In this research, a framework for modelling and simulation of hyper-elastic materials is proposed. The framework explains how to employ strain energy functions as a constitutive model, standard loading test data, and a powerful optimisation method to determine a mathematical function for explaining the mechanical behaviour of a hyper-elastic material using minimum types of loading test data. In the first part, a survey on hyper-elastic constitutive models is presented. Fifty models are collected and classified into six categories. Thereafter, five types of standard loading tests including uniaxial, biaxial, equi-biaxial, pure shear, and simple shear are introduced. It is shown that depending on the loading type, physical parameters, Cauchy, and nominal stress tensors, each constitutive model possesses a particular function. The genetic algorithm as a powerful optimisation method is used to determine the most accurate function for each type of loading test data. It is presented that based on the selected constitutive model and regardless of a number of existing loading types test data, a unique function can be determined for expressing and simulating the mechanical behaviour of the considered hyper-elastic material.

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