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Blurred constitutive laws and bipotential convex covers. (English) Zbl 1269.74008

Summary: In many practical situations, uncertainties affect the mechanical behavior that is given by a family of graphs instead of a single graph. In this paper, we show how the bipotential method is able to capture such blurred constitutive laws, using bipotential convex covers.

MSC:

74A20 Theory of constitutive functions in solid mechanics
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[1] Halphen, B., Journal de Mécanique 14 pp 39– (1975)
[2] DOI: 10.1080/08905459108905146
[3] de Saxcé, G., Proceedings of the 11th Polish Conference on Computer Methods in Mechanics at Kielce
[4] de Saxcé, G., Proceedings of the 10th International Conference on Mathematical and Computer Modelling and Scientific Computing at
[5] de Saxcé, G., Comptes-Rendus de l’Académie des Sciences de Paris Série II 314 pp 125– (1992)
[6] DOI: 10.1016/S0997-7538(00)01109-8 · Zbl 0997.74010
[7] Hjiaj, M., Comptes-Rendus de l’Académie des Sciences de Paris Série II Mécanique Physique Astronomie 328 pp 519– (2000)
[8] Bodovillé, G., Comptes-Rendus de l’Académie des Sciences de Paris Série II Mécanique Physique Astronomie 327 pp 715– (1999)
[9] DOI: 10.1007/978-3-7091-2558-8_4
[10] Vallée, C., Lerintiu, C., Fortuné , D., Ban , M., and de Saxcé, G. Hill’s bipotential, in ed. M. Mihailescu-Suliciu , New Trends in Continuum Mechanics, Theta Series in Advanced Mathematics, pp. 339-351, Theta Foundation, Bucarest, 2005. · Zbl 1177.74085
[11] DOI: 10.1016/S0020-7403(02)00135-2 · Zbl 1025.74028
[12] DOI: 10.1007/s00466-005-0674-5 · Zbl 1099.74047
[13] DOI: 10.1016/S0266-352X(02)00016-2
[14] DOI: 10.1002/nme.1037 · Zbl 1072.74060
[15] DOI: 10.1016/S0895-7177(98)00119-8 · Zbl 1126.74341
[16] DOI: 10.1002/mma.921 · Zbl 1132.74032
[17] Buliga, M., Journal of Convex Analysis 15 pp 87– (2008) · Zbl 1160.49011
[18] Buliga, M., Acta Applicandae Mathematicae (2009)
[19] Buliga, M., Journal of Convex Analysis 17 (2010) · Zbl 1273.53025
[20] DOI: 10.1002/nme.1620121010 · Zbl 0396.65068
[21] DOI: 10.1016/0045-7825(79)90042-2 · Zbl 0396.73077
[22] DOI: 10.1002/nme.1620191103 · Zbl 0534.65068
[23] Gago, J., International Journal of Numerical Methods in Engineering 19 pp 1921– (1983)
[24] DOI: 10.1016/0045-7825(89)90130-8 · Zbl 0723.73075
[25] DOI: 10.1002/nme.1620240206 · Zbl 0602.73063
[26] DOI: 10.1002/nme.1620330702 · Zbl 0769.73084
[27] DOI: 10.1002/nme.1620330703 · Zbl 0769.73085
[28] Fraeijs de Veubeke, Displacement and equilibrium models in the finite element method, in (1965) · Zbl 0359.73007
[29] DOI: 10.1016/0045-7825(94)00726-4 · Zbl 0851.73057
[30] Ladevèze, P., Thèse d’Etat (1975)
[31] Ladevèze, P., Coffignal, G., and Pelle, JP Accuracy of elastoplastic and dynamic analysis , in ed. I. Babuska, J. Gago, E. Oliveira and O. C. Zienkiewicz, Accuracy Estimates and Adaptative Refinements in Finite Element Computations , pp. 181-203, John Wiley, New York, 1986.
[32] DOI: 10.1108/eb023827
[33] DOI: 10.1080/12506559.1992.10511010 · Zbl 0973.74592
[34] DOI: 10.1016/S0045-7825(97)00212-0 · Zbl 0949.74067
[35] Ladevèze, P., La maîtrise du calcul en mécanique linéaire et non linéaire (2001)
[36] DOI: 10.1016/j.cma.2006.03.006 · Zbl 1120.74820
[37] DOI: 10.1016/j.cma.2004.10.011 · Zbl 1193.74049
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