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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 ...
While the neo-Hookean material model can be stable for contact without sliding, sliding often leads to instability. 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.
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 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 = + (); =
The model is based on Ronald Rivlin's observation that the elastic properties of rubber may be described using a strain energy density function which is a power series in the strain invariants,, of the Cauchy-Green deformation tensors. [2]
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 chief advantage of critical plane analysis over earlier approaches like Sines rule, or like correlation against maximum principal stress or strain energy density, is the ability to account for damage on specific material planes.
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.