Embedded crack model: I. Basic formulation

The recently emerged idea of enriching standard finite element interpolations by strain or displacement discontinuities has triggered the development of powerful techniques that allow efficient modelling of regions with highly localized strains, e.g. of fracture zones in concrete, or shear bands in metals or soils. The present paper describes a triangular element with an embedded displacement discontinuity that represents a crack. The constitutive model is formulated within the framework of damage theory, with crack closure effects and friction on the crack faces taken into account. Numerical aspects of the implementation are discussed. In a companion paper, the embedded crack approach is combined with the more traditional smeared crack approach. Copyright © 2001 John Wiley & Sons, Ltd.

[1]  E. Dvorkin,et al.  Finite elements with displacement interpolated embedded localization lines insensitive to mesh size and distortions , 1990 .

[2]  J. Chaboche,et al.  Mechanics of Solid Materials , 1990 .

[3]  J. Hutchinson,et al.  The relation between crack growth resistance and fracture process parameters in elastic-plastic solids , 1992 .

[4]  Michael Ortiz,et al.  Microcrack coalescence and macroscopic crack growth initiation in brittle solids , 1988 .

[5]  L. J. Sluys,et al.  Discontinuous failure analysis for mode-I and mode-II localization problems , 1998 .

[6]  Thomas Olofsson,et al.  Inner softening bands : a new approach to localization in finite elements , 1994 .

[7]  M. Ortiz,et al.  Computational modelling of impact damage in brittle materials , 1996 .

[8]  A. Hillerborg,et al.  Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements , 1976 .

[9]  Xiaopeng Xu,et al.  Numerical simulations of fast crack growth in brittle solids , 1994 .

[10]  Milan Jirásek,et al.  Comparative study on finite elements with embedded discontinuities , 2000 .

[11]  John W. Hutchinson,et al.  Models of Interface Separation Accompanied by Plastic Dissipation at Multiple Scales , 1999 .

[12]  M. Klisinski,et al.  FINITE ELEMENT WITH INNER SOFTENING BAND , 1991 .

[13]  M. Jirásek,et al.  ANALYSIS OF ROTATING CRACK MODEL , 1998 .

[14]  T. Belytschko,et al.  A finite element with embedded localization zones , 1988 .

[15]  M. Ortiz,et al.  A finite element method for localized failure analysis , 1987 .

[16]  D. S. Dugdale Yielding of steel sheets containing slits , 1960 .

[17]  J. Chaboche,et al.  On the Interface Debonding Models , 1997 .

[18]  Kenneth Runesson,et al.  Element-Embedded Localization Band Based on Regularized Displacement Discontinuity , 1996 .

[19]  M. Ortiz,et al.  FINITE-DEFORMATION IRREVERSIBLE COHESIVE ELEMENTS FOR THREE-DIMENSIONAL CRACK-PROPAGATION ANALYSIS , 1999 .

[20]  P. Krysl,et al.  Finite element simulation of ring expansion and fragmentation: The capturing of length and time scales through cohesive models of fracture , 1999 .

[21]  J. Oliver MODELLING STRONG DISCONTINUITIES IN SOLID MECHANICS VIA STRAIN SOFTENING CONSTITUTIVE EQUATIONS. PART 2: NUMERICAL SIMULATION , 1996 .

[22]  G. Maugin The Thermomechanics of Plasticity and Fracture , 1992 .

[23]  A. Needleman A Continuum Model for Void Nucleation by Inclusion Debonding , 1987 .

[24]  J. Hutchinson,et al.  The influence of plasticity on mixed mode interface toughness , 1993 .

[25]  Ulf Ohlsson,et al.  Mixed-mode fracture and anchor bolts in concrete analysis with inner softening bands , 1997 .

[26]  G. I. Barenblatt THE MATHEMATICAL THEORY OF EQUILIBRIUM CRACKS IN BRITTLE FRACTURE , 1962 .

[27]  R. Girard,et al.  Numerical analysis of composite systems by using interphase/interface models , 1997 .