Anisotropic subloading surface Cam-clay plasticity model with rotational hardening: Deformation gradient-based formulation for finite strain

Yuki Yamakawa, Koichi Hashiguchi, Tomohiro Sasaki, Masaki Higuchi, Kiyoshi Sato, Tadashi Kawai, Tomohiro Machishima, Takuya Iguchi

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


This study is aimed at developing an anisotropic elastoplastic constitutive model for geomaterials at finite strain and its stress calculation algorithm based on the fully implicit return-mapping scheme. The Cam-clay plasticity model is adopted as a specific prototype model of geomaterials. As a pertinent representation of deformation-induced anisotropy in geomaterials, nonlinear rotational hardening is incorporated into the model in a theoretically reasonable manner by introducing the dual multiplicative decompositions of the deformation gradient tensor. In addition to the usual decomposition into elastic and plastic parts, the plastic part is decomposed further into a part contributing to the rotational hardening and a remainder part. The former part leads to a back stress ratio tensor related to the rotational hardening via a hyperelastic-type hardening rule. The constitutive theory is thereby formulated on proper intermediate configurations entirely in terms of deformation-like tensorial variables possessing invariance property, without resort to any objective rates of stress or stress-like variables. Combining the Cam-clay plasticity with the concept of subloading surface, a class of unconventional plasticity, enables the model to be capable of reproducing complex hardening/softening accompanied by volumetric contractive/dilative responses. Basic characteristics and predictive capability of the proposed model, as well as the accuracy of the developed numerical scheme, are verified through several numerical examples including monotonic and cyclic loadings.

Original languageEnglish
Pages (from-to)2321-2370
Number of pages50
JournalInternational Journal for Numerical and Analytical Methods in Geomechanics
Issue number16
Publication statusPublished - 2021 Nov


  • anisotropy
  • cam-clay plasticity
  • finite strain
  • return-mapping algorithm
  • rotational hardening
  • subloading surface concept

ASJC Scopus subject areas

  • Computational Mechanics
  • Materials Science(all)
  • Geotechnical Engineering and Engineering Geology
  • Mechanics of Materials


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