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Title: Inverse problems in heterogeneous and fractured media using peridynamics

Abstract

The following work presents an adjoint-based methodology for solving inverse problems in heterogeneous and fractured media using state-based peridynamics. We show that the inner product involving the peridynamic operators is self-adjoint. The proposed method is illustrated for several numerical examples with constant and spatially varying material parameters as well as in the context of fractures. We also present a framework for obtaining material parameters by integrating digital image correlation (DIC) with inverse analysis. This framework is demonstrated by evaluating the bulk and shear moduli for a sample of nuclear graphite using digital photographs taken during the experiment. The resulting measured values correspond well with other results reported in the literature. Lastly, we show that this framework can be used to determine the load state given observed measurements of a crack opening. Furthermore, this type of analysis has many applications in characterizing subsurface stress-state conditions given fracture patterns in cores of geologic material.

Authors:
 [1];  [2];  [2]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Stellenbosch Univ., Stellenbosch (South Africa)
  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:
1248618
Report Number(s):
SAND-2014-17560J
Journal ID: ISSN 1559-3959; 537514
Grant/Contract Number:  
AC04-94AL85000
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Mechanics of Materials and Structures
Additional Journal Information:
Journal Volume: 10; Journal Issue: 5; Journal ID: ISSN 1559-3959
Publisher:
Mathematical Science Publishers
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; peridynamics; fractured media; inverse problems; digital image correlation

Citation Formats

Turner, Daniel Z., van Bloemen Waanders, Bart G., and Parks, Michael L. Inverse problems in heterogeneous and fractured media using peridynamics. United States: N. p., 2015. Web. doi:10.2140/jomms.2015.10.573.
Turner, Daniel Z., van Bloemen Waanders, Bart G., & Parks, Michael L. Inverse problems in heterogeneous and fractured media using peridynamics. United States. https://doi.org/10.2140/jomms.2015.10.573
Turner, Daniel Z., van Bloemen Waanders, Bart G., and Parks, Michael L. 2015. "Inverse problems in heterogeneous and fractured media using peridynamics". United States. https://doi.org/10.2140/jomms.2015.10.573. https://www.osti.gov/servlets/purl/1248618.
@article{osti_1248618,
title = {Inverse problems in heterogeneous and fractured media using peridynamics},
author = {Turner, Daniel Z. and van Bloemen Waanders, Bart G. and Parks, Michael L.},
abstractNote = {The following work presents an adjoint-based methodology for solving inverse problems in heterogeneous and fractured media using state-based peridynamics. We show that the inner product involving the peridynamic operators is self-adjoint. The proposed method is illustrated for several numerical examples with constant and spatially varying material parameters as well as in the context of fractures. We also present a framework for obtaining material parameters by integrating digital image correlation (DIC) with inverse analysis. This framework is demonstrated by evaluating the bulk and shear moduli for a sample of nuclear graphite using digital photographs taken during the experiment. The resulting measured values correspond well with other results reported in the literature. Lastly, we show that this framework can be used to determine the load state given observed measurements of a crack opening. Furthermore, this type of analysis has many applications in characterizing subsurface stress-state conditions given fracture patterns in cores of geologic material.},
doi = {10.2140/jomms.2015.10.573},
url = {https://www.osti.gov/biblio/1248618}, journal = {Journal of Mechanics of Materials and Structures},
issn = {1559-3959},
number = 5,
volume = 10,
place = {United States},
year = {Thu Dec 10 00:00:00 EST 2015},
month = {Thu Dec 10 00:00:00 EST 2015}
}

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Cited by: 2 works
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Works referenced in this record:

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Works referencing / citing this record:

Extracting Constitutive Mechanical Parameters in Linear Elasticity Using the Virtual Fields Method Within the Ordinary State-Based Peridynamic Framework
journal, January 2020