The remarkable Gent constitutive model for hyperelastic materials

In 1996, Alan Gent published a short paper that proposed the use of a very simple two parameter phenomenological constitutive model for hyperelastic isotropic incompressible materials. The model is empirical but has the advantages of mathematical simplicity, reflects the severe strain-stiffening at large strains observed experimentally, reduces to the classic neo-Hookean model for small strains and involves just two material parameters namely the shear modulus for infinitesimal deformations and a parameter that measures a maximum allowable value of strain. The model reflects the limiting chain extensibility characteristic of non-Gaussian molecular models for rubber. Here we review some of the numerous developments, extensions and widespread applications that have resulted from that groundbreaking paper not only in rubber elasticity but also in the area of biomechanics of soft biomaterials. The Gent model is remarkably robust: its mathematical simplicity combined with physical basis has ensured that it has reached status as a fundamental canonical phenomenological constitutive model for hyperelastic materials.