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For rubber and biological materials, more sophisticated models are necessary. Such materials may exhibit a non-linear stress–strain behaviour at modest strains, or are elastic up to huge strains. These complex non-linear stress–strain behaviours need to be accommodated by specifically tailored strain-energy density functions.
Yeoh model prediction versus experimental data for natural rubber. Model parameters and experimental data from PolymerFEM.com. The Yeoh hyperelastic material model [1] is a phenomenological model for the deformation of nearly incompressible, nonlinear elastic materials such as rubber.
The stress and strain can be normal, shear, or a mixture, and can also be uniaxial, biaxial, or multiaxial, and can even change with time. The form of deformation can be compression, stretching, torsion, rotation, and so on. If not mentioned otherwise, stress–strain curve typically refers to the relationship between axial normal stress and ...
The most common example of this kind of material is rubber, whose stress-strain relationship can be defined as non-linearly elastic, isotropic and incompressible. Hyperelasticity provides a means of modeling the stress–strain behavior of such materials. [2] The behavior of unfilled, vulcanized elastomers often conforms closely to the ...
The Gent hyperelastic material model [1] is a phenomenological model of rubber elasticity that is based on the concept of limiting chain extensibility. In this model, the strain energy density function is designed such that it has a singularity when the first invariant of the left Cauchy-Green deformation tensor reaches a limiting value .
Measurements showing how the tensile stress in a stretched rubber sample varies with temperature are shown in Fig. 4. In these experiments, [22] the strain of a stretched rubber sample was held fixed as the temperature was varied between 10 and 70 degrees Celsius. For each value of fixed strain, it is seen that the tensile stress varied ...
Elastic response of rubber-like materials are often modeled based on the Mooney–Rivlin model. The constants , are determined by fitting the predicted stress from the above equations to the experimental data. The recommended tests are uniaxial tension, equibiaxial compression, equibiaxial tension, uniaxial compression, and for shear, planar ...
Stress–strain curves for a filled rubber showing progressive cyclic softening, also known as the Mullins effect. The Mullins effect is a particular aspect of the mechanical response in filled rubbers, in which the stress–strain curve depends on the maximum loading previously encountered. [1]