Material characterization of curved shells under finite deformation using the virtual fields method

Abstract

Although full‐field measurement techniques have been well established, material characterization from these data remains challenging. Often, no closed‐form solution exists between measured quantities and sought material parameters. In this paper, a novel approach to determine the stiffness of thin curved membranes is proposed, based on the virtual fields method (VFM). Utilizing Kirchhoff‐Love shell theory, we show that the displacements can be decomposed into an in‐plane displacement and a rotation of the mid‐surface of the shell. Consequently, the strain tensor at the outer surface of the shell can then be decomposed into a membrane and a bending part. This allows for the VFM to be applied based only on data of the outer surface and on surfaces of arbitrary curvature. The method is first applied to simulated data. It is shown that the elastic modulus can be identified with less than 5% error if the thickness and Poisson ratio are known accurately. A 5% uncertainty in either the Poisson ratio or the thickness changes the identified value by 5%. Then, the method is applied on experimental data acquired on rubber samples having a dome‐like shape. Tensile tests are performed on the same samples, which permits to assess the linearized Young's modulus of this material for moderate strains (0–2.1%). Using regression analysis, a Young's modulus of 1.21 ± 0.08 MPa is found. Next, we performed pressurization tests on eight dome‐like shapes with pressures up to 4 kPa. The average Young's modulus obtained with the novel virtual fields method is 1.20 ± 0.13 MPa. The results are in good agreement with the ones from the tensile test. Future applications could benefit from this method to analyse more complex shapes, for example those found in biological structures like arteries or eardrums.