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The Coupled AdjointState Equation in forward and inverse linear elasticity: Incompressible plane stress
Abstract
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 wellposed state model is available. Two variants of residualbased stabilization are added. Our approach is applied to a simulated data set and experimental data from an ultrasound phantom.
 Authors:

 Sandia National Lab. (SNLNM), Albuquerque, NM (United States). Dept. of Optimization and Uncertainty Quantification
 Univ. of Southern California, Los Angeles, CA (United States). Dept. of Aerospace and Mechanical Engineering
 Boston Univ., MA (United States). Dept. of Mechanical Engineering
 Publication Date:
 Research Org.:
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA)
 OSTI Identifier:
 1559519
 Report Number(s):
 SAND20199694J
Journal ID: ISSN 00457825; 678599; TRN: US2000357
 Grant/Contract Number:
 AC0494AL85000
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Computer Methods in Applied Mechanics and Engineering
 Additional Journal Information:
 Journal Volume: 357; Journal Issue: C; Journal ID: ISSN 00457825
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 42 ENGINEERING
Citation Formats
Seidl, D. Thomas, Oberai, Assad A., and Barbone, Paul E. The Coupled AdjointState Equation in forward and inverse linear elasticity: Incompressible plane stress. United States: N. p., 2019.
Web. doi:10.1016/j.cma.2019.112588.
Seidl, D. Thomas, Oberai, Assad A., & Barbone, Paul E. The Coupled AdjointState Equation in forward and inverse linear elasticity: Incompressible plane stress. United States. doi:10.1016/j.cma.2019.112588.
Seidl, D. Thomas, Oberai, Assad A., and Barbone, Paul E. Sun .
"The Coupled AdjointState Equation in forward and inverse linear elasticity: Incompressible plane stress". United States. doi:10.1016/j.cma.2019.112588.
@article{osti_1559519,
title = {The Coupled AdjointState Equation in forward and inverse linear elasticity: Incompressible plane stress},
author = {Seidl, D. Thomas and Oberai, Assad A. and Barbone, Paul E.},
abstractNote = {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 wellposed state model is available. Two variants of residualbased stabilization are added. Our approach is applied to a simulated data set and experimental data from an ultrasound phantom.},
doi = {10.1016/j.cma.2019.112588},
journal = {Computer Methods in Applied Mechanics and Engineering},
number = C,
volume = 357,
place = {United States},
year = {2019},
month = {12}
}