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A study on finite elements for capturing strong discontinuities. (English) Zbl 1038.74645
Summary: The work focuses on the presently existing families of finite elements with embedded discontinuities and explores the possibilities of obtaining symmetric statically consistent finite elements that alleviate the stress-locking problem. For this purpose, mixed (reduced integration) and assumed enhanced strain techniques are applied to the basic symmetric four-noded element. Numerical simulations show the effectiveness of the proposed measures.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74R99 Fracture and damage
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[1] Dvorkin, International Journal for Numerical Methods in Engineering 30 pp 541– (1990)
[2] Larsson, International Journal for Numerical Methods in Engineering 36 pp 2087– (1993)
[3] Lofti, International Journal for Numerical Methods in Engineering 38 pp 1307– (1995)
[4] A new approach to the analysis and simulation of strong discontinuities. In Fracture and Damage in Quasi-brittle Structures, et al. (eds). E & FN. Spon, 1994; 25-39.
[5] Modelling strong discontinuities by means of strain softening constitutive equations. In Proceedings of the EURO-C 1994 Computer Modeling of concrete structures, et al. (eds). Pineridge Press: Swansea, 1994; 363-372.
[6] Oliver, International Journal for Numerical Methods in Engineering 39 pp 3601– (1996)
[7] Armero, International Journal of Solids and Structures 33 pp 2863– (1996)
[8] Larsson, International Journal of Solids and Structures 33 pp 3081– (1996)
[9] Celigoj, International Journal for Numerical Methods in Engineering 49 pp 769– (2000) · Zbl 1009.74061
[10] Belytschko, International Journal for Numerical Methods in Engineering 50 pp 993– (2001)
[11] Wells, International Journal for Numerical Methods in Engineering 50 pp 2667– (2001)
[12] Regueiro, International Journal of Solids and Structures 38 pp 3647– (2001)
[13] de Borst, Engineering Computations 10 pp 99– (1993)
[14] Jirasek, Computer Methods in Applied Mechanics and Engineering 188 pp 307– (2000)
[15] Continuum modelling of strong discontinuities in solid mechanics. In Computational Plasticity. Fundamentals and Applications, vol. 1, (eds). Pineridge Press: Swansea, 1995; 455-479.
[16] On the use of J2 plasticity models for the simulation of 2D strong discontinuities in solids. In Proceedings of the International Conference on Computational Plasticity, (eds). C.I.M.N.E.: Barcelona (Spain), 1997; 38-55.
[17] On the use of strain-softening models for the simulation of strong discontinuities in solids. In Material Instabilities in Solids, (eds), chapter 8. Wiley: New York, 1998; 107-123.
[18] The strong discontinuity approach: an overview. In Computational Mechanics. New Trends and Applications. (WCCM98) Proceedings (CD-ROM) of the IV World Congress on Computational Mechanics, (eds). CIMINE: Barcelona, 1998.
[19] Oliver, International Journal of Plasticity 15 pp 319– (1999)
[20] Oliver, Engineering Fracture Mechanics 69 pp 113– (2002)
[21] Oliver, International Journal for Numerical Methods in Engineering
[22] The Finite Element Method. Butterworth-Heinemann: Oxford, UK, 2000.
[23] Computational Inelasticity. Springer: Berlin, 1998. · Zbl 0934.74003
[24] Simo, International Journal for Numerical Methods in Engineering 29 pp 1595– (1990)
[25] Oliver, International Journal of Solids and Structures 37 pp 7207– (2000)
[26] Malkus, Computer Methods in Applied Mechanics and Engineering 15 pp 63– (1978)
[27] Fracture process zone of concrete. In Application of Fracture Mechanics to Cementitious Composites, (ed.). Marinus Nujhoff Publ.: Dordrecht, 1985; 25-50.
[28] Crack Growth and development of fracture zones in plain concrete and similar materials. Technical Report, Division of building material, 1981. Report No. 1006.
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