Abstract

Providing a quantitative description of the whole-field stress evolution in complex structures subjected to continuous loading processes using traditional photoelastic approaches is a significant challenge because of the difficulties with fabricating complex structures, identifying the stress distribution and evolution, and unwrapping isochromatic phase maps. To overcome the challenges, we proposed a novel method to quantify the continuous whole-field stress evolution in a complex porous structure that was fabricated with 3D printing technology. The stress fringes were identified by analysing a series of continuous frames extracted from a video recording of the fringe changes and determining the valleys of the light intensity change curve over the entire loading process. The experimental data were compared with the numerical results of the complex model with identical pore geometries, physical properties, and loading conditions to evaluate the accuracy and effectiveness of the method. In principle, the applicability of the reported method for identifying and unwrapping the continuous whole-field stress is not affected by the complexity of a structure.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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  28. Y. Liu, F. J. H. G. Kessels, W. D. V. Driel, J. A. S. V. Driel, F. L. Sun, and G. Q. Zhang, “Comparing drop impact test method using strain gauge measurements,” Microelectron. Reliab. 49(9–11), 1299–1303 (2009).
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  31. S. Takao, S. Yoneyama, and M. Takashi, “Minute displacement and strain analysis using lensless Fourier transformed holographic interferometry,” Opt. Lasers Eng. 38(5), 233–244 (2002).
    [Crossref]
  32. Z. Lei, M. Fu, and H. Yun, “Experimental study on interfacial shear transfer in partially-debonded aluminum/ epoxy joint,” Int. J. Adhes. 31(2), 104–111 (2011).
    [Crossref]
  33. J. T. Pinto, F. Touchard, S. Castagnet, C. Nadot-Martin, and D. Mellier, “DIC strain measurements at the micro-scale in a semi-crystalline polymer,” Exp. Mech. 53(8), 1311–1321 (2013).
    [Crossref]
  34. P. Forte, A. Paoli, and A. V. Razionale, “A CAE approach for the stress analysis of gear models by 3D digital photoelasticity,” Int. J. Interact. Des. Manuf. 9(1), 31–43 (2015).
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    [Crossref]
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    [Crossref]
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    [Crossref]
  49. A. Ajovalasit and G. Petrucci, “Developments in RGB photoelasticity,” Appl. Mech. Mater. 3–4, 205–210 (2005).
    [Crossref]
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    [Crossref]
  51. B. Zuccarello and G. Tripoli, “Photoelastic stress pattern analysis using Fourier transform with carrier fringes: influence of quarter-wave plate error,” Opt. Lasers Eng. 37(4), 401–416 (2002).
    [Crossref]
  52. J. H. Yang, F. Q. Wu, and J. Z. Sun, “Estimation of the tensile elastic modulus using Brazilian disc by applying diametrically opposed concentrated loads,” Int. J. Rock Mech. Min. Sci. 46(3), 568–576 (2009).
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  55. R. P. Singh, J. Lambros, A. Shukla, and A. J. Rosakis, “Investigation of the mechanics of intersonic crack propagation along a bimaterial interface using coherent gradient sensing and photoelasticity,” P. Roy Soc. A-Math. Phys. 453 (1967), 2649–2667 (1997).
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2017 (3)

Y. Ju, L. Wang, H. Xie, G. Ma, Z. Zheng, and L. Mao, “Visualization and transparentization of the structure and stress field of aggregated geomaterials through 3D printing and photoelastic techniques,” Rock Mech. Rock Eng. 50(6), 1383–1407 (2017).
[Crossref]

Y. Ju, Z. Zheng, H. Xie, J. Lu, L. Wang, and K. He, “Experimental visualisation methods for three-dimensional stress fields of porous solids,” Exp. Tech. 41(4), 331–344 (2017).
[Crossref]

L. Wang, Y. Ju, H. Xie, G. Ma, L. Mao, and K. He, “The mechanical and photoelastic properties of 3D printable stress-visualized materials,” Sci. Rep. 7(1), 10918 (2017).
[Crossref] [PubMed]

2016 (2)

P. A. Júnior, F. G. Vieira, C. A. Magalhães, J. S. Ribeiro, and I. G. Rios, “Numerical method to digital photoelasticity using plane polariscope,” Opt. Express 24(12), 12617–12624 (2016).
[Crossref] [PubMed]

