A Gradient-Enhanced Damage Model for Viscoplastic Thin-shell Structures

  • An Danh NguyenEmail author
  • Marcus Stoffel
  • Dieter Weichert
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 15)


A finite element model of non-local damage viscoplasticity for dynamic analysis of thin-walled shell structures is presented. To take void nucleation and growth into account, a non-local implicit gradient formulation is employed. The free energy function includes both a non-local damage variable on the mid-surface of shell structures and a local one in shell space.Local constitutive laws considering viscoplastic behavior,isotropic hardening and isotropic ductile damage leading tosoftening are used. The performance of the proposed approach is demonstrated through the numerical simulation of shock-wave loaded structures


Non-local damage Viscoplasticity Non-linear shells Finite element 


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  1. 1.
    FEAP-8.2.k Finite Element Analysis Program. University of CaliforniaGoogle Scholar
  2. 2.
    Stoffel, M. An experimental method for validating mechanical models. Habilitation thesis RWTH-Aachen. (2007)Google Scholar
  3. 3.
    Stoffel, M.: Evolution of plastic zones in dynamically loaded plates using different elastic-viscoplastic laws. Int. J. Sol. Struc. 41(24–25), 6813–6830 (2004)CrossRefGoogle Scholar
  4. 4.
    Dimitrijevic, B.J., Hackl, K.: A method for gradient enhancement of continuum damage models. Tech. Mech. 28(1), 43–52 (2008)Google Scholar
  5. 5.
    Simo, J.C., Fox, D.D.: On a stress resultant geometrically exact shell model. Part I. Formulation and optimal parametrization. Comput. Methods Appl. Mech. Eng. 72, 267–304 (1989)CrossRefGoogle Scholar
  6. 6.
    Simo, J.C., Rifai, M.S., Fox, D.D.: On stress resultant geometrically exact shell model. Part VI. Conserving algorithms for non-linear dynamics. Int. J. Numer. Methods Eng. 34, 117–164 (1992)CrossRefGoogle Scholar
  7. 7.
    Simo, J.C., Tarnow, N.: A new energy and momentum conserving algorithm for the non-linear dynamics of shells. Int. J. Numer. Methods Eng. 37, 2527–2549 (1994)CrossRefGoogle Scholar
  8. 8.
    Brank, B., Briseghella, L., Tonello, N., Damjanic, F.B.: On non-linear dynamics of shells: implementation of energy-momentum conserving algorithm for a finite rotation shell model. Int. J. Numer. Methods Eng. 42, 409–442 (1998)CrossRefGoogle Scholar
  9. 9.
    Velde, J., Kowalsky, U., Zümendorf, T., Dinkler, D.: 3D-FE-analysis of CT-speciemens including viscoplastic material behaviour and nonlocal damage. Comp. Mat. Sci. 46, 532–357 (2009)CrossRefGoogle Scholar
  10. 10.
    Chaboche, J.L., Rousselier, G.: On the plastic and viscoplastic constitutive equations–Part I: rules developed with internal variable concept. J. Pres. Vess. Tech. 105, 153–158 (1983)CrossRefGoogle Scholar
  11. 11.
    Chaboche, J.L., Rousselier, G.: On the Plastic and Viscoplastic Constitutive Equations–Part II: Application of Internal Variable Concepts to the 316 Stainless Steel. J. Pres. Vess. Tech. 105, 159–164 (1983)CrossRefGoogle Scholar
  12. 12.
    Gurson, A.L.: Continuum theory of ductile rupture by void nucleation and growth: Part I–Yield criteria and flow rules for porous ductile media. J. Eng. Mat. Tech. 99, 2–15 (1977)CrossRefGoogle Scholar
  13. 13.
    Tvergaard, V., Needleman, A.: Analysis of cup-cone fracture in a round tensile bar. Act. Metal. 32, 157–169 (1984)CrossRefGoogle Scholar
  14. 14.
    Lemaitre, J., Desmorat, R., Sauzay, M.: Anisotropic damage law of evolution. Eur. J. Mech. A/Solids 19(2), 187–208 (2000)CrossRefGoogle Scholar
  15. 15.
    Nguyen, A.D., Stoffel, M., Weichert, D.: A one-dimensional dynamic analysis of strain-gradient viscoplasticity. Eur. J. Mech. A/Solids 29, 1042–1050 (2010)CrossRefGoogle Scholar
  16. 16.
    Aifantis, E.C.: On the role of gradients in localization of deformation and fracture. Int. J. Eng. 30(30), 1279–1299 (1992)CrossRefGoogle Scholar
  17. 17.
    Nguyen, Q.S., Andrieux, S.: The non-local generalzed standard approach: a consistent gradient theory. Compt. Rend. Meca. 333, 139–145 (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • An Danh Nguyen
    • 1
    Email author
  • Marcus Stoffel
    • 1
  • Dieter Weichert
    • 1
  1. 1.Institute of General MechanicsAachenGermany

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