Abstract
The symmetric Galerkin boundary element method is applied to the analysis of fracture processes involving also heterogeneous (zonewise homogeneous) domains accounting for the presence of interfaces between different subdomains. This method is characterized by the combined use of static and kinematic sources (i.e. traction and displacement discontinuities) to generate a symmetric integral operator and its space-discretization in the Galerkin weighted-residual sense. By virtue of this procedure and in analogy with the analysis of fractures in homogeneous bodies, some meaningful properties (e.g. symmetry and sign definiteness) of key continuum operators are preserved in the discrete form. Some numerical examples are presented, concerning both two-dimensional and threedimensional analyses.
This text was written in the frame of a reasearch project supported by a MURST grant (“Cofinanziamento”) on “Integrity Assesment of Large Dams”
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References
Balakrishna, C., Gray, L.J. and Kane, J.H. (1994) Efficient analytical integration of symmetric Galerkin boundary integrals over curved elements: thermal conduction formulation, Comp. Meth. Appl. Mech. Engng., 117, 157–179.
Bazânt, Z.P. and Cedolin, L. (1991) Stability of Structures, Oxford University Press, New York.
Bolzon, G., Maier, G. and Novati, G. (1994) Some aspects of quasi-brittle fracture analysis as a linear complementarity problem, in Bazânt, Z.P., Bittnar, Z., Jirasek, M. and Mazars, J. eds. (eds.), Fracture and Damage in Quasibrittle Structures, E & FN Spon, 159–174.
Bolzon, G., Maier, G. and Tin Loi, F. (1995) Holonomic and nonholonomic simulations of quasi-brittle fracture: a comparative study of mathematical programming approaches, in Wittman, F.H. ed. (eds.), Fracture Mechanics of Concrete Structures, Aedificatio Publishers, 885–898.
Bolzon, G., Maier, G. and Tin Loi, F. (1997) On multiplicity of solutions in quasi-brittle fracture computations, Comp. Mech., 19, 511–516.
Bolzon, G. and Maier, G. (1998) Identification of cohesive crack models for concrete on the basis of three point bending tests, in de Borst, R., Bicanic, N., Mang, H eds. (eds.), Computational Modelling of Concrete Tests, Balkema, 301–310.
Bolzon, G., Fedele, R. and Maier, G. (2002) Parameter identification of a cohesive crack model by Kalman filter, Comp. Meth. Appl. Mech. Engng., to appear.
Bonnet, M. and Bui, H.D. (1993) Regularization of the displacements and traction BIE for 3D elastodynamics using indirect methods, in Kane, H., Maier, G., Tosaka, N. and Atluri, S.N. (eds.), Advances in Boundary Element Techniques, Springer Verlag, 1–29.
Bonnet, M. (1995) Regularized direct and indirect symmetric variational BIE formulation for three dimensional elasticity, Engng. Analysis with Boundary Elem., 15, 93–102.
Bonnet, M., Maier, G. and Polizzotto, C. (1998) Symmetric Galerkin boundary element method, Appl. Mech. Rev., 51, 669–704.
Bonnet, M. (1999) Boundary Integral Equation Methods for Solids and Fluids, Wiley, Chichester.
Carini, A., Diligenti, M. and Maier, G. (1991) Boundary integral equation analyses in linear viscoelasticity: variational and saddle point formulation, Comp. Mech., 8, 87–98.
Cen, Z. and Maier, G. (1992) Bifurcations and instabilities in fracture of cohesive-softening structures: a boundary element analysis, Fatigue Fract. Engng. Mater. Struct., 15, 911–928.
Comi, C. and Maier, G. (1992) Extremum, convergence and stability properties of the finite-increment problem in elastic-plastic boundary element analysis, Int. J. Solids Structures, 29, 249–270.
Comi, C., Maier, G. and Perego, U. (1992) Generalized variable finite element modelling and extremum theorems in stepwise holonomic elastoplasticity with internal variables, Comp. Meth. Appl. Mech. Engng., 96, 133–171.
Comi, C. and Perego, U. (1996) A generalized variable formulation for gradient dependent softening plasticity, Int. J. Num. Meth. Engng., 39, 3731–3755.
