Finite strain formulation of a strain space multiple mechanism model for granular materials

Abstract

SUMMARYThis paper presents the finite strain formulation of a strain space multiple mechanism model for granular materials. Because the strain space multiple mechanism model has an appropriate micromechanical background in which the branch and complementary vectors are defined in the material (or referential) coordinate, the finite strain formulation is carried out by following the change in these vectors, in direction and magnitude, associated with deformation in the material. By applying the methodology for compressible materials established in the finite strain continuum mechanics, decoupled formulation that decomposes the kinematic mechanisms into volumetric and isochoric components is adopted for the strain space multiple mechanism model. Lagrangian (material) description of integrated form is given by a relation between the second Piola-Kirchhoff effective stress tensor and the Green-Lagrange strain tensor; Eulerian (spatial) description by a relation between the Cauchy effective stress tensor and the Euler-Almansi strain tensor. In particular, the volumetric strain is defined as a logarithm of Jacobian determinant. Lagrangian (material) description of incremental form is derived through the material time derivative of the integrated form. The counterpart in the spatial description is derived through the Lie time derivative, given as a relation between the Oldroyd stress rate of Kirchhoff stress and the rate of deformation tensor (sometimes called stretching in the literatures). An example is shown to discuss the applicability of the finite strain formulation.

LEAP-UCD-2017 Type-B Predictions Through FLIP at Kyoto University

“…As is the case with the type-B and -C simulations for LEAP-GWU-2015 (Ueda and Iai 2018), a strain space multiple mechanism model based on the finite strain theory (Ueda 2009;Iai et al 2013) is used for LEAP-UCD-2017 type-B predictions. The original version of the model was proposed within the context of the infinitesimal strain theory (Iai et al 1992), and implemented in a FE program called "FLIP ROSE" (Finite Element Analysis Program of LIquefaction Process/Response Of Soil-structure Systems during Earthquakes).…”

“…With an aim to take into account the effect of geometrical nonlinearity in addition to material nonlinearity's effect, the model was extended within the context of the finite strain (or large deformation) theory (Ueda 2009;Iai et al 2013). Incorporating the extended model, a finite strain FE program called "FLIP TULIP" (Finite Element Analysis Program of LIquefaction Process/Total and Updated Lagrangian Program of LIquefaction Process) has been developed based on the original infinitesimal strain program (i.e., FLIP ROSE).…”

“…This chapter presents results of numerical simulations for the dynamic centrifuge model tests, within a framework of type-B prediction (e.g., Lambe (1973)) phases of the LEAP-UCD-2017. The simulations are carried out with a finite strain, effective stress finite element (FE) program, called "FLIP TULIP," which incorporates a strain space multiple mechanism model based on the finite strain theory (including both total and updated Lagrangian formulations) (Ueda 2009;Iai et al 2013). The program can take into account the effect of geometrical nonlinearity as well as that of material nonlinearity.…”

Centrifuge model tests and large deformation analyses of a breakwater subject to combined effects of tsunami

“…The push-forward operation of these equations results in the basis for the updated Lagrangian (UL) formulation written in terms of the current direction vectors n and t defined in Equation 7. See [14] and [15] for further details.…”

Numerical Predictions for Centrifuge Model Tests of a Liquefiable Sloping Ground Using a Strain Space Multiple Mechanism Model Based on the Finite Strain Theory

“…This paper presents results of numerical simulations for the dynamic centrifuge model tests, performed at the six centrifuge facilities, within a framework of Class A, B, and C prediction (e.g., [9]) phases of the LEAP. The simulations are performed by using a strain space multiple mechanism model based on the finite strain theory (including both total and updated Lagrangian formulations) [10], in which both material and geometrical nonlinearity are considered. In this paper, the identification process of model parameters is explained in details besides the computational conditions (e.g., geometric modeling, initial and boundary conditions).…”