Kyohei Ueda

Large Deformation (Finite Strain) Analysis: Theory

This chapter presents the finite strain formulation of a strain space multiple mechanism model for granular materials. Since 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, both 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. Material (Lagrangian) description of the integrated form is given by a relation between the second Piola-Kirchhoff effective stress and the Green-Lagrange strain tensors; spatial (Eulerian) description by a relation between the Cauchy effective stress and the Euler-Almansi strain tensors. Material description of the 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.

Modelling of Cohesive Soils: Soil Element Behaviors

The strain space multiple mechanism model, which was originally developed for the cyclic behavior of granular materials such as sand, is adapted to idealize the stress–strain behavior of clay under monotonic and cyclic loads. Compared to the conventional elasto-plastic models of the Cam-clay type, advantages of the proposed model include (1) the arbitrary initial K0 state can be analyzed by static gravity analysis, (2) the stress-induced anisotropy (i.e., the effect of initial shear) in the steady (critical) state can be analyzed based on Shibata’s dilatancy model (Ann Disaster Prev Res Inst Kyoto Univ 6:128–134, 1963), (3) over-consolidated clay can be analyzed by defining the dilatancy at the steady state based on the over-consolidation ratio, and (4) the strain-rate effects for monotonic and cyclic shears can be analyzed based on the Isotach/TESRA model proposed by Tatsuoka et al. (Soils Found 42(2):103–129, 2002) in a strain rate ranging from zero to infinity as well as by the conventional strain-rate effects of the secondary consolidation (creep) type. Simulations of the drained/undrained behaviors of clay under monotonic and cyclic loadings are used to demonstrate the performance of the proposed model.