By J. Sulem, I.G. Vardoulakis
This ebook examines the experimental and theoretical facets 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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Extra info for Bifurcation analysis in geomechanics
37) Similarly, a second-order tensor Sij is called objective if its property to map an objective vector onto an objective vector remains valid also for the assumed coordinate transformation. 39) we observe that the velocity is not an objective vector field. Similarly, it can be shown that neither the acceleration at nor the velocity gradient Lij are objective tensors. 43) From this property Dij derives its characterization as the ‘rate of the deformation’. Obviously the spin tensor Wij is not objective.
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. 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.
Y. (1961). Plastic Flow and Fracture in Solids. Academic Press, London. 46 BASIC CONCEPTS FROM CONTINUUM MECHANICS Truesdell, C. and Noll, W. (1965). Nonlinear Field Theories of Mechanics. Handbuch der Physik, Vol III/3, sections 21–25 and 79. Springer, Berlin. References Germain, P. (1973a). La méthode des pulssances virtuelles en mécanique des milieux continus. Première partie: Théorie du second gradient. J. de Mécanique, 12(2), 235–274. Germain, P. (1973b). The method of virtual power in continuum mechanics.