Estimating the non-homogeneous elastic modulus distribution from surface deformations

We present a novel approach to solve the inverse problem in finite elasticity for the non-homogeneous shear modulus distribution solely from known surface deformation fields. The inverse problem is posed as a constrained optimization problem under regularization and solved utilizing the adjoint equations. Hypothetical “measured” surface displacement fields are created, by inducing indentations on the exterior of the specimen. These surface displacement fields are used to test the inverse strategy on a problem domain consisting of a stiff circular inclusion in a softer homogeneous background. We observe that the shear modulus reconstruction as well as the shape of the circular inclusion improves with an increasing number of surface displacement fields. Furthermore, with increasing noise level in the surface displacement field, the contrast of the reconstructions decreases.