UMAT

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

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References in zbMATH (referenced in 10 articles )

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  1. Bellini, Chiara; Federico, Salvatore: Green-Naghdi rate of the Kirchhoff stress and deformation rate: the elasticity tensor (2015)
  2. Li, Huan; Pan, Xiaofei; Yuan, Huang: A nonlocal treatment technique based on the background cell concept for micro-mechanical damage modeling (2015)
  3. Duddu, Ravindra; Waisman, Haim: A nonlocal continuum damage mechanics approach to simulation of creep fracture in ice sheets (2013)
  4. 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)
  5. Bažant, Zdeněk P.; Gattu, Mahendra; Vorel, Jan: Work conjugacy error in commercial finite-element codes: its magnitude and how to compensate for it (2012)
  6. 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)
  7. 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)
  8. 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)
  9. Soare, S.; Yoon, J. W.; Cazacu, O.; Barlat, F.: Applications of a recently proposed anisotropic yield function to sheet forming (2007)
  10. Abu Al-Rub, Rashid K.; Voyiadjis, George Z.: A direct finite element implementation of the gradient-dependent theory (2005)