On Constitutive Models for Limited Elastic, Molecular Based Materials

The response function for a general class of elastic molecular based materials characterized by their limiting molecular chain extensibility and depending on only the first principal invariant of the Cauchy–Green deformation tensor together with a certain molecular based limiting extensibility parameter is introduced. The constitutive response function for the Gent material is then derived inversely as the [0/1] Padé approximant of this class, a result that leads naturally to an infinite geometric series representation of its response function. Truncation of this series function characterizes a familiar class of quadratic materials now having physically relevant material constants. It is shown that the [0/2] approximant of the response function for the general class of restricted elastic materials leads inversely to a new constitutive model and its series representation. Of course, many familiar limited elastic material models are members of the general class. The Padé approximants for some response functions are not, and empirical modifications that admit these as members of the general class are described. Examples of two limited elastic models in the class that are not Padé approximants are noted. The strain energy functions for a few of the restricted elastic models described are presented.