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Failure modes and effective strength of two-phase materials determined by means of numerical limit analysis

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Summary

In the most general case, composites composed of two materials, exhibiting a matrix-inclusion morphology, can be described by three phases: the matrix phase, the inclusion phase, and the interface between the inclusion and the matrix. In order to relate effective material properties to the matrix-inclusion behavior and the morphology, i.e., to the arrangement of the inclusions within the matrix phase, analytical and/or numerical schemes may be employed. Regarding effective strength properties, averaging schemes used, e.g., for upscaling elastic and viscoelastic properties are not able to capture the localized mode of material failure and do not provide information about the failure modes within the material. In this paper, the application of limit analysis to two-phase materials subjected to uniaxial/biaxial loading is proposed, giving access to the respective material strength and the corresponding failure modes. Based on a discretized form of limit analysis, different strength properties are assigned to the matrix, the inclusion, and the interface. The solution of the underlying optimization problem arising from the respective upper- and lower-bound formulation is based on second-order-cone-programming (SOCP). The presented upscaling scheme is used to illustrate the finer-scale origin of frequently observed failure and degradation scenaria in matrix-inclusion materials, highlighting the effect of strength properties, morphology, and interface degradation on the effective strength of the composite material.

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Authors and Affiliations

  1. Institute for Mechanics of Materials and Structures, Vienna University of Technology, Karlsplatz 13, 1040, Vienna, Austria

    J. Füssl, J. Eberhardsteiner & H. A. Mang

  2. Fachgebiet Computational Mechanics, Technical University of Munich, Munich, Germany

    R. Lackner

Authors
  1. J. Füssl
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  2. R. Lackner
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  3. J. Eberhardsteiner
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  4. H. A. Mang
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Correspondence to J. Füssl.

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Dedicated to Professor Franz Ziegler on the occasion of his 70th birthday

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Füssl, J., Lackner, R., Eberhardsteiner, J. et al. Failure modes and effective strength of two-phase materials determined by means of numerical limit analysis. Acta Mech 195, 185–202 (2008). https://doi.org/10.1007/s00707-007-0550-9

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  • DOI: https://doi.org/10.1007/s00707-007-0550-9

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