Estimation of crack opening from a two-dimensional continuum-based finite element computation

SUMMARY Damage models are capable of representing crack initiation and mimicking crack propagation within a continuum framework. Thus, in principle, they do not describe crack openings. In durability analyses of concrete structures however, transfer properties are a key issue controlled by crack pro...

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Published in:	International journal for numerical and analytical methods in geomechanics Vol. 36; no. 16; pp. 1813 - 1830
Main Authors:	Dufour, Frédéric, Legrain, Grégory, Pijaudier-Cabot, Gilles, Huerta, Antonio
Format:	Journal Article Publication
Language:	English
Published:	Chichester Blackwell Publishing Ltd 01.11.2012 Wiley
Subjects:	74 Mechanics of deformable solids 74S Numerical methods Anàlisi numèrica Applied sciences Building failures (cracks, physical changes, etc.) Building structure Buildings. Public works Chemical Physics Classificació AMS Computation methods. Tables. Charts Concrete structure Construction (buildings and works) Crack location Crack opening Damage mechanics Durability. Pathology. Repairing. Maintenance Exact sciences and technology Matemàtiques i estadística Mètodes numèrics Numerical methods and algorithms Physics Resistència de materials Structural analysis. Stresses Àrees temàtiques de la UPC Constitutive equation Damage mechanics Two dimensional model Modeling Crack location Crack propagation Finite element method Crack opening displacement Experimental result Failure analysis Concrete construction Crack opening Localization Comparative study Crack initiation Bending test
ISSN:	0363-9061, 1096-9853
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Abstract	SUMMARY Damage models are capable of representing crack initiation and mimicking crack propagation within a continuum framework. Thus, in principle, they do not describe crack openings. In durability analyses of concrete structures however, transfer properties are a key issue controlled by crack propagation and crack opening. We extend here a one‐dimensional approach for estimating a crack opening from a continuum‐based finite element calculation to two‐dimensional cases. The technique operates in the case of mode I cracking described in a continuum setting by a nonlocal isotropic damage model. We used the global tracking method to compute the idealized crack location as a post‐treatment procedure. The original one‐dimensional problem devised in Dufour et al. [4] is recovered as profiles of deformation orthogonal to the idealized crack direction are computed. An estimate of the crack opening and an error indicator are computed by comparing finite element deformation profiles and theoretical profiles corresponding to a displacement discontinuity. Two estimates have been considered: In the strong approach, the maxima of the profiles are assumed to be equal; in the weak approach, the integrals of each profile are set equal. Two‐dimensional numerical calculations show that the weak estimates perform better than do the strong ones. Error indicators, defined as the distance between the numerical and theoretical profiles, are less than a few percentages. In the case of a three‐point bending, test results are in good agreement with experimental data, with an error lower than 10% for widely opened crack (> 40µm). Copyright © 2011 John Wiley & Sons, Ltd.
AbstractList	Damage models are capable of representing crack initiation and mimicking crack propagation within a continuum framework. Thus, in principle, they do not describe crack openings. In durability analyses of concrete structures however, transfer properties are a key issue controlled by crack propagation and crack opening. We extend here a one‐dimensional approach for estimating a crack opening from a continuum‐based finite element calculation to two‐dimensional cases. The technique operates in the case of mode I cracking described in a continuum setting by a nonlocal isotropic damage model. We used the global tracking method to compute the idealized crack location as a post‐treatment procedure. The original one‐dimensional problem devised in Dufour et al. [4] is recovered as profiles of deformation orthogonal to the idealized crack direction are computed. An estimate of the crack opening and an error indicator are computed by comparing finite element deformation profiles and theoretical profiles corresponding to a displacement discontinuity. Two estimates have been considered: In the strong approach, the maxima of the profiles are assumed to be equal; in the weak approach, the integrals of each profile are set equal. Two‐dimensional numerical calculations show that the weak estimates perform better than do the strong ones. Error indicators, defined as the distance between the numerical and theoretical profiles, are less than a few percentages. In the case of a three‐point bending, test results are in good agreement with experimental data, with an error lower than 10% for widely opened crack (> 40 µm ). Copyright © 2011 John Wiley & Sons, Ltd. Damage models are capable of representing crack initiation and mimicking crack propagation within a continuum framework. Thus, in principle, they do not describe crack openings. In durability analyses of concrete structures however, transfer properties are a key issue controlled by crack propagation and crack opening. We extend here a one dimensional approach for estimating a crack opening from a continuum based fi nite element calculation to two dimensional cases. The technique operates in the case of mode I cracking described in a continuum setting by a nonlocal isotropic damage model. We used the global tracking method to compute the idealized crack location as a post treatment procedure. The orig inal one dimensional problem devised in Dufour et al . [4] is recovered as pro fi les of deformation orthog onal to the idealized crack direction are computed. An estimate of the crack opening and an error indicator are computed by comparing fi nite element deformation pro fi les and theoretical pro fi les corresponding to a displacement discontinuity. Two estimates have been considered: In the strong approach, the maxima of the