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Some thoughts on the material mechanics of materials.

Gérard A. Maugin — 1999

Extracta Mathematicae

This paper outlines recent developments and prospects in the application of the continuum mechanics expressed intrinsically on the material manifold itself. This includes applications to materially inhomogeneous materials, physical effects which, in this vision, manifest themselves as quasi-inhomogeneities, and the notion of thermodynamical driving force of the dissipative progress of singular point sets on the material manifold with special emphasis on fracture, shock waves and phase-transition...

Note on a mixed variational principle in finite elasticity

Gérard A. MauginCarmine Trimarco — 1992

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In the present context the variation is performed keeping the deformed configuration fixed while a suitable material stress tensor S and the material coordinates are required to vary independently. The variational principle turns out to be equivalent to an equilibrium problem of placements and tractions prescribed at the boundary of a body of finite extent.

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