K. Ramesh, M. P. Hariprasad, and S. Bhuvanewari, “Digital photoelastic analysis applied to implant dentistry,” Opt. Lasers Eng. 87, 204–213 (2016).
[Crossref]

2015 (8)

I. A. Takacs, A. I. Botean, M. Hardau, and S. Chindris, “Displacement-stress distribution in a femoral bone by optical methods,” Procedia Technol. 19, 901–908 (2015).
[Crossref]

P. Forte, A. Paoli, and A. V. Razionale, “A CAE approach for the stress analysis of gear models by 3D digital photoelasticity,” Int. J. Interact. Des. Manuf. 9(1), 31–43 (2015).
[Crossref]

R. Y. Makhnenko, J. Harvieux, and J. F. Labuz, “Paul-Mohr-Coulomb failure surface of rock in the brittle regime,” Geophys. Res. Lett. 42(17), 6975–6981 (2015).
[Crossref]

L. Yang, J. Zhao, W. Liu, Y. Li, M. Yang, and Y. Song, “Microstructure observations of natural gas hydrate occurrence in porous media using microfocus X-ray computed tomography,” Energy Fuels 29(8), 4835–4841 (2015).
[Crossref]

R. Zhang, T. Ai, H. W. Zhou, Y. Ju, and Z. T. Zhang, “Fractal and volume characteristics of 3D mining-induced fractures under typical mining layouts,” Environ. Earth Sci. 73(10), 6069–6080 (2015).
[Crossref]

H. Ma, C. Yang, Y. Li, X. Shi, J. Liu, and T. Wang, “Stability evaluation of the underground gas storage in rock salts based on new partitions of the surrounding rock,” Environ. Earth Sci. 73(11), 6911–6925 (2015).
[Crossref]

A. Mazaira and P. Konicek, “Intense rockburst impacts in deep underground construction and their prevention,” Can. Geotech. J. 52(10), 1426–1439 (2015).
[Crossref]

A. Ajovalasit, G. Petrucci, and M. Scafidi, “Review of RGB photoelasticity,” Opt. Lasers Eng. 68, 58–73 (2015).
[Crossref]

2014 (5)

Y. Ju, H. Xie, Z. Zheng, J. Lu, L. Mao, F. Gao, and R. Peng, “Visualization of the complex structure and stress field inside rock by means of 3D printing technology,” Chin. Sci. Bull. 59(36), 5354–5365 (2014).
[Crossref]

L. S. Dimas, T. Giesa, and M. J. Buehler, “Coupled continuum and discrete analysis of random heterogeneous materials: Elasticity and fracture,” J. Mech. Phys. Solids 63(63), 481–490 (2014).
[Crossref]

C. Farhat, P. Avery, T. Chapman, and J. Cortial, “Dimensional reduction of nonlinear finite element dynamic models with finite rotations and energy-based mesh sampling and weighting for computational efficiency,” Int. J. Numer. Methods Eng. 98(9), 625–662 (2014).
[Crossref]

L. Valoroso, L. Chiaraluce, and C. Collettini, “Earthquakes and fault zone structure,” Geology 42(4), 343–346 (2014).
[Crossref]

M. Zhang, H. Shimada, T. Sasaoka, K. Matsui, and L. Dou, “Evolution and effect of the stress concentration and rock failure in the deep multi-seam coal mining,” Environ. Earth Sci. 72(3), 629–643 (2014).
[Crossref]

2013 (2)

D. Li and L. N. Y. Wong, “The Brazilian disc test for rock mechanics applications: review and new insights,” Rock Mech. Rock Eng. 46(2), 269–287 (2013).
[Crossref]

J. T. Pinto, F. Touchard, S. Castagnet, C. Nadot-Martin, and D. Mellier, “DIC strain measurements at the micro-scale in a semi-crystalline polymer,” Exp. Mech. 53(8), 1311–1321 (2013).
[Crossref]

2012 (5)

V. Vajdova, P. Baud, L. Wu, and T. F. Wong, “Micromechanics of inelastic compaction in two allochemical limestones,” J. Struct. Geol. 43(7), 100–117 (2012).
[Crossref]

