The full-field coverage characterization over the energy domain of hyperelastic isotropic materials

In this work, the mechanical characterization of hyperelastic materials is critically reframed by presenting the full-field coverage characterization of the constitutive response of a material. We shift the focus from the experimental tests to the kinematic paths they trace over the energy domain, and from the measured stresses to the corresponding combinations of derivatives of the strain energy function. The key features of the full-field coverage characterization include the use of a single unequal biaxial experiment, the ability to reconstruct the effective response function of the material using simple equilibrium relations, and the coverage of the entire domain of the strain energy function. Conducting multiple experimental tests is costly. The standard tests, such as simple tension/compression, simple shear, and equi-biaxial tests, are not suited for characterizing the strain energy, as they only explore a single and limited kinematic path within the energy domain. For incompressible materials, the strain energy and its derivatives form surfaces on the stretches or strain invariants domain, which should be explicitly visualized using experiments. This two-dimensional nature is often overlooked and it is fundamentally reconsidered here. The analogy of a mountain relief surveyed by a terrestrial drone is proposed to highlight the often-overlooked two-dimensional nature of incompressible materials behavior. In silico simulations, based on a known energy function and constitutive parameters, are used to generate an "experimental" dataset to evaluate the proposed procedure. The results of the full-field coverage characterization introduce a novel paradigm that more accurately reproduces the behavior of soft materials than the simultaneous fitting of standard tests.