Systematic Fitting and Comparison of Hyperelastic Continuum Models for Elastomers

Abstract

Hyperelasticity is a common modeling approach to reproduce the nonlinear mechanical behavior of rubber materials at finite deformations. It is not only employed for stand-alone, purely elastic models but also within more sophisticated frameworks like viscoelasticity or Mullins-type softening. The choice of an appropriate strain energy function and identification of its parameters is of particular importance for reliable simulations of rubber products. The present manuscript provides an overview of suitable hyperelastic models to reproduce the isochoric as well as volumetric behavior of nine widely used rubber compounds. This necessitates firstly a discussion on the careful preparation of the experimental data. More specific, procedures are proposed to properly treat the preload in tensile and compression tests as well as to proof the consistency of experimental data from multiple experiments. Moreover, feasible formulations of the cost function for the parameter identification in terms of the stress measure, error type as well as order of the residual norm are studied and their effect on the fitting results is illustrated. After these preliminaries, invariant-based strain energy functions with decoupled dependencies on all three principal invariants are employed to identify promising models for each compound. Especially, appropriate parameter constraints are discussed and the role of the second invariant is analyzed. Thus, this contribution may serve as a guideline for the process of experimental characterization, data processing, model selection and parameter identification for existing as well as new materials.