An orthotropic plasticity model at finite strains with plasticity-induced evolution of orthotropy based on a covariant formulation

Manfred Hannes Ulz*, Christian Celigoj

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We present a rate-independent model for isotropic elastic–orthotropic plastic material behaviour in a hyper-elasto-plastic setting at finite strains, which is based on a covariant formulation that includes plastic-deformation-induced evolution of orthotropy. The model relies on a treatment by Lu and Papadopoulos, who made use of the postulate of covariance for an anisotropic elasto-plastic solid and derived constitutive equations of evolving anisotropies at finite strains. The latter is tantamount to the notion of plastic spin. This treatment does not rely on a multiplicative decomposition of the deformation gradient. We test our model on in-plane sheet-metal forming processes, which are governed by the evolution of pre-existing preferred material orientations. Hence, we advocate an orthotropic yield criterion directed by evolving structural tensors to describe this material behaviour. Our formulation yields two key findings. Firstly, the covariant formulation of plasticity yields suitable evolution equations for the structural tensors characterising the symmetry group of the orthotropic yield function. Secondly, the constitutive equations for the plastic variables and the structural tensors, which are both symmetric second-order tensors, give results that are in good agreement with experimental and numerical findings from in-plane sheet forming processes.

Original languageEnglish
Article number115567
Number of pages32
JournalComputer Methods in Applied Mechanics and Engineering
Publication statusPublished - 1 Nov 2022


  • Postulate of covariance
  • Orthotropy
  • Green/Naghdi plasticity
  • Multiplicative plasticity
  • Evolving anisotropy
  • Plastic spin

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mechanics

Fields of Expertise

  • Advanced Materials Science

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