Citation Link: https://doi.org/10.1002/pamm.202300211
An approach to stress conversion between different deformation states for incompressible first‐invariant hyperelastic models
Publication Type
Article
Author(s)
Subjects
Hyperelastic material
Deformation (meteorology)
Finite strain theory
Compressibility
Invariant (physics)
Strain energy density function
Plane stress
Cauchy stress tensor
Infinitesimal strain theory
Stress (linguistics)
Mathematics
Mathematical analysis
Mechanics
Classical mechanics
Materials science
Physics
Finite element method
Mathematical physics
Composite material
Thermodynamics
Date Issued
2023
Abstract
To characterize generally valid hyperelastic material parameters, tensile tests at different deformation states are essential. This necessity arises from the hyperelasticity theory for incompressible materials, which is based on the first and second invariants of the right Cauchy–Green tensor. These invariants describe the elongation and surface change during a deformation process. By comparing different deformation states using the incompressibility plane of invariants, an equivalent deformation state can be determined for first‐invariant hyperelastic models. This deformation equivalence results in equal strain energy and is used to derive a method for converting stress‐strain relations of different deformation modes. The presented approach is verified and validated with experimental data.
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