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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 ...
A neo-Hookean solid [1] [2] is a hyperelastic material model, similar to Hooke's law, that can be used for predicting the nonlinear stress–strain behavior of materials undergoing large deformations.
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 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 .
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 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
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 .
Yeoh model prediction versus experimental data for natural rubber. Model parameters and experimental data from PolymerFEM.com. The Yeoh hyperelastic material model [1] is a phenomenological model for the deformation of nearly incompressible, nonlinear elastic materials such as rubber.