of elliptic problems, Mathematics of Computation, 50, 1–17 (1988).
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© 2001 Springer Science+Business Media Dordrecht
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Carini, A., Salvadori, A. (2001). Implementation of a Symmetric Galerkin Boundary Element Method in Quasi-Brittle Fracture Mechanics. In: Burczynski, T. (eds) IUTAM/IACM/IABEM Symposium on Advanced Mathematical and Computational Mechanics Aspects of the Boundary Element Method. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9793-7_6
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DOI: https://doi.org/10.1007/978-94-015-9793-7_6
Publisher Name: Springer, Dordrecht
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