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A Time-Incremental Eshelby-Based Homogenization Scheme for Viscoelastic Heterogeneous Materials

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Abstract

A time-incremental Eshelby-based homogenization scheme for Maxwellian heterogeneous materials is proposed and discussed. This is based on the exact solution of the heterogeneous Eshelby ellipsoidal inclusion problem obtained in the time domain. In contrast with hereditary methods, the effective behavior and the evolution laws of the averaged stresses per phase are solved incrementally in the time domain without the need of inverse Laplace or Laplace–Carson transforms. This is made through a time differential equation to exactly solve a volume term in the integral equation that was generally approximated in previous internal variable methods. The present formulation works for any arbitrary anisotropic ellipsoidal Maxwellian inclusion embedded in an isotropic Maxwellian matrix without any other restrictive assumptions. In order to show the interest of the present approach, a Mori–Tanaka homogenization scheme is applied to two-phase composites using the developed strain rate concentration equations. The results are reported and discussed in comparisons with other existing methods, including hereditary approaches and more recent internal variable approaches, in order to show the efficiency of the present time-incremental homogenization scheme.

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Authors and Affiliations

  1. Laboratoire d’Etude des Microstructures et de Mécanique des Matériaux, UMR CNRS 7239, Université de Lorraine, 57045, Metz, France

    Stéphane Berbenni

  2. Laboratoire de Mécanique Biomécanique Polymères Structures, Ecole Nationale Ingénieurs de Metz, 57078, Metz, France

    Hafid Sabar

Authors
  1. Stéphane Berbenni
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  2. Hafid Sabar
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Correspondence to Stéphane Berbenni .

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Editors and Affiliations

  1. Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario, Canada

    Shaker A. Meguid

  2. Mechanical and Aerospace Engineering, Rutgers University, New Brunswick, New Jersey, USA

    George J Weng

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Berbenni, S., Sabar, H. (2018). A Time-Incremental Eshelby-Based Homogenization Scheme for Viscoelastic Heterogeneous Materials. In: Meguid, S., Weng, G. (eds) Micromechanics and Nanomechanics of Composite Solids. Springer, Cham. https://doi.org/10.1007/978-3-319-52794-9_12

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  • DOI: https://doi.org/10.1007/978-3-319-52794-9_12

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