Corigliano, A. (1993) Formulation, identification and use of interface models in the numerical analysis of composite delamination, Int. J. Solids Structures, 30, 2779–2811.
Dirkse, S.P. and Ferris, M.C. (1995) The PATH solver: a non-monotone stabilization scheme for mixed complementarity problems, Optimization Methods Software, 5, 123–156.
Frangi, A. and Novati, G. (1996) Symmetric BE method in two dimensional elasticity: evaluation of double integrals for curved elements, Comp. Mech., 19, 58–68.
Frangi, A. (1998) Regularization of Boundary. Element formulations by the derivative transfer method, in Slâdek, V., Slâdek, J. (eds.), Singular Integrals in Boundary Element Methods, Advances in Boundary Elements, Computational Mechanics Publications, 125–164.
Frangi, A. and Maier, G. (1999) Dynamic elastic-plastic analysis by a symmetric Galerkin boundary element method with time-independent kernels, Comp. Meth. Appl. Mech. Engng., 171, 281–308.
Frangi, A. and Novati, G. (2001) Fracture propagation in 3D, AIMETA 2001, Taormina.
Frangi, A., Novati, G., Springhetti, R. and Rovizzi, M. (2002) 3D fracture analysis by the symmetric Galerkin BEM, Comp. Mech.,to appear.
Gray, L.J. and Paulino, G.H. (1997) Symmetric Galerkin boundary integral formulation for interface and multi-zone problems, Int. J. Num. Meth. Engng., 40, 3085–3101.
Hartmann, F., Katz, C. and Protopsaltis, B. (1985) Boundary elements and symmetry, Ing. Arch., 55, 440–449.
Hillerborg, A., Modeer, M. and Petersson, P.E. (1976) Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements, Cern. Concr. Research, 6, 773–782.
Holzer, S. (1993) On the engineering analysis of 2D problems by the symmetric Galerkin boundary element method and coupled BEM/FEM, in Kane, H., Maier, G., Tosaka, N. and Atluri, S.N. (eds.), Advances in Boundary Element Techniques, Springer Verlag, 187–208.
Judice, J.J. and Mitra, G. (1988) An enumerative method for the solution of linear complementarity problems, Eur. J. Operat. Res., 36, 122–128.
Kane, J.H. (1994) Boundary Element Analysis in Engineering Continuum Mechanics, Prentice Hall, Englewood Cliffs, N.J..
Karihaloo, B.L. (1995) Fracture Mechanics and Structural Concrete, Longman Scientific & Technical, Harlow, Essex.
Kassir, M.K. and Sih, G.C. (1966) Three dimensional stress distribution around an elliptical crack under arbirary loadings, J. Applied Mech., 33, 602–615.
Lubliner, J. (1990) Plasticity Theory, Macmillan, New York.
Maier, G. (1971) Incremental plastic analysis in the presence of large displacements and physical instabilizing effects, Int. J. Solids Structures, 7, 345–372.
Maier, G. and Polizzotto, C. (1987) A Galerkin approach to boundary element elastoplastic analysis, Comp. Meth. Appl. Mech. Engng., 60, 175–194.
Maier, G., Cen, Z., Novati, G. and Tagliaferri, R. (1991) Fracture, path bifurcations and instabilities in elastic-cohesive-softening models: a boundary element approach, in Van Mier, J.G.M., Rots, J.G. and Bakker, A. eds. (eds.), Fracture Processes in Concrete, Rock and Ceramics -2, E. & FM. Spon, 561–570.
Maier, G., Diligenti, M. and Carini, A. (1991) A Variational Approach to Boundary Element Elastodynamic Analysis and extension to multidomain problems, Comp. Meth. Appl. Mech. Engng., 92, 192–213.
Maier, G., Miccoli, S., Novati, G. and Sirtori, S. (1992) A Galerkin symmetric boundary element method in plasticity: formulation and implementation, in Kane, J.H., Maier, G., Tosaka, N. and Atluri, S.N. eds. (eds.), Advances in Boundary Elements Techniques, Springer Verlag, 288–328.
