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Periodic homogenization in scalar Hencky plasticity

  • Gilles A. Francfort
  • Alessandro Giacomini
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Abstract

This paper investigates the periodic homogenization of a two-phase elasto-plastic material in the framework of Γ-convergence. It establishes the link between the homogenized functional and that which was previously obtained in [12] in the context of two-scale convergence. Although there is no gap between the two formulations and that involving two-scale has the hallmark of a (two-scale) elasto-plastic problem, we are unable to positively ascertain the elasto-plastic character of the homogenized energy except in a one-dimensional setting.

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Cite

BibTeXRIS
BibTeX
@misc{francfort2026periodic,
  title = {{Periodic homogenization in scalar Hencky plasticity}},
  author = {Gilles A. Francfort and Alessandro Giacomini},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.31404},
  eprint = {2609.31404},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.31404},
}
RIS
TY  - UNPB
TI  - Periodic homogenization in scalar Hencky plasticity
AU  - Gilles A. Francfort
AU  - Alessandro Giacomini
PY  - 2026
DA  - 2026/09/25
PB  - arXiv
DO  - 10.48550/arxiv.2609.31404
UR  - https://arxiv.org/abs/2609.31404
AB  - This paper investigates the periodic homogenization of a two-phase elasto-plastic material in the framework of Γ-convergence. It establishes the link between the homogenized functional and that which was previously obtained in [12] in the context of two-scale convergence. Although there is no gap between the two formulations and that involving two-scale has the hallmark of a (two-scale) elasto-plastic problem, we are unable to positively ascertain the elasto-plastic character of the homogenized energy except in a one-dimensional setting.
ER  -