Direct error in constitutive equation formulation for plane stress inverse elasticity problem

• Published in: Computer methods in applied mechanics and engineering 2017-02, Vol.314, p.3-18
• Main Authors: Babaniyi, Olalekan A., Oberai, Assad A., Barbone, Paul E.
• Format: Article
• Language: English
• Subjects: Biomechanical imaging; Breast; Deformation; Discontinuous; Elastic properties; Elastography; Error in constitutive equations; Finite element method; Formulations; Inverse problems; Mathematical models; Modulus of elasticity; Permissible error; Plane stress; Strain; Tumors
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2016.10.026

We present a new computational formulation for inverse problems in elasticity with full field data. The formulation is a variant of an error in the constitutive equation formulation, but allows direct solution for the modulus field and accommodates discontinuous strain fields. The development of the formulation is motivated by the relatively poor performance of current direct formulations, reported so far in literature, in dealing with discontinuities in the strain and material property distribution. The formulation relies on minimizing the error in the constitutive equation with a momentum equation constraint. Numerical results on model problems show that the formulation is capable of handling discontinuous and noisy strain fields, and also converging with mesh refinement for continuous and discontinuous material property distributions. The application to reconstruct the elastic modulus distribution in solid breast tumors is shown. •We present a new computational formulation for inverse elasticity problems.•We show application to imaging two stiff breast tumors.•The formulation provides a direct (i.e. non-iterative) inverse problem solution.•The new formulation is stable and convergent for discontinuous material properties.