Optimization of the stored energy and coaxiality of strain and stress in finite elasticity

✍ Scribed by Maurizio Vianello

• Publisher: Springer Netherlands
• Year: 1996
• Tongue: English
• Weight: 562 KB
• Volume: 44
• Category: Article
• ISSN: 0374-3535
• DOI: 10.1007/bf00042131

✦ Synopsis

The strain energy density of a hyperelastic anisotropic body which is rotated before being subjected to a given but arbitrary deformation is viewed as a smooth function defined on the group of rotations, parametrized by the deformation gradient. It is shown that the critical points of this function correspond to rotations which, when composed with the prescribed deformation, yield a total strain tensor which is coaxial with the corresponding stress. For any type of material symmetry, there are at least two such rotations. Coaxiality of stress and strain for all deformations is shown to be a sufficient condition for the isotropicity of hyperelastic materials.