K. Sun, J. Tan, and D. Wu, “The research on dynamic rules of crack extension during hydraulic fracturing for oil shale in-situ exploitation,” Procedia Environ. Sci. 12, 736–743 (2012).
[Crossref]

A. Lehtonen, J. W. Cosgrove, J. A. Hudson, and E. Johansson, “An examination of in situ rock stress estimation using the Kaiser effect,” Eng. Geol. 124(1), 24–37 (2012).
[Crossref]

C. Lempp, K. M. Shams, and N. Jahr, “Approaches to stress monitoring in deep boreholes for future CCS projects,” Environ. Earth Sci. 67(2), 435–445 (2012).
[Crossref]

Z. K. Lei, R. X. Bai, W. Qiu, L. B. Deng, and B. C. Huang, “Flexural effects of sandwich beam with a plate insert under in-plane bending,” Opt. Laser Technol. 44(5), 1223–1231 (2012).
[Crossref]

2011 (1)

Z. Lei, M. Fu, and H. Yun, “Experimental study on interfacial shear transfer in partially-debonded aluminum/ epoxy joint,” Int. J. Adhes. 31(2), 104–111 (2011).
[Crossref]

2010 (4)

R. Ikeda, Y. Iio, and K. Omura, “In situ stress measurements in NIED boreholes in and around the fault zone near the 1995 Hyogo-ken Nanbu earthquake Japan,” Isl. Arc 10(3–4), 252–260 (2010).

V. Vajdova, W. Zhu, T. M. N. Chen, and T. F. Wong, “Micromechanics of brittle faulting and cataclastic flow in Tavel limestone,” J. Struct. Geol. 32(8), 1158–1169 (2010).
[Crossref]

A. Ajovalasit, G. Petrucci, and M. Scafidi, “RGB photoelasticity: review and improvements,” Strain 46(2), 137–147 (2010).
[Crossref]

M. J. Huang and P. C. Sung, “Regional phase unwrapping algorithm for photoelastic phase map,” Opt. Express 18(2), 1419–1429 (2010).
[Crossref] [PubMed]

2009 (3)

J. H. Yang, F. Q. Wu, and J. Z. Sun, “Estimation of the tensile elastic modulus using Brazilian disc by applying diametrically opposed concentrated loads,” Int. J. Rock Mech. Min. Sci. 46(3), 568–576 (2009).
[Crossref]

Y. Liu, F. J. H. G. Kessels, W. D. V. Driel, J. A. S. V. Driel, F. L. Sun, and G. Q. Zhang, “Comparing drop impact test method using strain gauge measurements,” Microelectron. Reliab. 49(9–11), 1299–1303 (2009).
[Crossref]

P. Bénézeth, B. Ménez, and C. Noiriel, “CO2 geological storage: Integrating geochemical, hydro-dynamical, mechanical and biological processes from the pore to the reservoir scale,” Chem. Geol. 265(1–2), 1–2 (2009).
[Crossref]

2008 (1)

M. Ramji and K. Ramesh, “Whole field evaluation of stress components in digital photoelasticity-Issues, implementation and application,” Opt. Lasers Eng. 46(3), 257–271 (2008).
[Crossref]

2005 (2)

A. Ajovalasit and G. Petrucci, “Developments in RGB photoelasticity,” Appl. Mech. Mater. 3–4, 205–210 (2005).
[Crossref]

R. Katsman, E. Aharonov, and H. Scher, “Numerical simulation of compaction bands in high-porosity sedimentary rock,” Mech. Mater. 37(1), 143–162 (2005).
[Crossref]

2004 (1)

V. S. Prasad, K. R. Madhu, and K. Ramesh, “Towards effective phase unwrapping in digital photo-elasticity,” Opt. Lasers Eng. 42(4), 421–436 (2004).
[Crossref]

2002 (4)

J. A. Quiroga, A. García-Botella, and J. A. Gómez-Pedrero, “Improved method for isochromatic demodulation by RGB calibration,” Appl. Opt. 41(17), 3461–3468 (2002).
[Crossref] [PubMed]

B. Zuccarello and G. Tripoli, “Photoelastic stress pattern analysis using Fourier transform with carrier fringes: influence of quarter-wave plate error,” Opt. Lasers Eng. 37(4), 401–416 (2002).
[Crossref]

