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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 ...
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.
The concept of strain is used to evaluate how much a given displacement differs locally from a rigid body displacement. [1] [8] [9] One of such strains for large deformations is the Lagrangian finite strain tensor, also called the Green-Lagrangian strain tensor or Green–St-Venant strain tensor, defined as
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 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 = + (); =
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 .
To address this, regularization techniques are applied to the strain energy density function. Regularization is typically achieved by adding a regularization term to the strain energy density function of the material model. A common approach is the HuHu regularization, [1] expressed as:
The model was developed by Raymond Ogden in 1972. [1] The Ogden model, like other hyperelastic material models, assumes that the material behaviour can be described by means of a strain energy density function, from which the stress–strain relationships can be derived.