Acta Mechanica

, Volume 230, Issue 5, pp 1855–1868 | Cite as

On the thermo-mechanical coupling of the Bammann plasticity-damage internal state variable model

  • Nikolay DimitrovEmail author
  • Yucheng Liu
  • M. F. Horstemeyer
Original Paper


In this study, thermodynamic incompatibility issues of the thermo-mechanical coupling of the Bammann-temperature-dependent plasticity-damage internal state variable (ISV) model are investigated. The exclusion of the thermal expansion phenomena from the Helmholtz free energy, as assumed in the model, is proven to contradict the First and Second Law of Thermodynamics, as well as the omnipresence principle. Four different approaches are discussed to address those issues, and the inclusion of the thermal expansion as a dependent variable in the Helmholtz free energy is considered the most appropriate and efficient. Based on these findings, a multiphysics ISV theory that couples the elasto-visco-plasticity-damage model of Bammann with thermal expansion is presented in which the kinematics, thermodynamics, and kinetics are internally consistent. Other material models may benefit from the findings of this study and apply similar modifications with their thermo-mechanical couplings.


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  1. 1.
    Bammann, D.J.: Modelling the temperature and strain rate dependent large deformation of metals. Appl. Mech. Rev. 43, 312–319 (1990)CrossRefGoogle Scholar
  2. 2.
    Francis, D.K., Bouvard, J.L., Hammi, Y., Horstemeyer, M.F.: Formulation of a damage internal state variable model for amorphous glassy polymers. Int. J. Solids Struct. 51, 2765–2776 (2014). CrossRefGoogle Scholar
  3. 3.
    Guan, L., Tang, G., Chu, P.K.: Recent advances and challenges in electroplastic manufacturing processing of metals. J. Mater. Res. 25, 1215–1224 (2010). CrossRefGoogle Scholar
  4. 4.
    Horstemeyer, M.F.: Integrated Computational Materials Engineering (ICME) for Metals. Wiley, Hoboken (2012)CrossRefGoogle Scholar
  5. 5.
    Bammann, D.J., Chiesa, M.L., Johnson, G.C.: Modeling large deformation and failure in manufacturing processes. Theor. Appl. Mech. 9, 359–375 (1996)Google Scholar
  6. 6.
    Horstemeyer, M.F., Bammann, D.J.: Historical review of internal state variable theory for inelasticity. Int. J. Plast. 26, 1310–1334 (2010). CrossRefzbMATHGoogle Scholar
  7. 7.
    Bammann, D.J.: An internal variable model of viscoplasticity. In: Aifantis, E.C., Davison, L., (eds.) Media with Microstructures and Wage Propagation. Pergamon Press. International Journal of Engineering Science, 8–10, pp. 1041 (1984)Google Scholar
  8. 8.
    Bammann, D.J., Aifantis, E.C.: A model for finite deformation plasticity. Acta Mech. 69, 97–117 (1987)CrossRefzbMATHGoogle Scholar
  9. 9.
    Horstemeyer, M.F., Lathrop, J., Gokhale, A.M., Dighe, M.: Modeling stress state dependent damage evolution in a cast Al–Si–Mg aluminum alloy. Theor. Appl. Fract. Mech. 33, 31–47 (2000)CrossRefGoogle Scholar
  10. 10.
    Bammann, D.J., Solanki, K.N.: On kinematic, thermodynamic, and kinetic coupling of a damage theory for polycrystalline material. Int. J. Plast. 26, 775–793 (2010). CrossRefzbMATHGoogle Scholar
  11. 11.
    Walton, C.A., Horstemeyer, M.F., Martin, H.J., Francis, D.K.: Formulation of a macroscale corrosion damage internal state variable model. Int. J. Solids Struct. 51, 1235–1245 (2014). CrossRefGoogle Scholar
  12. 12.
    Coleman, B.D., Gurtin, M.E.: Thermodynamics with internal state variables. J. Chem. Phys. 47, 597–613 (1967). CrossRefGoogle Scholar
  13. 13.
    Freed, I.D., Chaboche, J.L., Walker, K.P.: A viscoplastic theory with thermodynamic considerations. Acta Mech. 90, 155–174 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Lemaitre, J.: A continuous damage mechanics model for ductile fracture. J. Eng. Materi. Technol. 107, 83–89 (2013)CrossRefGoogle Scholar
  15. 15.
    Maugin, G.A.: Continuum Mechanics of Electromagnetic Solids. Elsevier, New York City (1988)zbMATHGoogle Scholar
  16. 16.
    Rice, J.R.: Inelastic constitutive relations for solids: an internal-variable theory and its application to metal plasticity. J. Mech. Phys. Solids. 19, 433–455 (1971)CrossRefzbMATHGoogle Scholar
  17. 17.
    Follansbee, P.S., Kocks, U.F.: A constitutive description of the deformation of copper based on the use of the mechanical threshold stress as an internal state variable. Acta Metall. 36, 81–93 (1988)CrossRefGoogle Scholar
  18. 18.
    Hart, E.W.: Constitutive relations for the nonelastic deformation of metals. J. Eng. Mater. Technol. 98, 193–202 (1976)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  • Nikolay Dimitrov
    • 1
    Email author
  • Yucheng Liu
    • 1
    • 2
  • M. F. Horstemeyer
    • 1
    • 2
  1. 1.Department of Mechanical EngineeringMississippi State UniversityMississippi StateUSA
  2. 2.Center for Advanced Vehicular SystemsMississippi State UniversityMississippi StateUSA

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