Abstract
The description of the cyclic mobility observed prior to the liquefaction in geomaterials requires the sophisticated constitutive formulation to describe the plastic deformation induced during the cyclic loading with the small stress amplitude inside the yield surface. This requirement is realized in the subloading surface model, in which the surface enclosing a purely elastic domain is not assumed, while a purely elastic domain is assumed in other elastoplasticity models. The subloading surface model has been applied widely to the monotonic/cyclic loading behaviors of metals, soils, rocks, concrete, etc., and the sufficient predictions have been attained to some extent. The subloading surface model will be elaborated so as to predict also the cyclic mobility accurately in this article. First, the rigorous translation rule of the similarity center of the normal yield and the subloading surfaces, i.e., elastic core, is formulated. Further, the mixed hardening rule in terms of volumetric and deviatoric plastic strain rates and the rotational hardening rule are formulated to describe the induced anisotropy of granular materials. In addition, the material functions for the elastic modulus, the yield function and the isotropic hardening/softening will be modified for the accurate description of the cyclic mobility. Then, the validity of the present formulation will be verified through comparisons with various test data of cyclic mobility.
Highlights
It should be noticed that soils exhibit complex deformation behaviors, which are not observed in metals, e.g., the pressure dependence of the elastic moduli and the plastic deformation characteristics, the plastic compressibility, the plastic volumetric expansion induced by the deviatoric stress, i.e., the dilatancy and the rotational anisotropic hardening instead of the kinematic hardening
The subloading surface model is elaborated to describe the cyclic mobility observed prior to the liquefaction induced by earthquakes
The results obtained in this study are summarized as follows: 1. The elastoplastic constitutive equation of geomaterials is elaborated by the formulations of
Summary
It should be noticed that soils exhibit complex deformation behaviors, which are not observed in metals, e.g., the pressure dependence of the elastic moduli and the plastic deformation characteristics, the plastic compressibility, the plastic volumetric expansion induced by the deviatoric stress, i.e., the dilatancy and the rotational anisotropic hardening instead of the kinematic hardening Granular materials such as sands exhibit volumetric and deviatoric isotropic hardening, whereas metals and clays exhibit only the deviatoric isotropic hardening and volumetric isotropic hardening, respectively, usually. The description of the cyclic mobility requires the sophisticated constitutive formulation to describe the plastic deformation during the cyclic loading with a small stress amplitude inside the yield surface. 0 stands for the second-order zero tensor, I for the second-order identity tensor possessing the Kronecker delta components dij ðdij 1⁄4 1 for i 1⁄4 j; dij 1⁄4 0 for i 61⁄4 jÞ, tr A 1⁄4 Aijdij for the trace, A0 1⁄4
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