On Duality, Symmetry and Symmetry lost in Solid Mechanics - École polytechnique Access content directly
Conference Papers Year : 2012

On Duality, Symmetry and Symmetry lost in Solid Mechanics

Abstract

The paper recalls the concept of duality in Mathematics and extends it to Solid Mechanics. One important application of duality is to restore some symmetry between current fields and their adjoint ones. This leads to many alternative schemes for numerical analyses, different from the classical one as used in classical variational formulation of boundary value problems (Finite Element Method). Usually, Conservation laws in Fracture Mechanics make use of the current fields, displacement and stress. Many conservation laws of this type are not free of the source term. Consequently, one cannot derive path-independent integrals for use in Fracture Mechanics. The introduction of variables and dual or adjoint variables leads to true path-independent integrals. Duality also introduces some anti-symmetry in current fields and adjoint ones for some boundary value problems. The symmetry is lost between fields and adjoint fields. The last notion enables us to derive new variational formulation on dual subspaces and to exactly solve inverse problems for detecting cracks and volume defects.
Fichier principal
Vignette du fichier
HDBui-Acome_2012.pdf (164.94 Ko) Télécharger le fichier
Origin Files produced by the author(s)
Loading...

Dates and versions

hal-00728313 , version 1 (05-09-2012)

Identifiers

  • HAL Id : hal-00728313 , version 1

Cite

Hui Duong Bui. On Duality, Symmetry and Symmetry lost in Solid Mechanics. International Conference on Advances in Computational Mechanics ACOME, Aug 2012, Ho Chi Minh City, Vietnam. pp. 44-54. ⟨hal-00728313⟩
161 View
487 Download

Share

Gmail Mastodon Facebook X LinkedIn More