The Contact Problem in a Compressible Hyperelastic Material

2006 ◽  
Vol 74 (4) ◽  
pp. 829-831 ◽  
Author(s):  
G. F. Wang ◽  
T. J. Wang ◽  
P. Schiavone
Keyword(s):  
Contact Problem ◽  
Plane Problem ◽  
Complex Variable ◽  
Point Load ◽  
Finite Plane ◽  
Uniform Load ◽  
Finite Area ◽  
Hyperelastic Materials ◽  
Finite Plane Deformations ◽  
Plane Deformations

We consider the contact problem for a particular class of compressible hyperelastic materials of harmonic type undergoing finite plane deformations. Using complex variable techniques, we derive subsidiary results concerning a half-plane problem corresponding to this class of materials. Using these results, we solve the contact problem for a harmonic material in the case of a uniform load acting on a finite area. Finally, we show how we can then deduce the corresponding results for the case of a point load.

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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