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A constitutive model for micro-cracked bodies with growing inclusions

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Abstract

A model of micro-cracked bodies having rigid inclusions growing in their pores is proposed, based on the theories of generalized continua. We first use the balance equations of an existing model of micro-cracked bodies, and we then perform a multiscale description in order to determine constitutive laws that account for the growth of the inclusions. We call macroscopic, the description in which the material is considered as a continuum with microstructure, whereas we refer to microscopic scale when one crack is observed at a closer view. We finally use equivalences between both descriptions in order to write the constitutive laws in terms of variables that are characteristic of (i) the geometry of the crack field and (ii) the growth of the inclusions. Such an approach can find, for instance, application in the modeling of expansion due to delayed ettringite formation: we perform numerical simulations using mechanical and geometrical parameters that are characteristic of high strength sulfoaluminate concrete.

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Authors and Affiliations

  1. The University of Calgary, 2500 University Drive NW, Calgary, Alberta, T2N 1N4, Canada

    Malika Bongué Boma

  2. Laboratoire Navier (ENPC/LCPC/CNRS), Ecole des Ponts ParisTech, Université Paris-Est, 6 & 8 av Blaise Pascal, 77455, Marne-la-Vallée, France

    Amina Alaoui

Authors
  1. Malika Bongué Boma
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  2. Amina Alaoui
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Correspondence to Malika Bongué Boma.

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Communicated by Andreas Öchsner.

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Bongué Boma, M., Alaoui, A. A constitutive model for micro-cracked bodies with growing inclusions. Continuum Mech. Thermodyn. 24, 49–61 (2012). https://doi.org/10.1007/s00161-011-0212-y

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  • DOI: https://doi.org/10.1007/s00161-011-0212-y

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