zbMATH — the first resource for mathematics

A novel constrained LArge Time INcrement method for modelling quasi-brittle failure. (English) Zbl 1286.74091
Summary: A novel LArge Time INcrement (LATIN) method is developed. At variance with existing LATIN methods, the proposed algorithm is capable of tracing snap-backs in quasi-brittle materials. Special attention is given to algorithmic implementation as well as to robust and automated choice of algorithmic variables. The performance of the method is verified by its application to numerical examples exhibiting snap-back and bifurcation phenomena in their mechanical response.

74R10 Brittle fracture
74S30 Other numerical methods in solid mechanics (MSC2010)
65L05 Numerical methods for initial value problems
Full Text: DOI
[1] Wempner, G. A., Discrete approximations related to nonlinear theories of solids, Int. J. Solids Struct., 7, 11, 1581-1599, (1971) · Zbl 0222.73054
[2] Riks, E., The application of newton’s method to the problem of elastic stability, J. Appl. Mech., 39, 4, 1060-1065, (1972) · Zbl 0254.73047
[3] Riks, E., An incremental approach to the solution of snapping and buckling problems, Int. J. Solids Struct., 15, 7, 529-551, (1979) · Zbl 0408.73040
[4] Crisfield, M. A., A fast incremental/iterative solution procedure that handles snap-through, Comput. Struct., 13, 1-3, 55-62, (1981) · Zbl 0479.73031
[5] Ramm, E., Strategies for tracing non-linear responses near limit points, (Wunderlich, W.; Stein, E.; Bathe, K. J., Non-linear Finite Element Analysis in Structural Mechanics, Proceedings Europe-U.S. Workshop, Ruhr-Universität Bochum, Germany, (1981), Springer-Verlag New York), 68-89
[6] T. Pohl, M. Bischoff, Adaptive continuation methods for material softening, in: Proceedings of the 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS), 2012.
[7] E. Ramm, T. Pohl, M. Bischoff, On path-following methods in the post-critical regime, in: Proceedings of the 10th World Congress on Computational Mechanics, 2012.
[8] Geers, M. G.D., Enhanced solution control for physically and geometrically non-linear problems. part I - the subplane control approach, Int. J. Numer. Meth. Engrg., 46, 2, 177-204, (1999) · Zbl 0957.74034
[9] Chen, Z.; Schreyer, H. L., A numerical solution scheme for softening problems involving total strain control, Comput. Struct., 37, 6, 1043-1050, (1990)
[10] Gutiérrez, M. A., Energy release control for numerical simulations of failure in quasi-brittle solids, Int. J. Numer. Meth. Engrg., 20, 1, 19-29, (2004) · Zbl 1047.74551
[11] Verhoosel, C. V.; Remmers, J. J.C.; Gutiérrez, M. A., A dissipation-based arc-length method for robust simulation of brittle and ductile failure, Int. J. Numer. Meth. Engrg., 77, 9, 1290-1321, (2009) · Zbl 1156.74397
[12] van der Veen, H.; Vuik, K.; de Borst, R., Branch switching techniques for bifurcation in soil deformation, Comput. Meth. Appl. Mech. Engrg., 190, 5-7, 707-719, (2000) · Zbl 0967.74042
[13] J.G. Rots, Sequentially linear continuum model for concrete fracture, in: R. de Borst, J. Mazars, G. Pijaudier-Cabot, J.G.M. van Mier (Eds.), Fracture mechanics of concrete structures, 2001, pp. 831-839.
[14] Rots, J. G.; Invernizzi, S., Regularized sequentially linear saw-tooth softening model, Int. J. Numer. Anal. Meth. Geomech., 28, 7-8, 821-856, (2004) · Zbl 1112.74476
[15] Rots, J. G.; Belletti, B.; Invernizzi, S., Robust modelling of RC structures with an event-by-event strategy, Engrg. Fract. Mech., 75, 3-4, 590-614, (2008)
[16] Graça-e-Costa, R.; Alfaiate, J.; Dias-da-Costa, D.; Sluys, L. J., A non-iterative approach for the modelling of quasi-brittle materials, Int. J. Fract., 178, 1-2, 281-298, (2012)
[17] De Proft, K.; Heyens, K.; Sluys, L. J., Mesoscopic modelling of masonry failure, Proc. ICE - Engrg. Comput. Mech., 164, EM1, 41-46, (2010)
[18] Ladevèze, P., Nonlinear computational structural mechanics. new approaches and non-incremental methods of calculation, (1999), Springer-Verlag New York · Zbl 0912.73003
[19] Ph. Boisse, P. Bussy, J.-Y. Cognard, P. Ladevèze, On a class of large time increment algorithms, in: G.N. Pande and J. Middleton (Eds.), Proceedings of the International Conference on Numerical Methods in Engineering - Theory and Applications (NUMETA 87), vol. 2, 1987.
