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Rubber elasticity is the ability of solid rubber to be stretched up to a factor of 10 from its original length, and return to close to its original length upon release. This process can be repeated many times with no apparent degradation to the rubber. [1] Rubber, like all materials, consists of molecules.
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 .
The Yeoh model for incompressible rubber is a function only of . For compressible rubbers, a dependence on I 3 {\displaystyle I_{3}} is added on. Since a polynomial form of the strain energy density function is used but all the three invariants of the left Cauchy-Green deformation tensor are not, the Yeoh model is also called the reduced ...
The polynomial hyperelastic material model [1] is a phenomenological model of rubber elasticity. In this model, the strain energy density function is of the form of a polynomial in the two invariants I 1 , I 2 {\displaystyle I_{1},I_{2}} of the left Cauchy-Green deformation tensor.
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 second is that tension in a rubber band increases linearly with the length of the rubber band up to the elasticity limit, = ¯ = where τ is the tension, L 1 is the elasticity limit, L is the current length, b is a constant, T is the temperature and ΔL is change in length of the rubber band. [5] Requiring the consistency of two equations ...
In continuum mechanics, an Arruda–Boyce model [1] is a hyperelastic constitutive model used to describe the mechanical behavior of rubber and other polymeric substances. This model is based on the statistical mechanics of a material with a cubic representative volume element containing eight chains along the diagonal directions.
A Kelvin–Voigt material, also called a Voigt material, is the most simple model viscoelastic material showing typical rubbery properties. It is purely elastic on long timescales (slow deformation), but shows additional resistance to fast deformation.