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

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