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Embedded representation of fracture in concrete with mixed finite elements. (English) Zbl 0824.73070
Summary: As an alternative to the smeared and discrete crack representations, an embedded representation of fracture for finite element analysis of concrete structures is presented. The three-field Hu-Washizu variational statement is extended to bodies with internal discontinuities. The extended variational statement is then utilized for formulating elements with a discontinuous displacement field. The new elements are capable of modelling different deformation modes of an internal discontinuity at the element level. The satisfactory performance of the embedded crack representation is verified by several case studies on concrete fracture.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74R99 Fracture and damage
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[1] Ngo, J. Am. Concrete Instit. 64 pp 152– (1967)
[2] Rashid, Nucl. Eng. Des. 7 pp 334– (1968)
[3] Bocca, Int. J. Solids Struct. 27 pp 1139– (1991)
[4] and , ’Computational framework for 3D nonlinear discrete crack analysis’, in and (eds.), Proc. 9th Eng. Mech. Conf. ASCE, New York, 1992, pp. 788-791.
[5] Bazant, J. Eng. Mech. Div. ASCE 102 pp 331– (1976)
[6] Bazant, Mater. Struct., RILEM 16 pp 155– (1983)
[7] Cervenka, IABSE 32 pp 25– (1972)
[8] Lotfi, Comput. Struct. 41 pp 413– (1991)
[9] ’Computational modeling of concrete fracture’, Doctoral Thesis, Delft University of Technology, Netherlands, 1988.
[10] Introduction to the Mechanics of a Continuous Medium, Prentice-Hall, Englewood Cliffs, N.J., 1969.
[11] Dvorkin, Int. j numer. methods eng. 30 pp 541– (1990)
[12] ’The numerical modeling of shear bands in geological materials’, Doctoral Thesis, University of Alberta, Edmonton, Alberta, 1990.
[13] ’Finite element analysis of fracture in concrete and masonry structures’, Ph.D. Thesis, Department of Civil, Environmental, and Architectural Engineering, University of Colorado, Boulder, CO, 1992.
[14] Ortiz, Comput. Methods Appl. Mech. Eng. 70 pp 59– (1987)
[15] Belytschko, Comput. Methods Appl. Mech. Eng. 70 pp 59– (1988)
[16] Klisinski, J. Eng. Mech. ASCE 117 pp 575– (1991)
[17] Steinmann, Arch. Appl. Mech. 61 pp 259– (1991)
[18] ’Dynamic fracture analysis of concrete dams’, Ph.D. Thesis, Swiss Polytechnic Institute, Lausanne, 1987.
[19] and , The Finite Element Method, 4th edn. McGraw-Hill, Maidenhead, U.K., 1989.
[20] Simo, Int. j. numer. methods eng. 29 pp 1595– (1990)
[21] Taylor, Int. j. numer. methods eng. 10 pp 1211– (1976)
[22] Hillerborg, Cement Concrete Res. 6 pp 773– (1976)
[23] Lotfi, J. Struct. Eng. ASCE 120 pp 63– (1994)
[24] and ’Determination of the fracture energy of normal concrete and epoxy modified concrete’, Report 5-83-18, Delft University of Technology, Netherlands, 1983.
[25] and , ’Smeared analysis of concrete fracture using a microplane-based multicrack model with static constraint’, in et al., (eds.), Proc. Int. Conf. Fracture Processes in Brittle Disordered Materials, Chapman & Hall, London, 1991.
[26] ’Removal of finite elements in strain-softening analysis of tensile fracture’, in (ed.), Fracture Mechanics of Concrete Structures, Elsevier Applied Science, New York, 1992, pp. 330-338.
[27] , and , ’Fracture process zone of concrete’, in and (eds.), Mechanics of Concrete: Structural Application and Numerical Calculation, Martinus Nijhoff, Doordrecht, Boston, 1985, pp. 25-50.
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