Continuum Mechanics through the Ages - From the Renaissance to the Twentieth Century

Abstract

Porous media have obviously attracted the attention of hydraulicians and specialists of geo-materials as soon as the early nineteenth century. The essential breakthrough was presented by Henry Darcy who proposed a simple law for the flux of water per area in sand on the basis of careful experiments. Here the notion of porosity is essential. But the importance of the concept of viscosity was not fully made explicit in spite of Poiseuille’s pioneering work on flows in pipes (in truth, blood in arteries). Darcy’s law was to prove to be the driving force in further progress in the field, so that the present contribution is akin to a saga of this law through a hundred and fifty years. Thus, chronologically, Fillunger, introduced the concept of uplift, Terzaghi produced a basic theory of consolidation of soils, Fillunger approached the flow in porous media in the form of an elementary theory of mixtures, and Biot proposed a first satisfactory theory of poroelaticity with interesting dynamic properties. Modern authors in the 1960s–1970s followed Truesdell in his rational theory of mixtures. More mathematically oriented researchers used the homogenization technique to justify Darcy’s law and its generalizations. The thermo-mechanical continuum theories in finite strains are also evoked, as well as very briefly the importance of porosity in plastic behaviour.