A. Pawlak and A. Galeski, “Determination of stresses around beads in stressed epoxy resin by photoelasticity,” J. Appl. Polym. Sci. 86(7), 1436–1444 (2002).
[Crossref]

S. Takao, S. Yoneyama, and M. Takashi, “Minute displacement and strain analysis using lensless Fourier transformed holographic interferometry,” Opt. Lasers Eng. 38(5), 233–244 (2002).
[Crossref]

2001 (1)

P. Kulatilake, J. Liang, and H. Gao, “Experimental and numerical simulations of jointed rock block strength under uniaxial loading,” J. Eng. Mech. 127(12), 1240–1247 (2001).
[Crossref]

1999 (3)

A. J. Desbarats, D. R. Boyle, M. Stapinsky, and M. J. Robin, “A dual‐porosity model for water level response to atmospheric loading in wells tapping fractured rock aquifers,” Water Resour. Res. 35(5), 1495–1505 (1999).
[Crossref]

D. A. Demer, M. A. Soule, and R. P. Hewitt, “A multiple-frequency method for potentially improving the accuracy and precision of in situ target strength measurements,” J. Acoust. Soc. Am. 105(4), 2359–2376 (1999).
[Crossref]

A. J. Rosakis, O. Samudrala, and D. Coker, “Cracks faster than the shear wave speed,” Science 284(5418), 1337–1340 (1999).
[Crossref] [PubMed]

1997 (2)

R. P. Singh, J. Lambros, A. Shukla, and A. J. Rosakis, “Investigation of the mechanics of intersonic crack propagation along a bimaterial interface using coherent gradient sensing and photoelasticity,” P. Roy Soc. A-Math. Phys. 453 (1967), 2649–2667 (1997).
[Crossref]

T. W. Ng, “Photoelastic stress analysis using an object step-loading method,” Exp. Mech. 37(2), 137–141 (1997).
[Crossref]

1995 (1)

M. Bai, J. C. Roegiers, and D. Elsworth, “Poromechanical response of fractured-porous rock masses,” J. Petrol. Sci. Eng. 13(3–4), 155–168 (1995).
[Crossref]

1992 (2)

A. S. Voloshin and T. Leng-Tsun, “Investigation of the stress singularities by enhanced moiré interferometry,” Eng. Fract. Mech. 43(4), 477–486 (1992).
[Crossref]

K. Sakaguchi, Y. Obara, T. Nakayama, and K. Sugawara, “Accuracy of rock stress measurement by means of conical-ended borehole technique,” Shigen-to-Sozai 108(6), 455–460 (1992).
[Crossref]

1989 (1)

B. C. Haimson, L. W. Tunbridge, M. Y. Lee, and C. M. Cooling, “Measurement of rock stress using the hydraulic fracturing method in Cornwall, U.K.-Part II. Data reduction and stress calculation,” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 26(5), 361–372 (1989).
[Crossref]

1983 (1)

W. R. Judd, “Underground excavations in rock,” Eng. Geol. 19(3), 244–246 (1983).
[Crossref]

1982 (1)

G. W. Bird and W. S. Fyfe, “The nuclear waste disposal problem—An overview from a geological and geochemical perspective,” Chem. Geol. 36(1–2), 1–13 (1982).
[Crossref]

1980 (1)

J. G. Ramsay, “The crack-seal mechanism of rock deformation,” Nature 284(5752), 135–139 (1980).
[Crossref]

Aharonov, E.

R. Katsman, E. Aharonov, and H. Scher, “Numerical simulation of compaction bands in high-porosity sedimentary rock,” Mech. Mater. 37(1), 143–162 (2005).
[Crossref]

Ai, T.

R. Zhang, T. Ai, H. W. Zhou, Y. Ju, and Z. T. Zhang, “Fractal and volume characteristics of 3D mining-induced fractures under typical mining layouts,” Environ. Earth Sci. 73(10), 6069–6080 (2015).
[Crossref]

Ajovalasit, A.

