ISSN:
1573-2681
Keywords:
finite elasticity
;
incompressible
;
Varga strain-energy
;
small on large deformations
;
plane strain.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
,
Physics
Notes:
Abstract In three recent papers [6–8], the present authors show that both plane strain and axially symmetric deformations of perfectly elastic incompressible Varga materials admit certain first integrals, which means that solutions for finite elastic deformations can be determined from a second order partial differential equation, rather than a fourth order one. For plane strain deformations there are three such integrals, while for axially symmetric deformations there are two. The purpose of the present papers is to present the general equations for small deformations which are superimposed upon a large deformation, which is assumed to satisfy one of the previously obtained first integrals. The governing partial differential equations for the small superimposed deformations are linear but highly nonhomogeneous, and we present here the precise structure of these equations in terms of a second-order linear differential operator D2, which is first defined by examining solutions of the known integrals. The results obtained are illustrated with reference to a number of specific large deformations which are known solutions of the first integrals. For deformations of limited magnitude, the Varga strain-energy function has been established as a reasonable prototype for both natural rubber vulcanizates and styrene-butadiene vulcanizates. Plane strain deformations are examined in this present part while axially symmetric deformations are considered in Part II [16].
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1007672011954
Permalink
