We study the motion of a solid with large deformations. The solid may be loaded on its surface by needles, rods, beams, plates,. It turns out that it is wise to choose a third gradient theory for the body. The stretch matrix of the polar decomposition has to be symmetric. This is an internal constraint which introduces a reaction stress in the Piola-Kirchhoff-Boussinesq stress. By use of a Galerkin approximation, combined with suitable a priori estimates and a passage to the limit, we prove that there exists a motion which solves a variational formulation of the complete equations of mechanics, at least locally in time. This motion may be interrupted by crushing resulting in a discontinuity of velocity with respect to time, i.e.; an internal collision.
2D motion with large deformations / E. Bonetti, P. Colli, M. Frémond. - In: BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA. - ISSN 1972-6724. - 7:1(2014), pp. 19-44.
2D motion with large deformations
E. BonettiPrimo
;
2014
Abstract
We study the motion of a solid with large deformations. The solid may be loaded on its surface by needles, rods, beams, plates,. It turns out that it is wise to choose a third gradient theory for the body. The stretch matrix of the polar decomposition has to be symmetric. This is an internal constraint which introduces a reaction stress in the Piola-Kirchhoff-Boussinesq stress. By use of a Galerkin approximation, combined with suitable a priori estimates and a passage to the limit, we prove that there exists a motion which solves a variational formulation of the complete equations of mechanics, at least locally in time. This motion may be interrupted by crushing resulting in a discontinuity of velocity with respect to time, i.e.; an internal collision.Pubblicazioni consigliate
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