The theory of hyperelasticity is well established for isotropic materials, but open questions remain on how mechanical properties evolve with the strain state. At CMBM, we have developed a generalized approach for computing generalized incremental moduli [1] (i.e., material stiffness measures defined at a given stress–strain state) that extends the traditional definitions [2] used for uniaxial, volumetric, and shear loading. Given a hyperelastic potential and the stress at an arbitrary deformation, the method yields the corresponding incremental Young’s moduli, Poisson’s ratios, shear moduli, and bulk modulus. This framework captures the progressive stiffening, softening, and emergence of anisotropy with deformation, behaviors that fixed-stiffness (i.e., linear elastic) models cannot represent. The approach thus offers a general, state-dependent characterization of hyperelastic materials under arbitrary loading conditions.

For more information contact:

Emanuele Luigi Carniel
phone: +39 049 8276876
e-mail: emanueleluigi.carniel@unipd.it
 
[1] Carniel, E. L. (2025) Generalized incremental moduli of hyperelastic materials, ASME Journal of Applied Mechanics DOI: 10.1115/1.4069072.
[2] Carniel, E.L., Berardo, A., Toniolo, I., Fontanella, C.G. (2025a) Incremental moduli of isotropic hyperelasticity and parameters identification: polynomial, exponential and power law formulations, International Journal of Solids and Structures, 321, 113552. DOI: 10.1016/j.ijsolstr.2025.113552.