A straightforward numerical technique for finite element implementation of non-local gradient-dependent continuum damage mechanics theories. This paper presents a direct algorithm to implement non-local gradient-enhanced damage mechanics theories in the existing finite element codes with minor modifications and without the need to formulate a higher-order element. This method extends the algorithm of R. K. Abu Al-Rub and G. Z. Voyiadjis [Int. J. Numer. Methods Eng. 63, No. 4, 603–629 (2005; Zbl 1140.74545)] to gradient-dependent damage theories and to three-dimensional (3D) problems. The presented algorithm is implemented in the well-known finite element code Abaqus via the user material subroutine UMAT. The potential of the proposed numerical algorithm for non-local gradient-enhanced damage theories in eliminating mesh-dependent simulations is validated by conducting various numerical tests of the localised damage

References in zbMATH (referenced in 13 articles )

Showing results 1 to 13 of 13.
Sorted by year (citations)

  1. Jafaripour, Mostafa; Taheri-Behrooz, Fathollah: Creep behavior modeling of polymeric composites using Schapery model based on micro-macromechanical approaches (2020)
  2. de Geus, T. W. J.; Vondřejc, J.; Zeman, J.; Peerlings, R. H. J.; Geers, M. G. D.: Finite strain FFT-based non-linear solvers made simple (2017)
  3. Bellini, Chiara; Federico, Salvatore: Green-Naghdi rate of the Kirchhoff stress and deformation rate: the elasticity tensor (2015)
  4. Li, Huan; Pan, Xiaofei; Yuan, Huang: A nonlocal treatment technique based on the background cell concept for micro-mechanical damage modeling (2015)
  5. Duddu, Ravindra; Waisman, Haim: A nonlocal continuum damage mechanics approach to simulation of creep fracture in ice sheets (2013)
  6. Wang, Xiaodong; Li, Fei; Yang, Quan; He, Anrui: FEM analysis for residual stress prediction in hot rolled steel strip during the run-out table cooling (2013)
  7. Bažant, Zdeněk P.; Gattu, Mahendra; Vorel, Jan: Work conjugacy error in commercial finite-element codes: its magnitude and how to compensate for it (2012)
  8. Kan, Q. H.; Kang, G. Z.; Guo, S. J.: Finite element implementation of a super-elastic constitutive model for transformation ratchetting of NiTi alloy (2012)
  9. Fraś, T.; Nowak, Z.; Perzyna, P.; Pȩcherski, R. B.: Identification of the model describing viscoplastic behaviour of high strength metals (2011)
  10. Abu Al-Rub, Rashid K.; Darabi, Masoud K.; Masad, Eyad A.: A straightforward numerical technique for finite element implementation of non-local gradient-dependent continuum damage mechanics theories (2010)
  11. Li, M.; Lou, X. Y.; Kim, J. H.; Wagoner, R. H.: An efficient constitutive model for room-temperature, low-rate plasticity of annealed Mg AZ31B sheet (2010)
  12. Soare, S.; Yoon, J. W.; Cazacu, O.; Barlat, F.: Applications of a recently proposed anisotropic yield function to sheet forming (2007)
  13. Abu Al-Rub, Rashid K.; Voyiadjis, George Z.: A direct finite element implementation of the gradient-dependent theory (2005)