By J. Sulem, I.G. Vardoulakis
This ebook examines the experimental and theoretical points of bifurcation research as utilized to geomechanics. assurance contains simple 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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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.
28) which simply express the fact that across a material discontinuity surface the tractions must be in equilibrium. 4 Weak discontinuities Let us consider a wavefront D(t) across which the velocity is continuous and consequently all first-order derivatives of the displacement must be also continuous. 36) These conditions are restricting the jumps of the various fields across acceleration wavefronts. Acceleration waves in isotropic linear elastic solids. For small strains, the constitutive equations for a linear, isotropic elastic solid are where G and v are the elastic shear modulus and Poisson’s ratio, and εij the infinitesimal strain tensor.