Energy dissipation regarding transient response of concrete structures
Constitutive equations coupling damage and friction
Keywords:
cancrete, damage, sliding with friction, damping, seismicAbstract
This paper deals with the 3D expression of a constitutive relation for brittle materials such as concrete accounting for cracking with friction. Based on damage mechanics, a macroscopic description of the material behaviour introducing this new dissipative phenomenon allows one ta take into account, during cyclic loading, the hysteresis /oops at a fixed leve/ of damage. This mode/ has been implemented within a multilayered finite element code dedicated ta the analysis of structures subjected ta seismic loading. First computations enlighten the rote of an accurate description of the material physical dissipation towards the global damping at the structurallevel.
Downloads
References
[ARM 66] ARMSTRONG P.J. and FREDERICK C.O., A Mathematical Representation of the
Multiaxial Bauschinger Effect, G.E.G.B., Report RD/B/N, 731, 1966.
[BAT 82] BA THE K.J., Finite element procedures in engineering analysis, Prentice Hall (eds),
Inc. Englewood CJ.iffs, New Jersey, 1982.
[CHA 93] CHABOCHE J.L., "Cyclic Viscoplastic Constitutive Equations, Part 1: A
Thermodynamically Consistent formulation", J. Appl. Mech., Vol 60, p. 813-821, Dec.
[COR 79] CORDEBOIS J.P. and SIDOROFF F., "Damage lnduced Elastic Anisotropy", Colloque
Euromech, 115, Villars de Lans, p. 761-774, 1979.
[DRA 94] DRAGO:-; A .. CORMERY T.. DESOYER T. and HALM D., "Localised Failure Analysis
Using Damage Models". In Chambon R. et al. (cds). Localisation and Bifurcation Theory
for Soils and Rocks. p. 127-140. Rotterdam:Balkema. 1994.
[HALM 96] HAL:1 D. and DRAGO: A .. "A mode! of anisotropie damage by mesocrack
growth: unilateral effect". ln. J. Damage Mechs., Vol. 5, Oct. 1996, p. 384-402, 1996.
[JU 89] JL' J.W., "On energy-based coupled elastoplastic damage theories: constitutive
modelling and computational aspects", /nt. J. Sa/ids and Structures, 25(7), p. 803-833,
I989.
[KAC 58] KACHANOV L.M., "Ti me of the rupture process under creep conditions", /~v. Akad.
Nauk. S.S.R., Otd. Tekh. Nauk., no 8. p. 26-31. 1958.
[KRA 81) KRACJINOVIC D. et FONSEKA G.U .. "The continuous damage theories of brittle
materials, Part I and Il". J. of Appt. Mech., ASME, Vol. 48, p. 809-824, 1981.
[LAB 91] LA BORDERIE CH .. Phénomènes unilatéraux dans un matériau endommageable:
modélisation et application à l'analyse de structures en béton, Ph. D. thesis, Univ. Paris
VI, 1991.
[LAD 83] LADEVÈZE P .. "On an anisotropie damage theory", Proc. CNRS /nt. Coll. 351,
Villars-de-Lans, Ed. by J.P. Boehler, p. 355-363. 1983.
[LEM 90] LEMAITRE J. and CHABOCHE J.L.. Mechanics of sa/ids material, Cambridge
University Press, 1990.
[MRO 67] MROZ Z., "On the description of anisotropie workhardening", J. Mech. Phys.
Sa/ids, 15, p. 163, 1967.
[MUR 78] MLTRAKAMI S. and OIINO N., "A constitutive equation of creep damage in
polycristalline metal s", /.V. T.A.M. Colloquium Euromech Ill, Marienbad, 1978.
[NEW 59] NEWMARK N.M., "A method of computation for structural dynamics", A.S.C.E.
Journal of Engineering Mechanics Division., Vol. 85, p. 67-94, I959.
[ORT 86] 0RTIZ M. and SIMO J.C., "An analysis of a new class of integration algorithms for
elastoplastic constitutive relations", /nt. J. Numer. Meth., Eng. Vol. 23, p. 353-366, I986.
[QUE 98) QLJEVAL J.C., COMBESCLTRE D., SOLLOGOLTB P., COI:--J A. et MAZARS J., "CAMUS
experimental program. In-plane tests of 1/3 scaled R/C bearing walls", Proc. X/th ECEE-
, CD-ROM eds Bisch P., Labbé P. et Pecker A., Paris/CNIT La defense. 1998.
[RAG 00) RAGLIENEAll F., LA BORDERIE Ch. and MAZARS J., "Damage mode! for concrete
like materials coupling cracking and friction, contribution towards structural damping:
first uniaxiai application", Mechanics Cohesive Frictional Materials (to appear), 2000.
