The Strain‐Energy Function of a Hyperelastic Material in Terms of the Extension Ratios
作者:
K. C. Valanis,
R. F. Landel,
期刊:
Journal of Applied Physics
(AIP Available online 1967)
卷期:
Volume 38,
issue 7
页码: 2997-3002
ISSN:0021-8979
年代: 1967
DOI:10.1063/1.1710039
出版商: AIP
数据来源: AIP
摘要:
A simple form of the strain‐energy function of natural rubber results if the latter is expressed an an analytic function of the extension ratios rather than the invariants. For incompressible isotropic materials it is postulated that this is a separable symmetric function of the extension ratios, i.e.,W = w(&lgr;1) +w(&lgr;2) +w(&lgr;3). This form has been substantiated by critical plots using uniaxial and biaxial data reported in the literature by several investigators. The above form appears to be valid over a wide range of deformations (0.2≤&lgr;≤3.5). An explicit representation ofWfor this range is given in graphical form. In the more limited range (0.6≤&lgr;≤2.5)w(&lgr;) has the analytic formw=2 &mgr;&lgr; (ln&lgr;−1).
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