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Title: A Generalized Stress Inversion Approach With Application to Residual Stress Estimation

Abstract

In this work develop a generalized stress inversion technique (or the generalized inversion method) capable of recovering stresses in linear elastic bodies subjected to arbitrary cuts. Specifically, given a set of displacement measurements found experimentally from digital image correlation (DIC), we formulate a stress estimation inverse problem as a partial differential equation-constrained optimization problem. We use gradient-based optimization methods, and we accordingly derive the necessary gradient and Hessian information in a matrix-free form to allow for parallel, large-scale operations. By using a combination of finite elements, DIC, and a matrix-free optimization framework, the generalized inversion method can be used on any arbitrary geometry, provided that the DIC camera can view a sufficient part of the surface. We present numerical simulations and experiments, and we demonstrate that the generalized inversion method can be applied to estimate residual stress.

Authors:
 [1];  [1];  [2];  [2];  [2];  [2];  [2];  [2]
  1. Duke Univ., Durham, NC (United States)
  2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1668699
Report Number(s):
SAND-2020-10115J
Journal ID: ISSN 0021-8936; 690835
Grant/Contract Number:  
AC04-94AL85000; NA0003525
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Applied Mechanics
Additional Journal Information:
Journal Volume: 87; Journal Issue: 11; Journal ID: ISSN 0021-8936
Publisher:
ASME
Country of Publication:
United States
Language:
English
Subject:
computational mechanics; elasticity; stress analysis; stress; traction; noise; arches; inverse problems

Citation Formats

Chen, Mark J., Aquino, Wilkins, Walsh, Timothy F., Reu, Phillip L., Johnson, Kyle L., Rouse, Jerry W., Jared, Bradley H., and Bishop, Joseph E. A Generalized Stress Inversion Approach With Application to Residual Stress Estimation. United States: N. p., 2020. Web. doi:10.1115/1.4048097.
Chen, Mark J., Aquino, Wilkins, Walsh, Timothy F., Reu, Phillip L., Johnson, Kyle L., Rouse, Jerry W., Jared, Bradley H., & Bishop, Joseph E. A Generalized Stress Inversion Approach With Application to Residual Stress Estimation. United States. doi:10.1115/1.4048097.
Chen, Mark J., Aquino, Wilkins, Walsh, Timothy F., Reu, Phillip L., Johnson, Kyle L., Rouse, Jerry W., Jared, Bradley H., and Bishop, Joseph E. Mon . "A Generalized Stress Inversion Approach With Application to Residual Stress Estimation". United States. doi:10.1115/1.4048097.
@article{osti_1668699,
title = {A Generalized Stress Inversion Approach With Application to Residual Stress Estimation},
author = {Chen, Mark J. and Aquino, Wilkins and Walsh, Timothy F. and Reu, Phillip L. and Johnson, Kyle L. and Rouse, Jerry W. and Jared, Bradley H. and Bishop, Joseph E.},
abstractNote = {In this work develop a generalized stress inversion technique (or the generalized inversion method) capable of recovering stresses in linear elastic bodies subjected to arbitrary cuts. Specifically, given a set of displacement measurements found experimentally from digital image correlation (DIC), we formulate a stress estimation inverse problem as a partial differential equation-constrained optimization problem. We use gradient-based optimization methods, and we accordingly derive the necessary gradient and Hessian information in a matrix-free form to allow for parallel, large-scale operations. By using a combination of finite elements, DIC, and a matrix-free optimization framework, the generalized inversion method can be used on any arbitrary geometry, provided that the DIC camera can view a sufficient part of the surface. We present numerical simulations and experiments, and we demonstrate that the generalized inversion method can be applied to estimate residual stress.},
doi = {10.1115/1.4048097},
journal = {Journal of Applied Mechanics},
number = 11,
volume = 87,
place = {United States},
year = {2020},
month = {8}
}

Journal Article:
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