×

zbMATH — the first resource for mathematics

Multi-scale computational model for failure analysis of metal frames that includes softening and local buckling. (English) Zbl 1227.74067
Summary: In this work we present a new modelling paradigm for computing the complete failure of metal frames by combining the stress-resultant beam model and the shell model. The shell model is used to compute the material parameters that are needed by an inelastic stress-resultant beam model; therefore, we consider the shell model as the meso-scale model and the beam model as the macro-scale model. The shell model takes into account elastoplasticity with strain-hardening and strain-softening, as well as geometrical nonlinearity (including local buckling of a part of a beam). By using results of the shell model, the stress-resultant inelastic beam model is derived that takes into account elastoplasticity with hardening, as well as softening effects (of material and geometric type). The beam softening effects are numerically modelled in a localized failure point by using beam finite element with embedded discontinuity. The original feature of the proposed multi-scale (i.e. shell-beam) computational model is its ability to incorporate both material and geometrical instability contributions into the stress-resultant beam model softening response. Several representative numerical simulations are presented to illustrate a very satisfying performance of the proposed approach.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74R20 Anelastic fracture and damage
74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
Software:
ABAQUS; AceFEM; AceGen
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Fajfar, P.; Dolšek, M.; Marušić, D.; Stratan, A., Pre- and post-test mathematical modelling of a plan-asymmetric reinforced concrete frame building, Earthquake engrg. struct. dyn., 35, 1359-1379, (2006)
[2] E.L. Wilson, Three dimensional static and dynamic analysis of structures, CSi, 2002.
[3] G.H. Powell, Nonlinear structural analysis by computer code INSA, UC Berkeley reports SEMM 86-15, 1986.
[4] Ibrahimbegovic, A., Nonlinear solid mechanics: theoretical formulations and finite element solution methods, (2009), Springer · Zbl 1168.74002
[5] Jirasek, M., Analytical and numerical solutions for frames with softening hinges, ASCE J. engrg. mech. din., 123, 8-14, (1997)
[6] Ehrlich, D.; Armero, F., Finite element methods for the analysis of softening plastic hinges in beams and frames, Comput. mech., 35, 237-264, (2005) · Zbl 1109.74358
[7] Armero, F.; Ehrlich, D., Numerical modeling of softening hinges in thin euler – bernoulli beams, Comput. struct., 84, 641-656, (2006)
[8] Armero, F.; Ehrlich, D., An analysis of strain localization and wave propagation in plastic models of beams at failure, Comput. methods appl. mech. engrg., 193, 3129-3171, (2004) · Zbl 1060.74601
[9] Ibrahimbegovic, A.; Melnyk, S., Embedded discontinuity finite element method for modelling of localized failure in heterogeneous materials with structured mesh: an alternative to extended finite element method, Comput. mech., 40, 149-155, (2007) · Zbl 1178.74166
[10] Ibrahimbegovic, A.; Brancherie, D., Combined hardening and softening constitutive model of plasticity: precursor to shear slip line failure, Comput. mech., 31, 88-100, (2003) · Zbl 1038.74523
[11] Wackerfuss, J., Efficient finite element formulation for the analysis of localized failure in beam structures, Int. J. numer. methods engrg., 73, 1217-1250, (2008) · Zbl 1169.74052
[12] Kucerova, A.; Brancherie, D.; Ibrahimbegovic, A.; Zeman, J.; Bittnar, Z., Novel anisotropic continuum-discrete damage model capable of representing localized failure of massive structures. part II: identification from tests under heterogeneous stress field, Engrg. comput., 26, 128-144, (2009) · Zbl 1257.74141
[13] Brank, B.; Perić, D.; Damjanić, F.B., On large deformations of thin elasto-plastic shells: implementation of a finite rotation model for quadrilateral shell element, Int. J. numer. methods engrg., 40, 689-726, (1997) · Zbl 0892.73055
[14] Brank, B., Nonlinear shell models with seven kinematic parameters, Comput. methods appl. mech. engrg., 194, 2336-2362, (2005) · Zbl 1082.74050
[15] Reddy, J.N., An introduction to nonlinear finite element analysis, (2004), Oxford University Press
[16] Ibrahimbegovic, A.; Gharzeddine, F.; Chorfi, L., Classical plasticity and viscoplasticity models reformulated: theoretical basis and numerical implementation, Int. J. numer. methods engrg., 42, 1499-1535, (1998) · Zbl 0910.73018
[17] J. Lubliner, Plasticity Theory, Macmillian, 1990.
[18] Simo, J.C.; Hughes, T.J.R., Computational inelasticity, (1998), Springer · Zbl 0934.74003
[19] Dujc, J.; Brank, B., On stress resultant plasticity and viscoplasticity for metal plates, Finite elem. anal. des., 44, 174-185, (2008)
[20] J. Korelc, AceGen, AceFem. <http://www.fgg.uni-lj.si/Symech>.
[21] Hibbit, Karlsson, Sorensen, Abaqus Manuals.
[22] Darvall, P.L.; Mendis, P.A., Elastic – plastic-softening analysis of plane frames, J. struct. engrg. (ASCE), 111, 871-888, (1985)
[23] Bohinc, U.; Ibrahimbegovic, A.; Brank, B., Model adaptivity for finite element analysis of thin and thick plates based on equilibrated boundary stress resultants, Engrg. comput., 26, 69-99, (2009) · Zbl 1257.74147
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.