<p>This paper presents a theoretical procedure for obtaining the dissipation function for anisotropic rigid-plastic materials, the yielding of which is governed by the Barlat and co-workers-like plasticity criteria (Int J Plast 21:1009–1039, 2005. <a href="https://doi.org/10.1016/j.ijplas.2004.06.004">https://doi.org/10.1016/j.ijplas.2004.06.004</a>) incorporating several linear transformations of the stress in generic isotropic plasticity models, extending the proposal of Karafillis and Boyce (J Mech Phys Solids 41:1859–1886, 1993. <a href="https://doi.org/10.1016/0022-5096(93)90073-o">https://doi.org/10.1016/0022-5096(93)90073-o</a>). The underlying isotropic yield criterion can be very general including possible Lode angle effects in the material behaviour. The seeked dissipation function is needed for the construction of the macroscopic behavior of voided materials when it is for instance combined to appropriate representative volume elements of these materials and associated kinematically admissible velocity fields satisfying uniform boundary conditions at their boundary in the spirit of the Gurson’s approach (J Eng Mater Technol 99:2–15, 1977. <a href="https://doi.org/10.1115/1.3443401">https://doi.org/10.1115/1.3443401</a>) to ductile fracture.</p>

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On the dissipation function for anisotropic porous solids with matrix behaviour based on several linear transformations

  • A. Benallal,
  • A. R. Ferreira

摘要

This paper presents a theoretical procedure for obtaining the dissipation function for anisotropic rigid-plastic materials, the yielding of which is governed by the Barlat and co-workers-like plasticity criteria (Int J Plast 21:1009–1039, 2005. https://doi.org/10.1016/j.ijplas.2004.06.004) incorporating several linear transformations of the stress in generic isotropic plasticity models, extending the proposal of Karafillis and Boyce (J Mech Phys Solids 41:1859–1886, 1993. https://doi.org/10.1016/0022-5096(93)90073-o). The underlying isotropic yield criterion can be very general including possible Lode angle effects in the material behaviour. The seeked dissipation function is needed for the construction of the macroscopic behavior of voided materials when it is for instance combined to appropriate representative volume elements of these materials and associated kinematically admissible velocity fields satisfying uniform boundary conditions at their boundary in the spirit of the Gurson’s approach (J Eng Mater Technol 99:2–15, 1977. https://doi.org/10.1115/1.3443401) to ductile fracture.