A. Ajovalasit, G. Petrucci, and M. Scafidi, “Review of RGB photoelasticity,” Opt. Lasers Eng. 68, 58–73 (2015).
[Crossref]

A. Ajovalasit, G. Petrucci, and M. Scafidi, “RGB photoelasticity: review and improvements,” Strain 46(2), 137–147 (2010).
[Crossref]

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C. Farhat, P. Avery, T. Chapman, and J. Cortial, “Dimensional reduction of nonlinear finite element dynamic models with finite rotations and energy-based mesh sampling and weighting for computational efficiency,” Int. J. Numer. Methods Eng. 98(9), 625–662 (2014).
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A. J. Desbarats, D. R. Boyle, M. Stapinsky, and M. J. Robin, “A dual‐porosity model for water level response to atmospheric loading in wells tapping fractured rock aquifers,” Water Resour. Res. 35(5), 1495–1505 (1999).
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L. S. Dimas, T. Giesa, and M. J. Buehler, “Coupled continuum and discrete analysis of random heterogeneous materials: Elasticity and fracture,” J. Mech. Phys. Solids 63(63), 481–490 (2014).
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M. Zhang, H. Shimada, T. Sasaoka, K. Matsui, and L. Dou, “Evolution and effect of the stress concentration and rock failure in the deep multi-seam coal mining,” Environ. Earth Sci. 72(3), 629–643 (2014).
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Y. Liu, F. J. H. G. Kessels, W. D. V. Driel, J. A. S. V. Driel, F. L. Sun, and G. Q. Zhang, “Comparing drop impact test method using strain gauge measurements,” Microelectron. Reliab. 49(9–11), 1299–1303 (2009).
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M. Bai, J. C. Roegiers, and D. Elsworth, “Poromechanical response of fractured-porous rock masses,” J. Petrol. Sci. Eng. 13(3–4), 155–168 (1995).
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C. Farhat, P. Avery, T. Chapman, and J. Cortial, “Dimensional reduction of nonlinear finite element dynamic models with finite rotations and energy-based mesh sampling and weighting for computational efficiency,” Int. J. Numer. Methods Eng. 98(9), 625–662 (2014).
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P. Forte, A. Paoli, and A. V. Razionale, “A CAE approach for the stress analysis of gear models by 3D digital photoelasticity,” Int. J. Interact. Des. Manuf. 9(1), 31–43 (2015).
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Z. Lei, M. Fu, and H. Yun, “Experimental study on interfacial shear transfer in partially-debonded aluminum/ epoxy joint,” Int. J. Adhes. 31(2), 104–111 (2011).
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G. W. Bird and W. S. Fyfe, “The nuclear waste disposal problem—An overview from a geological and geochemical perspective,” Chem. Geol. 36(1–2), 1–13 (1982).
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A. Pawlak and A. Galeski, “Determination of stresses around beads in stressed epoxy resin by photoelasticity,” J. Appl. Polym. Sci. 86(7), 1436–1444 (2002).
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Y. Ju, H. Xie, Z. Zheng, J. Lu, L. Mao, F. Gao, and R. Peng, “Visualization of the complex structure and stress field inside rock by means of 3D printing technology,” Chin. Sci. Bull. 59(36), 5354–5365 (2014).
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Giesa, T.

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Haimson, B. C.

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I. A. Takacs, A. I. Botean, M. Hardau, and S. Chindris, “Displacement-stress distribution in a femoral bone by optical methods,” Procedia Technol. 19, 901–908 (2015).
[Crossref]

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K. Ramesh, M. P. Hariprasad, and S. Bhuvanewari, “Digital photoelastic analysis applied to implant dentistry,” Opt. Lasers Eng. 87, 204–213 (2016).
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R. Y. Makhnenko, J. Harvieux, and J. F. Labuz, “Paul-Mohr-Coulomb failure surface of rock in the brittle regime,” Geophys. Res. Lett. 42(17), 6975–6981 (2015).
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L. Wang, Y. Ju, H. Xie, G. Ma, L. Mao, and K. He, “The mechanical and photoelastic properties of 3D printable stress-visualized materials,” Sci. Rep. 7(1), 10918 (2017).
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Y. Ju, Z. Zheng, H. Xie, J. Lu, L. Wang, and K. He, “Experimental visualisation methods for three-dimensional stress fields of porous solids,” Exp. Tech. 41(4), 331–344 (2017).
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D. A. Demer, M. A. Soule, and R. P. Hewitt, “A multiple-frequency method for potentially improving the accuracy and precision of in situ target strength measurements,” J. Acoust. Soc. Am. 105(4), 2359–2376 (1999).
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Z. K. Lei, R. X. Bai, W. Qiu, L. B. Deng, and B. C. Huang, “Flexural effects of sandwich beam with a plate insert under in-plane bending,” Opt. Laser Technol. 44(5), 1223–1231 (2012).
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Hudson, J. A.

