By J. Sulem, I.G. Vardoulakis
This e-book examines the experimental and theoretical points of bifurcation research as utilized to geomechanics. assurance contains easy continuum mechanics for dry and fluid unfiltrated porous media, bifurcation and balance analyses utilized to layered geological media and granular fabrics, and theories for generalized continua as utilized to fabrics with microstructure and with regards to pressure localization phenomena.
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Additional info for Bifurcation analysis in geomechanics
8) This means that the material time derivative in Eulerian description is a mixed with and . 8, called the ‘local’ variation, corresponds to the change of the field at a fixed-in-space position xk. The second term, called the ‘convective’ term, is a correction, which accounts for the change of position of the considered material point in time. The convective term, being the inner product of the velocity and the spatial gradient of , is a ‘non-linear’ term and occasionally may be neglected. 9) As a first example let us consider the displacement field ui(xk, t).
See also: Truesdell, C. and Noll, W. (1965). The Non-Linear Field Theories of Mechanics, Handbuch der Physik, Vol. III/3, section 119, Springer, Berlin. H. (1970). The influence of strains in soil mechanics. Géotechnique, 16, 129–170. 1). Relative to a fixed-in-space Cartesian coordinate system a particle X has the coordinates ξi and xi in C(0) and C, respectively. 1 Initial and current configuration of a deforming solid. 1. 25). 5) where δij is the Kronecker delta. e. 2). Accordingly, Rij is called the rotation tensor and Uij the right-stretching tensor.
For a great variety of clays, the primary compression curve, the unloading (or swelling) curves and the recompression curves are then fairly approximated by straight lines. In a semi-logarithmic plot, these straight-line fits are characterized by their slopes, the socalled Terzaghi ‘compression’ and ‘swelling’ indices Cc and Cs, respectively. In most cases, straight-line fits are also generated if, instead of the ambiguous logarithmic stress and the inappropriate for large deformations engineering strain, one resorts to conjugate Eulerian measures like the Kirchhoff stress Tij and the logarithmic strain λ.