Abstract
Let π be the plane perpendicular to the unit vector u from the interior point P of C, and let dσ be an infinitely small region of π including P. π divides the body into two parts, and I shall call positive that part which contains u, and the other one negative. In the mathematical theory of continuous media it is fundamental to consider the contact forces which the particles of the body near π and belonging to the negative part exert across dσ on the particles belonging to the other part.
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References
Equations (2.12), (2.13) have been known since the last century. For brevity, I omit listing other Lagrangean forms of the basic equations [Boussinesq, Kirchhoff]. For the various forms of the equations of statics in curvilinear coordinates see [Tonolo, 1, 2].
Equations (2.16) correspond to [Signorini, 3, p. 112].
An interesting definition of thermal equilibrium has been given recently by Coleman and Noll. That definition is based on a local inequality regarding a kind of free energy per unit mass of the local state. The stress-strain relations are a corollary of the condition of equilibrium.
See also Udeschini.
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© 1962 Springer-Verlag OHG, Berlin · Göttingen · Heidelberg
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Grioli, G. (1962). Basic Equations of the Statics of Continuous Media. In: Mathematical Theory of Elastic Equilibrium. Ergebnisse der Angewandten Mathematik, vol 7. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-87432-1_2
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DOI: https://doi.org/10.1007/978-3-642-87432-1_2
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