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“Computational Civil Engineering 2005”, International Symposium 125Stress function particularizationSimo and Ju stress function [26, 27] is used in the paper( σ ) = 2 Ψ ( ε = ε C : ετ = f (A.19)0 0 )Taking into account this function, parameter A used in Equation (A.18) canbe written asA =gf11−0 2( f ( σ )) 20: 0(A.20)whereg frepresents the maximum of the fracture energy to be dissipated at eachpoint of the solid andfirst damage threshold.f 0 ( σ 0) is the value given by the threshold equation for the
126 S. Oller, Al.H. BarbatReferences[1] R. Aguiar and A. H. Barbat, “Daño sísmico en estructuras de hormigón armado”.Universidad Politécnica del Ejercito, Quito, Ecuador., 1997.[2] S. Arman and M. Grigoriu, Markov model for local and global damage indexes in seismicanalysis, NCEER-94-0003, National Center for Earthquake Engineering Research, 1994.[3] A. H. Barbat, S. Oller, E. Oñate and A. Hanganu, “Viscous Damage Model for TimoshenkoBeam Structures”. International Journal of Solids and Structures, Vol.34, No.30, pp. 3953-3976. 1997.[4] E. Car, S. Oller and E. Oñate, “An anisotropic elastoplastic constitutive model for largestrain analysis of fiber reinforced composite materials”. Computer Methods in AppliedMechanics and Engineering, Vol. 185, No. 2-4, 245-277, 2000.[5] J. Chaboche, “Continuum damage mechanics part I. General Concepts”. Journal of AppliedMechanics, 55, 59-64, 1988.[6] J. Chaboche, “Continuum damage mechanics part II. Damage Growth”. Journal of AppliedMechanics, 55, 65-72, 1988.[7] R. W. Clough and J. Penzien, Dynamics of Structures. McGraw-Hill, 1992.[8] R. Faria, N. Vila Pouca and R. Delgado, “Simulation of the cyclic behaviour of r/crectangular hollow section bridge piers via a detailed numerical model”. Journal ofEarthquake Engineering, Vol. 8, No. 5, 725-748, 2004.[9] C. Gómez-Soberón, S. Oller and A. Barbat, Seismic vulnerability of bridges using simplemodels”. Monographs of Seismic Engineering, Monograph series in EarthquakeEngineering, CIMNE IS-47, International Center of Numerical Methods in Engineering,Barcelona, Spain, 2002.[10] D. Hull, “Materiales compuestos”, Reverté Editorial, Spain, 1987.[11] J. E. Hurtado and A. H. Barbat, “Monte Carlo techniques in computational stochasticmechanics”. Archives of Computational Methods in Engineering, Vol. 5, No.1, 3-30, 1998.[12] L. M Kachanov,. “Time of rupture process under creep conditions”. Izvestia AkaademiiNauk; Otd Tech Nauk, 8 26-31, 1958, .[13] J. Lemaitre “A course on damage mechanics”, 2 nd edition, Springer, 1992.[14] J. Lemaitre and J. L. Chaboche “Aspects phénoménologiques de la rupture parendommagement”. Journal of Applied Mechanics, 2, 317-365, 1978.[15] J. Lubliner, J. Oliver, S. Oller and E. Oñate, “A plastic damage model for non linear analysisof concrete”. Int. Solids and Structures, Vol. 25, No. 3, pp. 299-326, 1989.[16] B. Luccioni and S. Oller, “A directional damage model”, Computer Methods in AppliedMechanics and Engineering. Vol. 192, No. 9-10, 1119-1145, 2003.[17] B. Luccioni, S. Oller and R. Danesi, “Coupled plastic-damaged model”. Computer Methodsin Applied Mechanics and Engineering, Vol. 129, No. 1-2, 81-89, 1996.[18] G. A. Maugin, The thermomechanics of plasticity and fracture. Cambridge University Press,1992.[19] J. Oliver, M. Cervera, S. Oller and J. Lubliner, “Isotropic damage models and smeared crackanalysis of concrete”. Second International Conference on Computer Aided Analysis andDesign of Concrete Structures, 2, 945-958, Austria, 1990.[20] S. Oller, E. Car and J. Lubliner, “Definition of a general implicit orthotropic yield criterion”.Computer Methods in Applied Mechanics and Engineering, Vol. 192, No. 7-8, 895-912,2003.[21] S. Oller, B. Luccioni and A. Barbat, “Un método de evaluación del daño sísmico deestructuras de hormigón armado”. Revista Internacional de Métodos Numéricos para elCálculo y Diseño en Ingeniería, 12(2), 215-238, 1996.
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