On the work theorems for finite and incremental elastic deformations with discontinuous fields: A unified treatment of different versions
Identifieur interne : 003F55 ( Main/Exploration ); précédent : 003F54; suivant : 003F56On the work theorems for finite and incremental elastic deformations with discontinuous fields: A unified treatment of different versions
Auteurs : H. Bufler [Allemagne]Source :
- Computer Methods in Applied Mechanics and Engineering [ 0045-7825 ] ; 1981.
Abstract
Starting from the statical and kinematical relations in three different versions characterized by the use of Piola's, Kirchhoff's or Biot's (Jaumann's) stresses respectively and the corresponding deformation quantities a unified abstract formulation of the basic equations is given. Because of certain properties of the statical and geometrical operators various material independent work theorems follow including the (generalized and modified) principles of virtual displacements and virtual forces. For a hyperelastic body under conservative loading these are transformed into generalized variational principles and strengthened to complementary extremum principles. Finally the abstract formulation is applied to the incremental equations. The admissible functions are allowed to have relaxed continuity properties. Therefore the presented work theorems may be used as a basis for a consistent finite element approximation according to the mixed version or to the classical displacement formulation.
Url:
DOI: 10.1016/0045-7825(83)90156-1
Affiliations:
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