This paper illustrates Gabrio Piola’s view on continuum models, especially how contact actions are defined. Piola presented his mechanical theory before the 1850s, in an attempt to generalize Lagrange’s analytical mechanics. He conceived, among the rest, an ideal state for physical bodies (which nowadays we would call a natural state), a very general set of what we would now call state variables, and obtained balance equations via the superposition of a rigid infinitesimal motion on the present configuration. These views look quite modern even today and seem to historically precede among other things the introduction of structured continua.
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