Incremental moduli of isotropic hyperelasticity and parameters identification: polynomial, exponential and power law formulations

Linear elasticity is the most widely used modelling technique for characterizing the mechanical behavior of materials, both in practical applications and in scientific research. The explicit physical meaning of the associated constitutive parameters and the simplicity of the procedures for their identification, as well as the intuitive conditions for model stability, are the basis for the success of the formulation. The situation is different in the case of non-linear hyperelastic models, where it is often difficult to identify the admissibility domain of the constitutive parameters, as well as the types of experimental tests and inverse analysis procedures required for the univocal identification of parameters. Therefore, an engineering strategy for stability and acceptability assessment, and constitutive parameters identification is proposed, using the concept of incremental moduli, with particular reference to the incremental Young's modulus and the incremental Poisson's ratio. The ...