pro fi les are assumed to be equal; in the weak approach, the integrals of each pro fi le are set equal. Two dimensional numerical calculations show that the weak estimates perform better than do the strong ones. Error indicators, de fi ned as the distance between the numerical and theoretical pro fi les, are less than a few percentages. In the case of a three point bending, test results are in good agreement with experimental data, with an error lower than 10% for widely opened crack ( > 40 m m ) Peer Reviewed SUMMARY Damage models are capable of representing crack initiation and mimicking crack propagation within a continuum framework. Thus, in principle, they do not describe crack openings. In durability analyses of concrete structures however, transfer properties are a key issue controlled by crack propagation and crack opening. We extend here a one‐dimensional approach for estimating a crack opening from a continuum‐based finite element calculation to two‐dimensional cases. The technique operates in the case of mode I cracking described in a continuum setting by a nonlocal isotropic damage model. We used the global tracking method to compute the idealized crack location as a post‐treatment procedure. The original one‐dimensional problem devised in Dufour et al. [4] is recovered as profiles of deformation orthogonal to the idealized crack direction are computed. An estimate of the crack opening and an error indicator are computed by comparing finite element deformation profiles and theoretical profiles corresponding to a displacement discontinuity. Two estimates have been considered: In the strong approach, the maxima of the profiles are assumed to be equal; in the weak approach, the integrals of each profile are set equal. Two‐dimensional numerical calculations show that the weak estimates perform better than do the strong ones. Error indicators, defined as the distance between the numerical and theoretical profiles, are less than a few percentages. In the case of a three‐point bending, test results are in good agreement with experimental data, with an error lower than 10% for widely opened crack (> 40µm). Copyright © 2011 John Wiley & Sons, Ltd. Damage models are capable of representing crack initiation and mimicking crack propagation within a continuum framework. Thus, in principle, they do not describe crack openings. In durability analyses of concrete structures however, transfer properties are a key issue controlled by crack propagation and crack opening. We extend here a one-dimensional approach for estimating a crack opening from a continuum-based finite element calculation to two-dimensional cases. The technique operates in the case of mode I cracking described in a continuum setting by a nonlocal isotropic damage model. We used the global tracking method to compute the idealized crack location as a post-treatment procedure. The original one-dimensional problem devised in Dufour et al. [4] is recovered as profiles of deformation orthogonal to the idealized crack direction are computed. An estimate of the crack opening and an error indicator are computed by comparing finite element deformation profiles and theoretical profiles corresponding to a displacement discontinuity. Two estimates have been considered: In the strong approach, the maxima of the profiles are assumed to be equal; in the weak approach, the integrals of each profile are set equal. Two-dimensional numerical calculations show that the weak estimates perform better than do the strong ones. Error indicators, defined as the distance between the numerical and theoretical profiles, are less than a few percentages. In the case of a three-point bending, test results are in good agreement with experimental data, with an error lower than 10% for widely opened crack (>40μm).
Author	Legrain, Grégory Pijaudier-Cabot, Gilles Dufour, Frédéric Huerta, Antonio
Author_xml	– sequence: 1 givenname: Frédéric surname: Dufour fullname: Dufour, Frédéric email: F. Dufour, Laboratoire 3S-R, BP 53, 38041 Grenoble Cedex 9, France., Frederic.Dufour@grenoble-inp.fr organization: Laboratoire 3S-R Grenoble-INP/Université Joseph Fourier/CNRS UMR 5521, France – sequence: 2 givenname: Grégory surname: Legrain fullname: Legrain, Grégory organization: GeM-Institut de Recherche en génie civil et mécanique, Ecole Centrale de Nantes, France – sequence: 3 givenname: Gilles surname: Pijaudier-Cabot fullname: Pijaudier-Cabot, Gilles organization: Laboratoire des Fluides Complexes, Université de Pau et des Pays de l'Adour, France – sequence: 4 givenname: Antonio surname: Huerta fullname: Huerta, Antonio organization: Laboratori de Càlcul Numèric, Universitat Politècnica de Catalunya, Barcelona, Spain
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Keywords	Constitutive equation Damage mechanics Two dimensional model Modeling Crack location Crack propagation Finite element method Crack opening displacement Experimental result Failure analysis Concrete construction Crack opening Localization Comparative study Crack initiation Bending test
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Snippet	SUMMARY Damage models are capable of representing crack initiation and mimicking crack propagation within a continuum framework. Thus, in principle, they do... Damage models are capable of representing crack initiation and mimicking crack propagation within a continuum framework. Thus, in principle, they do not...
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SubjectTerms	74 Mechanics of deformable solids 74S Numerical methods Anàlisi numèrica Applied sciences Building failures (cracks, physical changes, etc.) Building structure Buildings. Public works Chemical Physics Classificació AMS Computation methods. Tables. Charts Concrete structure Construction (buildings and works) Crack location Crack opening Damage mechanics Durability. Pathology. Repairing. Maintenance Exact sciences and technology Matemàtiques i estadística Mètodes numèrics Numerical methods and algorithms Physics Resistència de materials Structural analysis. Stresses Àrees temàtiques de la UPC
Title	Estimation of crack opening from a two-dimensional continuum-based finite element computation
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