Inverse problems in heterogeneous and fractured media using peridynamics

Turner, Daniel Z.; van Bloemen Waanders, Bart G.; Parks, Michael L.

doi:10.2140/jomms.2015.10.573

Inverse problems in heterogeneous and fractured media using peridynamics

Journal Article · Thu Dec 10 00:00:00 EST 2015 · Journal of Mechanics of Materials and Structures

DOI:https://doi.org/10.2140/jomms.2015.10.573· OSTI ID:1248618

Turner, Daniel Z. ^[1]; van Bloemen Waanders, Bart G. ^[2]; Parks, Michael L. ^[2]

Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Stellenbosch Univ., Stellenbosch (South Africa)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1248618

Report Number(s):: SAND--2014-17560J; 537514

Journal Information:: Journal of Mechanics of Materials and Structures, Journal Name: Journal of Mechanics of Materials and Structures Journal Issue: 5 Vol. 10; ISSN 1559-3959

Publisher:: Mathematical Science PublishersCopyright Statement

Country of Publication:: United States

Language:: English

References (17)

A two-dimensional ordinary , state-based peridynamic model for linearly elastic solids: 2D PERIDYNAMICS FOR LINEARLY ELASTIC SOLIDS Le, Q. V.; Chan, W. K.; Schwartz, J. International Journal for Numerical Methods in Engineering, Vol. 98, Issue 8 https://doi.org/10.1002/nme.4642	journal	March 2014
Image Correlation for Shape, Motion and Deformation Measurements Schreier, Hubert; Orteu, Jean-José; Sutton, Michael A. https://doi.org/10.1007/978-0-387-78747-3	book	March 2009
Applications of digital-image-correlation techniques to experimental mechanics Chu, T. C.; Ranson, W. F.; Sutton, M. A. Experimental Mechanics, Vol. 25, Issue 3 https://doi.org/10.1007/BF02325092	journal	September 1985
Peridynamic States and Constitutive Modeling Silling, S. A.; Epton, M.; Weckner, O. Journal of Elasticity, Vol. 88, Issue 2 https://doi.org/10.1007/s10659-007-9125-1	journal	July 2007
Convergence of Peridynamics to Classical Elasticity Theory Silling, S. A.; Lehoucq, R. B. Journal of Elasticity, Vol. 93, Issue 1 https://doi.org/10.1007/s10659-008-9163-3	journal	April 2008
Analysis of the Volume-Constrained Peridynamic Navier Equation of Linear Elasticity Du, Qiang; Gunzburger, Max; Lehoucq, R. B. Journal of Elasticity, Vol. 113, Issue 2 https://doi.org/10.1007/s10659-012-9418-x	journal	November 2012
Nonlocal Constrained Value Problems for a Linear Peridynamic Navier Equation Mengesha, Tadele; Du, Qiang Journal of Elasticity, Vol. 116, Issue 1 https://doi.org/10.1007/s10659-013-9456-z	journal	August 2013
Reformulation of elasticity theory for discontinuities and long-range forces Silling, S. A. Journal of the Mechanics and Physics of Solids, Vol. 48, Issue 1 https://doi.org/10.1016/S0022-5096(99)00029-0	journal	January 2000
The use of full-field measurement methods in composite material characterization: interest and limitations Grédiac, Michel Composites Part A: Applied Science and Manufacturing, Vol. 35, Issue 7-8 https://doi.org/10.1016/j.compositesa.2004.01.019	journal	July 2004
A meshfree method based on the peridynamic model of solid mechanics Silling, S. A.; Askari, E. Computers & Structures, Vol. 83, Issue 17-18 https://doi.org/10.1016/j.compstruc.2004.11.026	journal	June 2005
Digital image correlation and biaxial test on composite material for anisotropic damage law identification Périé, Jean Noël; Leclerc, Hugo; Roux, Stéphane International Journal of Solids and Structures, Vol. 46, Issue 11-12 https://doi.org/10.1016/j.ijsolstr.2009.01.025	journal	June 2009
On the variational limit of a class of nonlocal functionals related to peridynamics Mengesha, Tadele; Du, Qiang Nonlinearity, Vol. 28, Issue 11 https://doi.org/10.1088/0951-7715/28/11/3999	journal	October 2015
Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review Pan, Bing; Qian, Kemao; Xie, Huimin Measurement Science and Technology, Vol. 20, Issue 6 https://doi.org/10.1088/0957-0233/20/6/062001	journal	April 2009
Digital Image Correlation: from Displacement Measurement to Identification of Elastic Properties - a Review Hild, F.; Roux, S. Strain, Vol. 42, Issue 2 https://doi.org/10.1111/j.1475-1305.2006.00258.x	journal	May 2006
A Nonlocal Vector Calculus with Application to Nonlocal Boundary Value Problems Gunzburger, Max; Lehoucq, R. B. Multiscale Modeling & Simulation, Vol. 8, Issue 5 https://doi.org/10.1137/090766607	journal	January 2010
A Nonlocal Vector Calculus, Nonlocal Volume-Constrained Problems, and Nonlocal Balance laws Du, Qiang; Gunzburger, Max; Lehoucq, R. B. Mathematical Models and Methods in Applied Sciences, Vol. 23, Issue 03 https://doi.org/10.1142/S0218202512500546	journal	January 2013
Sensitivity technologies for large scale simulation. Collis, Samuel Scott; Bartlett, Roscoe Ainsworth; Smith, Thomas Michael https://doi.org/10.2172/921606	report	January 2005

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Extracting Constitutive Mechanical Parameters in Linear Elasticity Using the Virtual Fields Method Within the Ordinary State-Based Peridynamic Framework Delorme, Rolland; Diehl, Patrick; Tabiai, Ilyass Journal of Peridynamics and Nonlocal Modeling, Vol. 2, Issue 2 https://doi.org/10.1007/s42102-019-00025-7	journal	January 2020

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97 MATHEMATICS AND COMPUTING
digital image correlation
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inverse problems
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Inverse problems in heterogeneous and fractured media using peridynamics

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