Applied Mathematics and Mechanics

, Volume 28, Issue 9, pp 1145–1152 | Cite as

Coupled viscoplasticity damage constitutive model for concrete materials

  • Liu Chang-chun  (刘长春)Email author
  • Lü He-xiang  (吕和祥)
  • Guan Ping  (关萍)


A coupled viscoplasticity damage constitutive model for concrete materials is developed within the framework of irreversible thermodynamics. Simultaneously the Helmholtz free energy function and a non-associated flow potential function are given, which include the internal variables of kinematic hardening, isotropic hardening and damage. Results from the numerical simulation show that the model presented can describe the deformation properties of the concrete without the formal hypotheses of yield criterion and failure criteria, such as the volume dilatancy under the compression, strain-rate sensitivity, stiffness degradation and stress-softening behavior beyond the peak stress which are brought by damages and fractures. Moreover, we could benefit from the application of the finite element method based on this model under complex loading because of not having to choose different constitutive models based on the deformation level.

Key words

concrete viscoplasticity damage irreversible thermodynamics 

Chinese Library Classification

TU452 O344.3 

2000 Mathematics Subject Classification

73B05 73B30 73E60 


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Copyright information

© Editorial Committee of Appl. Math. Mech. 2007

Authors and Affiliations

  • Liu Chang-chun  (刘长春)
    • 1
    Email author
  • Lü He-xiang  (吕和祥)
    • 1
  • Guan Ping  (关萍)
    • 2
  1. 1.State Key Laboratory of Structural Analysis for Industrial EquipmentDalian University of TechnologyDalianP. R. China
  2. 2.Dalian UniversityDalianP. R. China

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