[20] Allix, O.; Ladevèze, P.; Gilletta, D.; Ohayon, R., A damage prediction method for composite structures, Int. J. Numer. Meth. Engrg., 27, 2, 271-283, (1989) · Zbl 0717.73059
[21] Boisse, Ph.; Ladevèze, P.; Rougée, P., A large time increment method for elastoplastic problems, Eur. J. Mech. A/Solids, 8, 4, 257-275, (1989) · Zbl 0692.73038
[22] Boisse, Ph.; Bussy, P.; Ladevèze, P., A new approach in non-linear mechanics: the large time increment method, Int. J. Numer. Meth. Engrg., 29, 3, 647-663, (1990) · Zbl 0712.73029
[23] Boisse, Ph.; Ladevèze, P.; Poss, M.; Rougée, P., A new large time increment algorithm for anisotropic plasticity, Int. J. Plast., 7, 1-2, 65-77, (1991) · Zbl 0761.73037
[24] Cognard, J.-Y.; Ladevèze, P., A large time increment approach for cyclic viscoplasticity, Int. J. Plast., 9, 2, 141-157, (1993) · Zbl 0772.73028
[25] Boucard, P.-A.; Ladevèze, P.; Poss, M.; Rougée, P., A nonincremental approach for large displacement problems, Comput. Struct., 64, 1-4, 499-508, (1997) · Zbl 0919.73167
[26] Dureisseix, D.; Ladevèze, P.; Schrefler, B. A., A LATIN computational strategy for multiphysics problems: application to poroelasticity, Int. J. Numer. Meth. Engrg., 56, 10, 1489-1510, (2003) · Zbl 1106.74425
[27] Bussy, P.; Liu, B.; Vauchez, P., New algorithm for numerical simulation of metal forming processes, (Chenot, J. L., Proceedings of the International Conference on Numerical Methods in Industrial Forming Processes (NUMIFORM 92), (1992), Balkema), 433-438
[28] Abdali, A.; Benkrid, K.; Bussy, P., Simulation of sheet cutting by the large time increment method, J. Mater. Process. Technol., 60, 1-4, 255-260, (1996)
[29] Bellenger, E.; Bussy, P., Plastic and viscoplastic damage models with numerical treatment for metal forming processes, J. Mater. Process. Technol., 80-81, 591-596, (1998)
[30] J.E. Dolbow, An extended finite element method with discontinuous enrichment for applied mechanics. PhD thesis, Northwestern University, 1999.
[31] Dolbow, J.; Moës, N.; Belytschko, T., An extended finite element method for modelling crack growth with frictional contact, Comput. Meth. Appl. Mech. Engrg., 190, 51-52, 6825-6846, (2001) · Zbl 1033.74042
[32] Boucard, P.-A.; Champaney, L., A suitable computational strategy for the parametric analysis of problems with multiple contact, Int. J. Numer. Meth. Engrg., 57, 9, 1259-1281, (2003) · Zbl 1062.74607
[33] Ribeaucourt, R.; Baietto-Dubourg, M.-C.; Gravouil, A., A new fatigue frictional contact crack propagation model with the coupled X-FEM/LATIN method, Comput. Meth. Appl. Mech. Engrg., 196, 33-34, 3230-3247, (2007) · Zbl 1173.74385
[34] Gravouil, A.; Pierres, E.; Baietto, M.-C., Stabilized global-local X-FEM for 3D non-planar frictional crack using relevant meshes, Int. J. Numer. Meth. Engrg., 88, 13, 1449-1475, (2011) · Zbl 1242.74121
[35] Trollé, B.; Gravouil, A.; Baietto, M.-C.; Nguyen-Tajan, T. M.L., Optimization of a stabilized X-FEM formulation for frictional cracks, Finite Elem. Anal. Des., 59, 18-27, (2012)
[36] Kerfriden, P.; Allix, O.; Gosselet, P., A three-scale domain decomposition method for the 3D analysis of debonding in laminates, Comput. Mech., 44, 3, 343-362, (2009) · Zbl 1166.74039
[37] L. Champaney, Outils de conception et d’analyse pour les assemblages de structures complexes, Mémoire d’habilitation, Université de Versailles St. Quentin en Yvelines, 2004.
[38] Hu, W.; Thomson, P. F., An evaluation of a large time increment method, Comput. Struct., 58, 3, 633-637, (1996) · Zbl 0900.73164
[39] Ladevèze, P.; Perego, U., Duality preserving discretization of the large time increment methods, Comput. Meth. Appl. Mech. Engrg., 189, 1, 205-232, (2000) · Zbl 0983.74081
[40] Oñate, E., On the derivation and possibilities of the secant stiffness matrix for non linear finite element analysis, Comput. Mech., 15, 6, 572-593, (1995) · Zbl 0826.73059
[41] Lourenço, P. B.; Rots, J. G., Multisurface interface model for analysis of masonry structures, J. Engrg. Mech., 123, 7, 660-668, (1997)
[42] de Borst, R., Computation of post-bifurcation and post-failure behavior of strain-softening solids, Comput. Struct., 25, 2, 211-224, (1987) · Zbl 0603.73046
[43] Vandoren, B.; De Proft, K.; Simone, A.; Sluys, L. J., Mesoscopic modelling of masonry using weak and strong discontinuities, Comput. Meth. Appl. Mech. Engrg., 255, 167-182, (2013) · Zbl 1297.74100
[44] T.M.J. Raijmakers, A.T. Vermeltfoort, Deformation controlled tests in masonry shear walls - Report B-92-1156, Technical Report TNO Bouw, 1992.
[45] Simone, A., Partition of unity-based discontinuous elements for interface phenomena: computational issues, Commun. Numer. Meth. Engrg., 20, 6, 465-478, (2004) · Zbl 1058.74082
[46] Simone, A.; Duarte, C. A.; Van der Giessen, E., A generalized finite element method for polycrystals with discontinuous grain boundaries, Int. J. Numer. Meth. Engrg., 67, 8, 1122-1145, (2006) · Zbl 1113.74076
[47] Stehly, M.; Remond, Y., On numerical simulation of cyclic viscoplastic and viscoelastic constitutive laws with the large time increment method, Mech. Time-Depend. Mater., 6, 2, 147-170, (2002)
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.