An approach for hyperelastic model-building and parameters estimation a review of constitutive models

• We develop a practical approach for building adequate hyperelastic models.
• Foundations of original attractive models building-strategy have been investigated.
• Stable parameter’s values and the validity of a model are established from data.
• We construct a new constitutive model generalizing that of Hart-Smith.

This work presents a mathematical approach for the best way to structure hyperelastic models applicable to incompressible rubber-like materials; and it describes a model validation procedure using a step-by-step method for parameters estimation. This technique allows the validation of a restrained model as well as a complete one by doing it by graduation as the deformation increases. It builds on the restrained form (constrained model) essentially by progressively adding a higher degree term. The contribution of the added terms is irrelevant to the regime in which this constrained model provides a good fit to data. It becomes significant only where the deviation between the data and the restrain model prediction is important. It is a nonlinear process that leads to an optimal solution. After a concise appraisal of the underlying theoretical framework, the model-building strategies and parameters estimation method are presented. An attempt to understand and to elucidate how the existing attractive phenomenological models have been built is discussed. Furthermore, analytical and numerical results from hyperelastic modeling are compared using each of the two procedures first by deriving an optimal strain energy function which is then used in the formulation of a new constitutive model that generalizes the Hart-Smith model and second, by evaluating the correct and stable parameters values of rubbery materials taking into account the physical constraints that must be imposed on a realistic and physical model.

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