The Coupled Adjoint-State Equation in forward and inverse linear elasticity: Incompressible plane stress

Journal Article · 01 December 2019 · Computer Methods in Applied Mechanics and Engineering

DOI: https://doi.org/10.1016/j.cma.2019.112588 · OSTI ID:1559519

Seidl, D. Thomas ^[1]; Oberai, Assad A.  ^[2]; Barbone, Paul E. ^[3]

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1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Dept. of Optimization and Uncertainty Quantification
2. Univ. of Southern California, Los Angeles, CA (United States). Dept. of Aerospace and Mechanical Engineering
3. Boston Univ., MA (United States). Dept. of Mechanical Engineering

A persistent challenge present in inverse or parameter estimation problems with interior data is how to deal with uncertainty in the boundary conditions employed in the forward or state model. In this work we focus on a linear plane stress inverse elasticity problem with measured displacement data where one component of the measured displacement field is known with considerably greater precision than the other. This situation is commonly encountered when the displacement field is measured using ultrasound or optical coherence tomography. We present a novel computational formulation in which no displacement or traction boundary conditions are assumed. The formulation results in coupling the state and adjoint equations, that are typically uncoupled when a well-posed state model is available. Two variants of residual-based stabilization are added. Our approach is applied to a simulated data set and experimental data from an ultrasound phantom.

• Research Organization: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: AC04-94AL85000
• OSTI ID: 1559519
• Report Number(s): SAND2019-9694J; 678599; TRN: US2000357
• Journal Information: Computer Methods in Applied Mechanics and Engineering, Vol. 357, Issue C; ISSN 0045-7825
• Publisher: ElsevierCopyright Statement
• Country of Publication: United States
• Language: English