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A generalization of Mv integral to axisymmetric problems for viscoelastic materials

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Abstract

A generalization of the M integral to axisymmetric problems is proposed, it is noted M axi. The Mv axi integral providing the mixed-mode crack growth in time-dependent materials is presented. This analytical generalization is based on the conservative law, the Arbitrary Lagrangian Euleurian description, the non-dependent integrals and on a combination of real and virtual displacement fields. The time-dependent behavior of the material is considered to be non-ageing linear viscoelastic. It is modeled by a Generalized Kelvin–Voigt model introduced with a finite element algorithm resolved with an incremental constitutive law. The modified Compact Tension Shear specimen is used to obtained the corresponding energy release rate.

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Authors and Affiliations

  1. Laboratoire de Mécanique et Ingénieries, Clermont Université, Université Blaise Pascal, EA 3867, BP 206, 63000, Clermont Ferrand, France

    Rostand Moutou Pitti

  2. GEMH Laboratory, Limoges University, Centre Universitaire Génie Civil, Boulevard Jacques Derche, 19300, Egletons, France

    Claude Chazal

  3. Laboratoire de Mécanique et Ingénieries, Clermont Université, UBP-IUT, Avenue Aristide Briand, BP 2235, 03101, Montlucon Cedex, France

    Florence Labesse-Jied

  4. French Institute of Advanced Mechanics, LAMI/IFMA/Clermont Université, Campus des Cézeaux, BP 265, 63175, Aubière Cedex, France

    Yuri Lapusta

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  1. Rostand Moutou Pitti
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  2. Claude Chazal
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  3. Florence Labesse-Jied
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  4. Yuri Lapusta
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Correspondence to Rostand Moutou Pitti.

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Moutou Pitti, R., Chazal, C., Labesse-Jied, F. et al. A generalization of Mv integral to axisymmetric problems for viscoelastic materials. Acta Mech 220, 365–373 (2011). https://doi.org/10.1007/s00707-011-0460-8

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  • DOI: https://doi.org/10.1007/s00707-011-0460-8

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