Direct determination of multi-axial elastic potentials for incompressible elastomeric solids: an accurate, explicit approach based on rational interpolation. (English) Zbl 1343.74051
Summary: With a novel approach based on certain logarithmic invariants, we demonstrate that a multi-axial elastic potential for incompressible, isotropic rubber-like materials may be obtained directly from two onedimensional elastic potentials for uniaxial case and simple shear case, in a sense of exactly matching finite strain data for four benchmark tests, including uniaxial extension, simple shear, bi-axial extension, and planestrain extension. As such, determination of multi-axial elastic potentials may be reduced to that of two onedimensional elastic potentials. We further demonstrate that the latter two may be obtained by means of rational interpolating procedures for uniaxial data and shear data displaying strain-stiffening effects. Numerical examples are presented in fitting Treloar’s data and other data.
MSC:
| 74S25 | Spectral and related methods applied to problems in solid mechanics |
| 74B05 | Classical linear elasticity |
Keywords:
elastomers; elastic potentials; logarithmic strain; invariants; benchmark tests; strain limit; rational interpolation; accurate matchingReferences:
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