Material Failure Process Simulation by Improve Finite Elements with Embedded Discontinuities

Authors: Juárez-Luna Gelacio, Ayala Gustavo, Retama-Velasco Jaime

Abstract:

This paper shows the advantages of the material failure process simulation by improve finite elements with embedded discontinuities, using a new definition of traction vector, dependent on the discontinuity length and the angle. Particularly, two families of this kind of elements are compared: kinematically optimal symmetric and statically and kinematically optimal non-symmetric. The constitutive model to describe the behavior of the material in the symmetric formulation is a traction-displacement jump relationship equipped with softening after reaching the failure surface.

To show the validity of this symmetric formulation, representative numerical examples illustrating the performance of the proposed formulation are presented. It is shown that the non-symmetric family may over or underestimate the energy required to create a discontinuity, as this effect is related with the total length of the discontinuity, fact that is not noticed when the discontinuity path is a straight line.

Keywords: Variational formulation, strong discontinuity, embedded discontinuities, strain localization.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1093566

References:

[1] J. Alfaiate, A. Simone, andL.J. Sluys,"Non-homogeneous displacement jumps in strong embedded discontinuities”,Int J Solids Struct, vol. 40, no. 21, pp. 5799–5817, 2003.
[2] F. Armero, and K.Garikipati,"An analysis of strong discontinuities in multiplicative finite strain plasticity and their relation with the numerical simulation of strain localization in solids”,Int J Solids Struct, vol. 33, no. 20-22, pp. 2863–2885, 1996.
[3] F. Armero, and C. Linder,"New finite elements with embedded strong discontinuities in the finite deformation range”,Comput Methods ApplMechEng, vol. 197, no. 37-40, pp. 3138–3170, 2008.
[4] F. Armero, and C. Linder,"Finite elements with embedded branching”Finite Elem Anal Des,vol. 45, no. 4, pp. 280–293,2009.
[5] F. Armero, and D. Ehrlich,"Numerical modeling of softening hinges in thin Euler-Bernoulli beams”, Comp Struct, vol. 84, no. 10-11, pp. 641–656,2006.
[6] F. Armero, and D. Ehrlich,"Finite element methods for the multi-scale modelling of softening hinge lines in plates at failure”,Comput Methods ApplMechEng, vol.195, no. 13-16, pp.1283–1324, 2006b.
[7] R.Borja, "A Finite element model for strain localization analysis of strongly discontinuous field based on standard Galerkin approximation”, Comput Methods ApplMechEng, vol. 190, pp. 1529–1549, 2000.
[8] L. Contrafatto, M. Cuomo, and G.T. Di Venti,"Finite elements with non-homogeneous embedded discontinuities”,inProc.Eberhardsteiner J et. al. (Eds.), 6th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS, Vienna - Austria, 2012, pp.1–20.
[9] L. Contrafatto, M. Cuomo, and F. Fazio,"An enriched finite element for crack opening and rebar slip in reinforced concrete members”,Int J Fracture, vol. 178, no.1-2, pp. 33–50, 2012.
[10] D. Dias-da Costa, J. Alfaiate, L. Sluys, and E. Júlio,"Towards a generalization of a discrete strong discontinuity approach”,Comput Methods ApplMechEng, vol. 198, pp. 3670–3681, 2009.
[11] D. Dias-da-Costa, J. Alfaiate, LJ. Sluys, and E. Júlio,"A discrete strong discontinuity approach”,EngFractMech, vol.76, no. 9, pp. 1176–1201,2009.
[12] J. Dujc, B. Brank, and A. Ibrahimbegovic,"Quadrilateral finite element with embedded strong discontinuity for failure analysis of solids”,CMES-Comp Model Eng, vol. 69, no.3, pp. 223–260, 2010a.
