A Mixed Variational Framework for Eigenstrain and Residual Stress Reconstruction
Publication: Journal of Engineering Mechanics
Volume 149, Issue 11
Abstract
This paper proposes an inverse eigenstrain analysis procedure to estimate full-field residual stress from an incompletely measured residual elastic strain or stress field. The inverse problem is solved by minimizing the linear elastic constitutive relation discrepancy that arises from different admissible stress and strain fields within an alternating minimization framework. First, a standard forward thermoelastic problem is solved to obtain a statically admissible total strain field. Then, full-field residual stress (or elastic strain) that satisfies partial measurement is obtained by minimizing a Hellinger-Reissner-type energy functional under a mixed variational framework. We have used standard two and three-dimensional hybrid finite elements to obtain a stress field. Finally, a full-field eigenstrain field is obtained by minimizing constitutive disparity due to dissimilar elastic strain and total strain fields. We show the efficacy of the proposed procedure with some numerically obtained and experimentally reported data.
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Data Availability Statement
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
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Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 149 • Issue 11 • November 2023
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Jan 7, 2023
Accepted: Jul 23, 2023
Published online: Sep 15, 2023
Published in print: Nov 1, 2023
Discussion open until: Feb 15, 2024
ASCE Technical Topics:
- Constitutive relations
- Construction engineering
- Construction management
- Elastic analysis
- Elasticity and Inelasticity
- Engineering fundamentals
- Material mechanics
- Material properties
- Materials engineering
- Mathematics
- Mechanical properties
- Residual stress
- Strain
- Stress (by type)
- Stress analysis
- Stress strain relations
- Structural analysis
- Structural engineering
- Thermoelasticity
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