Maier, G., Novati, G. and Cen, Z. (1993) Symmetric Galerkin boundary element method for quasi-brittle fracture and frictional contact problems, Comp. Mech., 13, 74–89.
Maier, G., Miccoli, S., Novati, G. and Perego, U. (1995) Symmetric Galerkin boundary element method in plasticity and gradient plasticity, Comp. Mech., 17, 115–129.
Maier, G. and Frangi, A. (1997) Quasi-brittle fracture mechanics by a symmetric Galerkin boundary element method, in Karihaloo, B.L., Mai, Y.W., Ripley, M.I. and Ritchie, R.O. (eds.), Advances in Fracture Research -4, Pergamon, 1837–1848.
Maier, G. and Frangi, A. (1998) Symmetric boundary element method for “discrete” crack modelling of fracture processes, Comp. Assisted Mech. and Engng. Science, 5, 201–226.
Maier, G. and Comi, C. (2000) Energy properties of solutions to quasi-brittle fracture mechanics problems with piecewise linear cohesive crack models, in Benallal, A. ed. (eds.), Continuous Damage and Fracture, Elsevier, 197–205.
Li, S., Mear, M.E. and Xiao, L. (1998) Symmetric weak-form integral equation method for three-dimensional fracture analysis, Comp. Meth. Appl. Mech. Engng., 151, 435–459.
Mi, Y. (1996) Three-dimensional Analysis of Crack Growth, Computational Mechanics Publi-cations, Southampton.
Pan, E. and Maier, G. (1997) A variational formulation of the boundary element method in transient poroelasticity, Comp. Mech., 19, 167–178.
Polizzotto, C. (1988) An energy approach to the boundary element method, part I: elastic solids, Comp. Meth. Appl. Mech. Engng., 69, 167–184.
Polizzotto, C. (1988) An energy approach to the boundary element method,part II: elastic-plastic solids, Comp. Meth. Appl. Mech. Engng., 69, 263–276.
Ralph, D. (1994) Global convergence of damped Newton’s method for nonsmooth equations via the path search, Math. Oper. Res., 19, 352–389.
Raju, I.S. and Newman, J.C. (1977) Three dimensional finite-element analysis of finite-thickness fracture specimens, NASA-TN, D-8414.
Saouma, V.E., Brühwiler, E. and Boggs, H.L. (1990) A review of fracture mechanics applied to concrete dams, Dam Engng., 1, 41–57.
Sirtori, S. (1979) General stress analysis method by means of integral equations and boundary elements, Meccanica, 14, 210–218.
Sirtori, S., Maier, G., Novati, G. and Miccoli, S. (1992) A Galerkin symmetric boundary element method in elasticity: formulation and implementation, Int. J. Num. Meth. Engng., 35, 255–282.
Sirtori, S., Miccoli, S. and Korach, E. (1993) Symmetric coupling of finite elements and boundary elements, in Kane, H., Maier, G., Tosaka, N. and Atluri, S.N. (eds.), Advances in Boundary Element Techniques, Springer Verlag, 407–427.
Slâdek, J. and Slâdek, V. (1983) Three dimensional curved crack in an elastic body, Int. J. Solids Structures, 19, 425–436.
Tin-Loi, F.H. and Ferris, X. (1997) Holonomic analysis of quasi-brittle fracture with nonlinear softening, in Karihaloo, B.L., Mai, Y.W., Ripley, M.I. and Ritchie, R.O. eds. (eds.), Advances in Fracture Research -4, Pergamon
Wittman, F.H. and Hu, X. (1991) Fracture process zone in cementitious materials, Int. Journal of Fracture, 51, 3–18.
Xu, X. and Needleman, A. (1994) Numerical simulation of fast crack growth in brittle solids, J. Mech. Phys. Solids, 42, 1397–1434.
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Frangi, A., Maier, G. (2003). The Symmetric Galerkin BEM in Linear and Non-Linear Fracture Mechanics. In: Beskos, D., Maier, G. (eds) Boundary Element Advances in Solid Mechanics. International Centre for Mechanical Sciences, vol 440. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2790-2_4
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DOI: https://doi.org/10.1007/978-3-7091-2790-2_4
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