A modified Gurson-type plasticity model at finite strains

formulation, numerical analysis and phase-field coupling

authored by: Fadi Aldakheel, Peter Wriggers, Christian Miehe
Abstract: The modeling of failure in ductile materials must account for complex phenomena at the micro-scale, such as nucleation, growth and coalescence of micro-voids, as well as the final rupture at the macro-scale, as rooted in the work of Gurson (J Eng Mater Technol 99:2–15, 1977). Within a top–down viewpoint, this can be achieved by the combination of a micro-structure-informed elastic–plastic model for a porous medium with a concept for the modeling of macroscopic crack discontinuities. The modeling of macroscopic cracks can be achieved in a convenient way by recently developed continuum phase field approaches to fracture, which are based on the regularization of sharp crack discontinuities, see Miehe et al. (Comput Methods Appl Mech Eng 294:486–522, 2015). This avoids the use of complex discretization methods for crack discontinuities, and can account for complex crack patterns. In this work, we develop a new theoretical and computational framework for the phase field modeling of ductile fracture in conventional elastic–plastic solids under finite strain deformation. It combines modified structures of Gurson–Tvergaard–Needelman GTN-type plasticity model outlined in Tvergaard and Needleman (Acta Metall 32:157–169, 1984) and Nahshon and Hutchinson (Eur J Mech A Solids 27:1–17, 2008) with a new evolution equation for the crack phase field. An important aspect of this work is the development of a robust Explicit–Implicit numerical integration scheme for the highly nonlinear rate equations of the enhanced GTN model, resulting with a low computational cost strategy. The performance of the formulation is underlined by means of some representative examples, including the development of the experimentally observed cup–cone failure mechanism.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): University of Stuttgart
Type: Article
Journal: Computational mechanics
Volume: 62
Pages: 815-833
No. of pages: 19
ISSN: 0178-7675
Publication date: 28.12.2017
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Ocean Engineering, Mechanical Engineering, Computational Theory and Mathematics, Computational Mathematics, Applied Mathematics
Electronic version(s): https://doi.org/10.1007/s00466-017-1530-0 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{0e7e32397fc74e0095af05c807d30617,
title = "A modified Gurson-type plasticity model at finite strains: formulation, numerical analysis and phase-field coupling",
abstract = "The modeling of failure in ductile materials must account for complex phenomena at the micro-scale, such as nucleation, growth and coalescence of micro-voids, as well as the final rupture at the macro-scale, as rooted in the work of Gurson (J Eng Mater Technol 99:2–15, 1977). Within a top–down viewpoint, this can be achieved by the combination of a micro-structure-informed elastic–plastic model for a porous medium with a concept for the modeling of macroscopic crack discontinuities. The modeling of macroscopic cracks can be achieved in a convenient way by recently developed continuum phase field approaches to fracture, which are based on the regularization of sharp crack discontinuities, see Miehe et al. (Comput Methods Appl Mech Eng 294:486–522, 2015). This avoids the use of complex discretization methods for crack discontinuities, and can account for complex crack patterns. In this work, we develop a new theoretical and computational framework for the phase field modeling of ductile fracture in conventional elastic–plastic solids under finite strain deformation. It combines modified structures of Gurson–Tvergaard–Needelman GTN-type plasticity model outlined in Tvergaard and Needleman (Acta Metall 32:157–169, 1984) and Nahshon and Hutchinson (Eur J Mech A Solids 27:1–17, 2008) with a new evolution equation for the crack phase field. An important aspect of this work is the development of a robust Explicit–Implicit numerical integration scheme for the highly nonlinear rate equations of the enhanced GTN model, resulting with a low computational cost strategy. The performance of the formulation is underlined by means of some representative examples, including the development of the experimentally observed cup–cone failure mechanism.",
keywords = "Ductile fracture, GTN model, Numerical algorithms, Phase-field modeling, Porous plasticity",
author = "Fadi Aldakheel and Peter Wriggers and Christian Miehe",
note = "Funding information: Fig. 14 Cup–cone formation in axisymmetric tension test. Contour plots of the hardening variable ? in (a–c); the void volume fraction f in (d, e) and the fracture phase field d in (f–h). Load (force F/initial cross Acknowledgements F. A. wants to thank the late Professor Christian Miehe, whose continuous scientific support and great mentorship will always be remembered. Support for this research was provided by the “German Research Foundation” (DFG) within project WR 19/58-1.",
year = "2017",
month = dec,
day = "28",
doi = "10.1007/s00466-017-1530-0",
language = "English",
volume = "62",
pages = "815--833",
journal = "Computational mechanics",
issn = "0178-7675",
publisher = "Springer Verlag",
number = "4",
}