A generalized thermodynamic approach for modeling nonlinear hardening behaviors

Yuzhong Xiao, Jun Chen*, Jian Cao

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

38 Scopus citations


The capability of accurately modeling nonlinear behaviors is essential to simulation-based engineering. Giving better descriptions of actual constitutive behaviors, nonlinear kinematic hardening models are frequently considered as an ad hoc approach by directly prescribing the hardening laws. The necessity has been recognized for accommodating this effective yet empirical methodology into extreme principles which theoretically underlie the derivation of evolutionary equations in irreversible dissipative processes. In contrast to the published efforts, this paper presents a systematic approach for characterizing both nonlinear kinematic and isotropic hardening behaviors of rate-independent polycrystalline metals. With the modified principle of maximum mechanical dissipation and the method of Lagrangian multipliers, the typical rate-independent constitutive laws are derived. Enlightening decompositions of the mechanical dissipation and its implications are discussed. Control functions are introduced to provide useful specifications about formulating hardening models. In contrast to the ad hoc origins, the relationship of many existing hardening models (both nonlinear kinematic and isotropic types) has been clarified through the unified framework. Moreover both saturating and non-saturating behaviors of the two hardening types can be properly modeled and numerical implementations are presented. Particularly permanent softening can be automatically given by non-saturating kinematic hardening modeling along with other features of cyclic loading. With this approach this phenomenon is explained from the viewpoint of energy and reproduced with only one back-stress and single yield surface. Finally comparisons between the methodology in this work and other classical theories are given to clarify the relationships and analogies. Pressure-dependent yield is also discussed to show the generality of the approach.

Original languageEnglish (US)
Pages (from-to)102-122
Number of pages21
JournalInternational journal of plasticity
StatePublished - Nov 2012


  • Flow rule
  • Maximum dissipation principle
  • Metal plasticity
  • Nonlinear kinematic hardening
  • Thermodynamic of solids

ASJC Scopus subject areas

  • General Materials Science
  • Mechanics of Materials
  • Mechanical Engineering


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