DiscussionComment on “Averaging theory for description of environmental problems: What have we learned?” by William G. Gray, Cass T. Miller, and Bernhard A. Schrefler
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2015, International Journal of Solids and StructuresCitation Excerpt :When proceeding from a theoretical approach, research has necessarily focused on endowing the notions of total stress and partial phase stresses with precise, mechanically-consistent (Bedford and Drumheller, 1979; Hassanizadeh and Gray, 1979) and thermodynamically admissible (Gray et al., 2009; Svendsen and Hutter, 1995) mechanical definitions, as well as on the deduction of the stress partitioning law in the context of the many existing rational continuum theories of immiscible mixtures. In this respect, a multiplicity of immiscible continuum theories of mixtures has been proposed, see, e.g., the many works referenced in surveys (Baveye, 2013; Bedford and Drumheller, 1983; Gray et al., 2013), although these do not often collimate neither in the macroscopic balance equations (Albers and Wilmanski, 2006; Biot, 1955; Bowen, 1982; Goodman and Cowin, 1972; Hassanizadeh and Gray, 1979; Wilmanski, 1998), nor for the very physical–mathematical, or engineering, definition considered to introduce macroscopic stress measures in the theory (Bedford and Drumheller, 1979; Biot and Willis, 1957; Bishop, 1959; Coussy et al., 1998; de Boer and Ehlers, 1990; de Boer, 2005; Gray and Hassanizadeh, 1991; Gray et al., 2009; Lancellotta, 2002; Nur and Byerlee, 1971; Schrefler, 2002; Skempton, 1960a; Wilmanski, 2004). Similarly, when proceeding from an experimental point of view, non-exhaustive answers are found when trying to extend, to laws of more broad applicability, the stress partitioning regime measured for a particular class of biphasic media.
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