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A strain energy density function or stored energy density function is a scalar-valued function that relates the strain energy density of a material to the deformation ...
The strain energy in the form of elastic deformation is mostly recoverable in the form of mechanical work. For example, the heat of combustion of cyclopropane (696 kJ/mol) is higher than that of propane (657 kJ/mol) for each additional CH 2 unit. Compounds with unusually large strain energy include tetrahedranes, propellanes, cubane-type ...
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 .
A hyperelastic or Green elastic material [1] is a type of constitutive model for ideally elastic material for which the stress–strain relationship derives from a strain energy density function. The hyperelastic material is a special case of a Cauchy elastic material.
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.
In continuum mechanics, a Mooney–Rivlin solid [1] [2] is a hyperelastic material model where the strain energy density function is a linear combination of two invariants of the left Cauchy–Green deformation tensor.
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
The primary, and likely most widely employed, strain-energy function formulation is the Mooney-Rivlin model, which reduces to the widely known neo-Hookean model. The strain energy density function for an incompressible Mooney—Rivlin material is = + (); =