Large deformations and extreme behaviours

Large deformations of a solid are investigated. We use a polar decomposition of gradient matrix F = RW (R is rotation matrix, W is stretch matrix). Large deformations of solids involve local spacial interactions either in an extension or in a rotation. Because local interactions are well described by spacial gradient, matrix W intervene for extensions and matrix grad R intervene for rotations. Thus the free energy depends on W and on grad R. Moreover, free energy takes into account the local impenetrability condition. Reactions to this impenetrability condition are important in constitutive laws. Within our parti-pris, self contact and extreme behaviours like the flattening (for example, structure flattened by a power hammer evolving from dimension 3 to dimension 2) are accounted for. To cite this article: M. Fremond, C R. Mecanique 337 (2009). (C) 2009 Academie des sciences. Publid par Elsevier Masson SAS. Tous droits reserves.