## This content will become publicly available on December 1, 2020

## The Coupled Adjoint-State 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 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.

- Authors:

- Sandia National Lab. (SNL-NM), 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. (SNL-NM), Albuquerque, NM (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1559519

- Report Number(s):
- SAND2019-9694J

Journal ID: ISSN 0045-7825; 678599

- Grant/Contract Number:
- AC04-94AL85000

- 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 0045-7825

- 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 Adjoint-State 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 Adjoint-State 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 Adjoint-State 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 Adjoint-State 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 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.},

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}

}