An ignored source in the foundations of continuum physics " Die Allgemeinen Ansätze der Mechanik der Kontinua " by E. Hellinger

Abstract : In 1913, Ernst Hellinger finished his remarkable article DIE ALLGEMEINEN ANSÄTZE DER MECHANIK DER KON-TINUA, which appeared in German language in the " Encyklopädie der mathematischen Wissenschaften mit Einschluss ihrer Anwendungen ". Following his predecessors J.-L. Lagrange, G. Piola and the Cosserat brothers, Hellinger presents in this paper a nonlinear field theory of continuum physics entirely based on a variational principle " the principle of virtual displacements ". Even though Hellinger focuses on the fundamentals of continuum mechanics, he presents within the very same variational framework the physics of optics, electrodynamics, thermodynamics and the theory of relativity. Accordingly, Hellinger's paper can be understood as a contribution to continuum physics in general. However, due to the establishment of English as the upcoming scientific language and due to the refusal of a variational formulation of continuum mechanics in the subsequent period, Hellinger's contribution to the foundations of continuum physics has been ignored for decades and has almost fallen into oblivion.
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Simon R. Eugster, Francesco Dell'Isola. An ignored source in the foundations of continuum physics " Die Allgemeinen Ansätze der Mechanik der Kontinua " by E. Hellinger. Proceedings in Applied Mathematics and Mechanics, John Wiley & Sons, Inc. 2017. ⟨hal-01689686⟩

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