Physical interpretation and quantitative description of cyclic mobility by the subloading surface model

Abstract

Cyclic mobility occurring prior to the liquefaction in sands is a peculiar phenomenon exhibiting a butterfly-shaped stress path and a S-shaped stress-strain curve under undrained cyclic loading. Accurate prediction of this phenomenon is of great importance for the earthquake-resistant design of soil structures. However, it has not been achieved, even though near a half century has passed since it became the object of public attention after the Chile (2010.12.27 受付)

Anisotropic subloading surface Cam‐clay plasticity model with rotational hardening: Deformation gradient‐based formulation for finite strain

“…• is some proper objective rate of , p dev is the deviatoric part of the plastic deformation rate tensor, r is the evolution coefficient, and r is the constant specifying the stress ratio at a rotation limit. Equation (15) has a form different from the one originally proposed in the earlier studies by him and his co-workers, 68,69,72,73 but it is an improved version consistent with the development presented herein. The small strain counterpart of Equation ( 15) can be expressed aṡ…”

“…The rotational hardening has widely been accepted as a pertinent plastic hardening model to describe induced anisotropy observed in geomaterials. [66][67][68][69][70][71][72][73][74] Figure 3 illustrates a conceptual diagram of the rotational hardening, in which the modified stress tensor…”

“…When t = 0, the center of rotation is specified to be at the origin of the stress space, similar to the rotational hardening models in past studies. 67,68,70,[72][73][74] The pull-back operation for̄m od leads to the modified stress tensor based on the reference configuration  0 , namely,…”

“…According to Hashiguchi and Mase, 73 and Zhang et al, 71 we extend the evolution coefficient in Equation ( 145) by introducing the functional dependence of on the mean normal stress , the Lode angle Θ mod , and the accumulated logarithmic plastic deviatoric strain p s,accum , in order to improve the model capability to describe cyclic behavior. This extension leads to 7 ( , Θ mod , p s,accum…”

“…Motivated by the status of past related researches mentioned above, the objective of this study is aimed at developing a novel Cam-clay plasticity model combined with an induced anisotropy at finite strain within the framework of multiplicative elastoplasticity. As a pertinent expression of the plastically induced anisotropy in geomaterials, 66 the rotational hardening [67][68][69][70][71][72][73][74] is incorporated into the model. To this end, according to the proposal by Lion, 36 we adopt the dual multiplicative decompositions of the deformation gradient tensor; the rotational hardening is thereby described in terms of a strain-type tensorial internal variable, and then the back stress ratio tensor is given via a hyperelastic-type hardening rule defined on a proper intermediate configuration.…”