By J. Sulem, I.G. Vardoulakis
This ebook examines the experimental and theoretical features of bifurcation research as utilized to geomechanics. insurance 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 in terms of pressure localization phenomena.
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Additional info for Bifurcation analysis in geomechanics
Englewood Cliffs, New Jersey. Mróz, Z. (1966). On forms of constitutive laws for elastic-plastic solids. Archiwum Mecaniki Stosowanej, 1(18), 3–35. Prager, W. (1961). Einführung in die Kontinuumsmechanik. Birkhäuser. Truesdell, C. and Toupin, R. (1960). The Classical Field Theories of Mechanics. Handbuch der Physik, Vol III/1, sections 173–194. Springer, Berlin.
Chapter 6 summarizes the basic concepts from plasticity theory as applied to granular soils and rocks. Starting from the basic concepts of classical flow theory of plasticity with a yield criterion and a plastic potential, we present, in a hierarchical manner, the possible extensions of isotropic hardening plasticity. We believe that an integral part of constitutive modeling is the calibration procedure. Since there is no unique strategy for calibration, examples given in chapter 6 should be understood as a suggestion which proved itself appropriate in number of applications.
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. e. 27) This can be shown as follows: We consider the balance of linear momentum equation 2. 27. 27bis) The quantity, ρ−1P, is called the specific stress power (Elementarleistung). Accordingly, the Cauchy stress tensor σij and the rate of deformation tensor Dij are called dual in energy (Macvean, 1968). It should be noticed also that if in a continuum the stress power depends only on the rate of deformation tensor, then this continuum will be called a first-grade continuum.