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Evolution of Fabric Tensors in Continuum Damage Mechanics of Solids with Micro-cracks: Studying the Effects of Length and Orientation

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Handbook of Damage Mechanics

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Abstract

In this chapter, the evolution of fabric tensors, based on micro-crack distributions, is formulated within the framework of thermodynamics. The exact definition of fabric tensors based on micro-crack distributions is presented. This definition is seen to incorporate both the orientation and length of a micro-crack. In this regard, the micro-crack distribution is assumed to be radially symmetric, i.e., symmetric about a line through the origin. A thermodynamic force that is associated with the fabric tensor is defined and utilized in the derivation of the evolution equations. The application of the theory to the case of uniaxial tension is derived and presented.

Specific uncoupled equations for the evolution of the length and orientation of micro-cracks are also derived. In this regard, some interesting results are obtained. It is concluded that the micro-crack length and orientation cannot evolve simultaneously for the same set of micro-cracks. However, two different sets of micro-cracks may be considered in the same representative volume element (RVE) where in one set the micro-crack length evolves, while in the second set the micro-crack orientation evolves.

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Authors and Affiliations

  1. Civil and Environmental Engineering Department, Louisiana State University, 3508B Patrick F. Taylor Hall, Baton Rouge, LA, 70803, USA

    George Z. Voyiadjis & Peter I. Kattan

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

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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). Evolution of Fabric Tensors in Continuum Damage Mechanics of Solids with Micro-cracks: Studying the Effects of Length and Orientation. In: Voyiadjis, G. (eds) Handbook of Damage Mechanics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8968-9_4-1

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  • DOI: https://doi.org/10.1007/978-1-4614-8968-9_4-1

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