By J. Sulem, I.G. Vardoulakis
This ebook 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 relating to pressure localization phenomena.
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Extra info for Bifurcation analysis in geomechanics
1. 25). 5) where δij is the Kronecker delta. e. 2). Accordingly, Rij is called the rotation tensor and Uij the right-stretching tensor. As already mentioned, the deformation gradient gives the change of the metric of the be two neighboring material points in C(0), which deformed body. Let X(ξi) and respectively. 11) We notice that Uij is not very convenient strain measure since its evaluation involves . Furthermore, the eigenvalues of Uij principal axes transformation of the tensor are the square roots of the eigenvalues of Cij.
42) If the deformation is isochoric, then , and the Kirchhoff and Cauchy stress tensors coincide. In order to illustrate the usefulness of the Kirchhoff stress, we briefly comment here on the behavior of highly compressible geomaterials, like clays, and to the representation of corresponding experimental results. As it is common in the soil mechanics literature, the experimental data are plotted in terms of Cauchy stress and the infinitesimal strain resulting to non-linear stress-strain curves.
As opposed to a Boltzmann continuum, in a Cosserat continuum the Cauchy stress tensor is non-symmetric either due to the existence of couple boundary stresses and/or due to the existence of body couples, which in turn might be only due to inertia, stemming from the spinning of the unit cells (grains) of the material; cf. Schaeffer (1967). e. e. 23) where e(xk, t) is the specific internal energy of the body. 24) cf. 10. 25) where σij is the Cauchy stress tensor in C and ni is the unit outward normal vector on ∂V in C.
Bifurcation analysis in geomechanics by J. Sulem, I.G. Vardoulakis