The numerical identification of hyperelastic constitutive model parameters is a common problem that reveals often in finite element (FE) simulations. First, for such complex models, a basic step-by-step classical identification through experimental stress-strain curves could not be performed. Moreover, for numerous models such as observed for Fung model, some non-explicit convexity conditions, greatly influenced by the chosen material parameters, should be taken into account during the identification process; the omission of these conditions could lead to major instabilities and divergences in the numerical FE implementations. Thus, the integration of these convexity conditions in a process of rheological parameter direct identification represents a great difficulty. It therefore requires specific identification tools based on global optimization procedures.

In the present work, we focused on the identification of the parameters of an orthotropic woven tissue using Fung hyperelastic-orthotropic model that is implemented in the commercial FE software ABAQUS. We proposed a direct numerical identification process, taking directly into account the convexity conditions, allowing to determine the corresponding material parameters. The developed identification tool is based on the evolutionary global optimization approach, using a genetic algorithm (GA). This identification strategy thus allows to establish parameter identifications performed simultaneously on several experimental stress-stretch curves, in the warp and the weft directions, which is substantial for the identification of orthotropic materials.

The accuracy and reproducibility of this identification method was evaluated by comparing the corresponding analytical stress-stretch response with the experimental curves of the studied orthotropic tissue. More validation tests for other types of orthotropic hyperelastic tissues from the literature have confirmed the effectiveness of our identification approach. At last, the identified material parameters were tested for different FE calculations, that converged correctly and demonstrated a good numerical stability.