The Computational Reconstruction of a Spherical Inclusion within a Cylindrical Geometry using Inverse Techniques

Abstract

For common homogenous engineering materials, traditional testing methods, such as uniaxial tensile testing, provide effective means to determine important material properties such as the elastic modulus. However, characterizing an unknown nonhomogeneous material property distribution is a non-trivial problem. This thesis seeks to demonstrate the feasibility of using inverse problems in elasticity to reconstruct the nonhomogeneous material property distribution within a 3D incompressible elastic domain using limited surface displacement data. This will be demonstrated through simulated results and the reconstruction of known domains using a constrained minimization formulation of the inverse problem. Successful simulated results are discussed that consider realistic experimental equipment, measurement feasibility, and noise. In addition, attempts to experimentally validate the results are discussed, although these attempts were ultimately unsuccessful.