On finite plane deformations of compressible isotropic hyperelastic solids

1982 ◽  
Vol 43 (3-4) ◽  
pp. 159-168 ◽  
Author(s):  
C. Perdikis
Keyword(s):  
Finite Plane ◽  
Finite Plane Deformations ◽  
Plane Deformations

Harmonic Shapes in Finite Elasticity Under Nonuniform Loading

2004 ◽  
Vol 72 (5) ◽  
pp. 691-694 ◽  
Author(s):  
G. F. Wang ◽  
P. Schiavone ◽  
C.-Q. Ru
Keyword(s):  
Stress Field ◽  
Finite Elasticity ◽  
Normal Stresses ◽  
Finite Plane ◽  
Hyperelastic Materials ◽  
Nonuniform Loading ◽  
Final Stress ◽  
Remote Loading ◽  
Finite Plane Deformations ◽  
Plane Deformations

We investigate the classic (inverse) problem concerned with the design of so-called harmonic shapes for an elastic material undergoing finite plane deformations. In particular, we show how to identify such shapes for a particular class of compressible hyperelastic materials of harmonic type. The “harmonic condition,” in which the sum of the normal stresses in the original stress field remains unchanged everywhere after the introduction of the harmonic hole or inclusion, is imposed on the final stress field. Using complex variable techniques, we identify particular harmonic shapes arising when the material is subjected nonuniform (remote) loading and discuss conditions for the existence of such shapes.

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