The numerical analysis of ductile damage and failure in engineering materials is often based on the micromechanical model of Gurson [1,2,3] and is quite sufficient for a large number of applications in solid mechanics. However, numerical studies in the context of the finite-element method demonstrate that, as with other such types of local damage models, the numerical simulation of the initiation and propagation of damage zones is not reliable and strongly mesh-dependent. The numerical problems concern the global load-displacement response as well as the onset, size and orientation of damage zones and thus to the reliability of the obtained results [4,5]. One possible way to overcome these problems with and shortcomings of the local modeling is the application of so-called non-local damage models. In particular, these are based on the introduction of a gradient type evolution equation of the damage variable regarding the spatial distribution of damage and thus the incorporation of a material length scale [6,7,8]. In this work we investigate the (material) stability behaviour of local Gurson-based damage modelling and a recently developed non-local gradient-extension at large deformation in order to be able to model the width and other physical aspects of the localization of the damage and failure process in metallic materials [8]. Such a non-local formulation of a damage model exhibits a multifield problem, which needs a closer look on the formulation of possible criteria for the preservation of the well-posedness of the underlying constitutive equations and thus the stability of the deformation process [9,10,11] and the uniqueness of the obtained solution [9,10,11]. The development and application of a criterion for loss of ellipticity is presented and accounts for the regularisation of the solution obtained by the non-local Gurson model [8,11]. Furthermore the regularizing effects of the non-locality of the damage evolution are investigated and it's effect on the stability of the numerical solution is presented.

Based on the obtained results, we demonstrate the application of new advanced techniques for the modelling and simulation of damage and failure in structures with the finite element method. The results of numerical simulations are presented using displacement-damage coupled element concepts for multiscale and multifield problems [11] together with the outlined gradient dependent non-local extension of the Gurson-model, in order to be able to model the width and other physical aspects of the localization of the damage and failure process in metallic materials.

1

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. Engng. Materials and Technology", 99, 2-15, 1977.

2

Tvergaard, V. and Needleman, A., "Effects of non-local damage in porous plastic solids, Int. J. Solids Structures", 32, 1063-1077, 1995. doi:10.1016/0020-7683(94)00185-Y

3

Needleman A., Tvergaard, V., "An analysis of ductile rupture in notched bars, J. Mech. Phys. Solids", 32, 461-490, 1984. doi:10.1016/0022-5096(84)90031-0

4

Klingbeil, D. and Brocks, W., "Verifikation von Schädigungsmodellen zur Vorhersage von Risswiderstandskurven für verschiedene Probengeometrien und Materialien im Rissinitiierungsbereich und bei großem Risswachstum", Final report Br521/5, Federal Institute for Materials Research and Testing, Berlin, 1988.

5

Besson, J., Steglich, D., Brocks, W., "Modeling of plane strain ductile rupture, International Journal of Plasticity", 19, 1517-1541, 2003. doi:10.1016/S0749-6419(02)00022-0

6

Feucht, M., "Ein gradientenabhängiges Gursonmodell zur Beschreibung duktiler Schädigung mit Entfestigung", Dissertation, Institut für Mechanik, Technische Universität Darmstadt. 1988.

7

Ramaswamy, S., Avaras, N., "Finite element implementation of gradient plasticity models. Part II: Gradient dependent evolutions equations", Comput. Methods Appl. Mech. Engrg., 163, 33-53, 1998. doi:10.1016/S0045-7825(98)00027-9

8

Reusch, F., Klingbeil, D., Svendsen, B., "Local and non-local Gurson-based ductile damage and failure modelling at large deformation", European Journal of Mechanics A/Solids, 22, 779-792, 2003. doi:10.1016/S0997-7538(03)00070-6

9

Benallal, A., Tvergaard, V., <"Nonlocal continuum effects on bifurcation in the plane strain tension-compression test", J. Mech. Phys. Solids, 5, 741-770, 1995. doi:10.1016/0022-5096(95)00002-Z

10

Liebe, T., Steinmann, P., Benallal, A., "Theoretical and computational aspects of a thermodynamically consistent framework for geometrically linear gradient damage", Comp. Meth. Appl. Mech. Engrg., 190, 6555-6657, 2001. doi:10.1016/S0045-7825(01)00250-X

11

Reusch, F., "Entwicklung und Anwendung eines nicht-lokalen Materialmodells zur Simulation duktiler Schädigung", dissertation, Department of Mechanical Engineering, University Dortmund, BAM-Dissertationsreihe", 1, Verlag für neue Wissenschaft GmbH, 2003.

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