[13] J. Dujc, B. Brank, A. Ibrahimbegovic, and D. Brancherie, "An embedded crack model for failure analysis of concrete solids”, Comput Concrete, vol. 7, no.4, pp. 331–346, 2010b.
[14] J. Dujc, B. Brank, and A. Ibrahimbegovic, "Stress-hybrid quadrilateral finite element with embedded strong discontinuity for failure analysis of plane stress solids”, Int J Numer Meth Engng, vol. 94, pp. 1075–1098,2013a.
[15] J. Dujc, B. Brank, and A. Ibrahimbegovic,"Embedded discontinuity finite element formulation for failure analysis of planar reinforced concrete beams and frames”,EngStruct, vol. 50, pp. 115–125, 2013b.
[16] D. Ehrlich, and F. Armero,"Finite element methods for the analysis of softening plastic hinges in beams and frames”, ComputMech, vol. 435, no. 4, pp. 237–264, 2005.
[17] A. E. Huespe, J. Oliver, P. J. Sanchez, S. Blanco, and V. Sonzogni,"Strong discontinuity approach in dynamic fracture simulations”,MecánicaComputacional, vol. XXV, pp. 1997–2018, 2006.
[18] M. Jirásek, "Comparative study on finite elements with embedded discontinuities”,Comput Methods ApplMechEng, vol. 188, no. 1-3, pp. 307–330, 2000.
[19] G. Juárez, and G. Ayala,"Variational formulation of the material failure process in solids by embedded discontinuities model”,Numer Methods Partial Differ Equ, vol. 25, no. 1, pp. 26–62, 2009.
[20] G. Juárez-Luna, and G.A. Ayala, "Improvement of some features of finite elements with embedded discontinuities”, EngFractMech, vol. 118, pp. 31–48, 2014.
[21] H. R. Lotfi, and P. Shing,"Embedded representation of fracture in concrete with mixed finite elements”,Int J Numer Methods Eng, vol. 38, no. 8, pp. 1307–1325, 1995.
[22] J. Oliver,"Modelling strong discontinuities in solid mechanics via strain softening constitutive equations”, Part 1: Fundamentals, vol. 39, no. 21, pp. 3575–3600, 1996. Part 2: Numerical simulation. Int J Numer Methods Eng, vol. 39, no. 21, pp. 3601–3623, 1996.
[23] J. Oliver, A. E. Huespe, M. D. G. Pulido, and E. Chaves,"From continuum mechanics to fracture mechanics: the strong discontinuity approach”,EngFractMech, vol. 69, no. 2, pp. 113–136, 2002.
[24] J. Oliver, A. E. Huespe, and E. Samaniego, "A study on finite elements for capturing strong discontinuities”,Int J Numer Methods Eng, vol. 56, no. 14, pp. 2135–2161, 2003.
[25] J. Oliver, A. E. Huespe, S. Blanco, and D. L. Linero,"Stability and robustness issues in numerical modeling of material failure with the strong discontinuity approach”,Comput Methods ApplMechEng, vol. 195no. 52, pp. 7093–7114,2006.
[26] M. Ortiz, Y. Leroy, and A. Needleman,"A finite element method for localized failure analysis”,Comput Methods ApplMechEng, vol. 61, no. 2, pp. 189–214, 1987.
[27] J. M. Sancho, J. Planas, DA. Cendón, E. Reyes, and J. C.Gálvez,"An embedded crack model for finite element analysis of concrete fracture”, EngFractMech, vol. 74, no. 1-2, pp. 75–86, 2007.
[28] J. C. Simo, and J. Ju,"Strain and stress based continuum damage models, I. Formulation”,Int J Solids Struct, vol. 23, no. 7, pp. 821–840, 1987.
[29] J. C. Simo, J. Oliver, and F. Armero, "An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids”, ComputMech, vol. 12, no. 5, pp. 277–296, 1993.
[30] J. C. Simo, and J. Oliver, "A new approach to the analysis and simulation of strain softening in solids”,in Proc: Bazant ZP et. al. (Eds.), Fracture and Damage in Quasibrittle Structures, E. and F.N. Spon, London, 1994, pp. 25–39.
[31] G. N. Wells,and L. J. Sluys, ”A new method for modelling cohesive cracks using finite elements”Int J Numer Methods Eng, vol. 50, no. 12, pp. 2667–2682, 2001.