Unique Identification of Stiffness Parameters in Hyperelastic Models for Anisotropic, Deformable, Thin Materials Based on a Single Experiment - A Feasibility Study Based on Virtual Full-Field Data

Abstract

Background

Characterizing material properties of thin sheets for design or manufacturing purposes is an essential concern in many engineering applications. This task is particularly challenging for materials with a pronounced anisotropic and nonlinear mechanical behavior.

Objective

A hybrid, experimental-numerical approach for the characterization of the mechanical, nonlinear response of thin, anisotropic, deformable materials is proposed. In contrast to classical approaches where various biaxial tension tests are analyzed, the main goal here is the complete characterization based on one single experiment.

Methods

The proposed approach is based on a novel non-standard experimental setup which is on the one hand easy to install and use, and which on the other hand intentionally induces a strongly inhomogeneous strain field in the specimen capturing as many deformation modes and intensities as possible. The resulting displacement field can be measured using e.g., digital image correlation, and is then accessible to the parameter identification as full-field data. To allow for an efficient identification, an extended equilibrium gap method is presented, where unknown boundary force distributions applied in the experiment are computed iteratively. The approach’s feasibility is assessed through virtual full-field data obtained by numerical simulation of the proposed experimental setup using predefined parameter values and applying realistic noise. That way, a quantitative assessment of the method’s performance regarding two specifically chosen material models is enabled.

Results

Provided that the stiffness-related material parameters are indeed linear in the stress equations, a quadratic optimization problem can be constructed to allow for a unique identification of the parameter values. Analysis show that reference parameter values for calendered rubber as well as coated textile fabric can be identified, even when realistic noise is applied to the virtual test data.

Conclusion

Based on the presented investigations, the proposed method has been found to be feasible for the accurate identification of stiffness-related parameters of anisotropic, nonlinear thin sheets using a single experiment.