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Use of Fabric Tensors in Continuum Damage Mechanics of Solids with Micro-cracks

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Handbook of Damage Mechanics

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Abstract

In this chapter, a new formulation is presented to link continuum damage mechanics with the concept of fabric tensors within the framework of classical elasticity theory. A fourth-rank damage tensor is used and its exact relationship to the fabric tensors is illustrated. A model of damage mechanics for directional data is formulated using fabric tensors. The applications of the new formulation to micro-crack distributions are well illustrated in two solved examples. In the first example, a micro-crack distribution is considered with its data represented by a circular histogram. The values of the fabric tensors and damage tensor are calculated in this case. In the second example, two sets of parallel micro-crack distributions with two different orientations are investigated.

A general hypothesis for damage mechanics is postulated. It is seen that the two available hypotheses of elastic strain equivalence and elastic energy equivalence may be obtained as special cases of the postulated general hypothesis. This general hypothesis is then used to derive the sought relationship between the damage tensor and fabric tensors. Finally, the evolution of the damage tensor is derived in a mathematically consistent manner that is based on sound thermodynamic principles.

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Authors and Affiliations

  1. Civil and Environmental Engineering Department, Louisiana State University, Baton Rouge, LA, 70803, USA

    George Z. Voyiadjis & Peter I. Kattan

  2. Civil Engineering Department, Applied Science University, Shafa Badran, Amman, 11931, Jordan

    Ziad N. Taqieddin

Authors
  1. George Z. Voyiadjis
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  2. Peter I. Kattan
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  3. Ziad N. Taqieddin
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Correspondence to George Z. Voyiadjis .

Editor information

Editors and Affiliations

  1. Department of Civil and Environmental Engineering, Louisiana State University, Baton Rouge, Louisiana, USA

    George Z. Voyiadjis

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Voyiadjis, G.Z., Kattan, P.I., Taqieddin, Z.N. (2014). Use of Fabric Tensors in Continuum Damage Mechanics of Solids with Micro-cracks. In: Voyiadjis, G. (eds) Handbook of Damage Mechanics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8968-9_3-1

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  • DOI: https://doi.org/10.1007/978-1-4614-8968-9_3-1

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  • Online ISBN: 978-1-4614-8968-9

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