On improving the accuracy of nonhomogeneous shear modulus identification in incompressible elasticity using the virtual fields method

TL;DR

This paper enhances the virtual fields method for identifying nonhomogeneous shear moduli in nearly incompressible solids by proposing new virtual fields that improve accuracy and robustness against noise and boundary uncertainties.

Contribution

It introduces two novel virtual fields derived from finite element analysis and curl computations, significantly improving shear modulus identification in challenging materials.

Findings

Proposed virtual fields outperform conventional ones in accuracy.

The approach is moderately sensitive to noise.

It effectively handles unknown boundary conditions.

Abstract

This paper discusses an important issue about the virtual fields method when it is used to identify nonhomogeneous shear moduli of nearly incompressible solids. From simulated examples, we observed that conventional virtual fields, which assign null displacements on the entire boundary, do not perform well on nonhomogeneous and nearly incompressible solids. Thus, these conventional virtual fields should not be used for such materials. We propose two novel types of virtual fields derived from either finite element analyses performed on the same domain with homogeneous properties or computing the curl of a potential vector field. From a variety of simulated and experimental examples, we observe that the proposed virtual fields significantly improve the accuracy of the estimated shear moduli of nonhomogeneous and nearly incompressible solids. Furthermore, the sensitivity to noise of the proposed approach is moderate and the approach can handle cases with unknown boundary conditions. Therefore, based on this careful and thorough analysis, it is concluded that the proposed approaches are a significant improvement of the VFM to identify nonhomogeneous shear moduli in nearly incompressible solids.