The RAMBERG – OSGOOD model, is a non-linear hysteretic model, aiming at accurately simulating the shear modulus degradation and the hysteretic damping increase with cyclic shear strain. The model is used for non-linear dynamic ground response analyses, aiming mainly to small and medium cyclic strains. In all cases, the soil is modeled as a non-linear hysteretic material using constantly updating values of the tangential bulk Kt and shear Gt moduli. Following isotropic elasticity, the Kt and Gt are interrelated via a constant elastic Poisson’s ratio ν (a model constant). Based on Andrianopoulos et al (2010a, 2010b, 2011), and Papadimitriou et al. (2001, 2002), the non-linear hysteretic form of Gt uses a generalized in stress-space formula of Ramberg and Osgood (1943) model. The degradation of moduli is related to the distance in generalized stress space of the ever-current deviatoric stress ratio tensor r (= s/p, where s is the deviatoric stress tensor and p is the mean effective stress) from its value at the last reference state. The reference state for monotonic loading is the equilibrium state, while for cyclic loading the reference state is updated at each shear reversal state.

*Relevant references*

**Andrianopoulos K. I.**, Papadimitriou A., Bouckovalas G. (2010), “Explicit integration of bounding surface model for the analysis of earthquake soil liquefaction”, International Journal for Numerical and Analytical Methods in Geomechanics, DOI: 10.1002/nag. 875**Andrianopoulos K. I.**, Papadimitriou A. G., Bouckovalas G. D. (2010), “Bounding surface plasticity model for the seismic liquefaction analysis of geostructures”, Soil Dynamics and Earthquake Engineering, doi: 10.1016/j.soildyn.2010.04.001**Andrianopoulos, K. I.**, Papadimitriou and G. D. Bouckovalas. (2011), “Applications of the NTUA-SAND Model for the Seismic Liquefaction Analysis of Geostructures, in Continuum and Distinct Element Modeling in Geomechanics” --- 2011 (Proceedings, 2nd International FLAC/DEM Symposium (Melbourne, February 2011). Keynote Lecture, Paper 13-01, pp. 709-718, D. Sainsbury et al., Eds. Minneapolis: Itasca International Inc.*Papadimitriou A. G., Bouckovalas G. D., Dafalias Y. F. (2001), “Plasticity model for sand under small and large cyclic strains”, Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 127(11): 973-983**Papadimitriou A. G., Bouckovalas G. D. (2002), “Plasticity model for sand under small and large cyclic strains: a multiaxial formulation”, Soil Dynamics and Earthquake Engineering, 22: 191-204**Ramberg W. and Osgood W.R. (1943), “Description of stress-strain curves by three parameters”, Technical note 902, National Advisory Committee for Aeronautics, Washington D.C.*

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