Gent hyperelastic model
The Gent hyperelastic material model 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 strain energy density function for the Gent model is where is the shear modulus and . In the limit where , the Gent model reduces to the Neo-Hookean solid model. This can be seen by expressing the Gent model in the form A Taylor series expansion of around and taking the limit as leads to which is the expression for the strain energy density of a Neo-Hookean solid. Several compressible versions of the Gent model have been designed. One such model has the form (the below strain energy function yields a non zero hydrostatic stress at no deformation, refer for compressible Gent models). where , is the bulk modulus, and is the deformation gradient. Consistency condition We may alternatively express the Gent model in the form For the model to be consistent with linear elasticity, the following condition has to be satisfied: where is the shear