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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 ...
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]
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 ...
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.
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 ...
Similarly, the total stress will be the sum of the stress in each component: [4] σ Total = σ S + σ D . {\displaystyle \sigma _{\text{Total}}=\sigma _{\rm {S}}+\sigma _{\rm {D}}.} From these equations we get that in a Kelvin–Voigt material, stress σ , strain ε and their rates of change with respect to time t are governed by equations of ...
The Hertzian contact stress usually refers to the stress close to the area of contact between two spheres of different radii. It was not until nearly one hundred years later that Kenneth L. Johnson , Kevin Kendall , and Alan D. Roberts found a similar solution for the case of adhesive contact. [ 5 ]
If the rubber is compressible, a dependence on = can be introduced into the strain energy density; being the deformation gradient. Several possibilities exist, among which the Kaliske–Rothert [5] extension has been found to be reasonably accurate. With that extension, the Arruda-Boyce strain energy density function can be expressed as