A. Lehtonen, J. W. Cosgrove, J. A. Hudson, and E. Johansson, “An examination of in situ rock stress estimation using the Kaiser effect,” Eng. Geol. 124(1), 24–37 (2012).
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R. Ikeda, Y. Iio, and K. Omura, “In situ stress measurements in NIED boreholes in and around the fault zone near the 1995 Hyogo-ken Nanbu earthquake Japan,” Isl. Arc 10(3–4), 252–260 (2010).

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Y. Ju, Z. Zheng, H. Xie, J. Lu, L. Wang, and K. He, “Experimental visualisation methods for three-dimensional stress fields of porous solids,” Exp. Tech. 41(4), 331–344 (2017).
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L. Wang, Y. Ju, H. Xie, G. Ma, L. Mao, and K. He, “The mechanical and photoelastic properties of 3D printable stress-visualized materials,” Sci. Rep. 7(1), 10918 (2017).
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P. Kulatilake, J. Liang, and H. Gao, “Experimental and numerical simulations of jointed rock block strength under uniaxial loading,” J. Eng. Mech. 127(12), 1240–1247 (2001).
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R. Y. Makhnenko, J. Harvieux, and J. F. Labuz, “Paul-Mohr-Coulomb failure surface of rock in the brittle regime,” Geophys. Res. Lett. 42(17), 6975–6981 (2015).
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A. Lehtonen, J. W. Cosgrove, J. A. Hudson, and E. Johansson, “An examination of in situ rock stress estimation using the Kaiser effect,” Eng. Geol. 124(1), 24–37 (2012).
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Z. Lei, M. Fu, and H. Yun, “Experimental study on interfacial shear transfer in partially-debonded aluminum/ epoxy joint,” Int. J. Adhes. 31(2), 104–111 (2011).
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Lei, Z. K.

Z. K. Lei, R. X. Bai, W. Qiu, L. B. Deng, and B. C. Huang, “Flexural effects of sandwich beam with a plate insert under in-plane bending,” Opt. Laser Technol. 44(5), 1223–1231 (2012).
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C. Lempp, K. M. Shams, and N. Jahr, “Approaches to stress monitoring in deep boreholes for future CCS projects,” Environ. Earth Sci. 67(2), 435–445 (2012).
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H. Ma, C. Yang, Y. Li, X. Shi, J. Liu, and T. Wang, “Stability evaluation of the underground gas storage in rock salts based on new partitions of the surrounding rock,” Environ. Earth Sci. 73(11), 6911–6925 (2015).
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L. Yang, J. Zhao, W. Liu, Y. Li, M. Yang, and Y. Song, “Microstructure observations of natural gas hydrate occurrence in porous media using microfocus X-ray computed tomography,” Energy Fuels 29(8), 4835–4841 (2015).
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[Crossref]

Lu, J.

Y. Ju, Z. Zheng, H. Xie, J. Lu, L. Wang, and K. He, “Experimental visualisation methods for three-dimensional stress fields of porous solids,” Exp. Tech. 41(4), 331–344 (2017).
[Crossref]

Y. Ju, H. Xie, Z. Zheng, J. Lu, L. Mao, F. Gao, and R. Peng, “Visualization of the complex structure and stress field inside rock by means of 3D printing technology,” Chin. Sci. Bull. 59(36), 5354–5365 (2014).
[Crossref]

Ma, G.

Y. Ju, L. Wang, H. Xie, G. Ma, Z. Zheng, and L. Mao, “Visualization and transparentization of the structure and stress field of aggregated geomaterials through 3D printing and photoelastic techniques,” Rock Mech. Rock Eng. 50(6), 1383–1407 (2017).
[Crossref]

L. Wang, Y. Ju, H. Xie, G. Ma, L. Mao, and K. He, “The mechanical and photoelastic properties of 3D printable stress-visualized materials,” Sci. Rep. 7(1), 10918 (2017).
[Crossref] [PubMed]

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H. Ma, C. Yang, Y. Li, X. Shi, J. Liu, and T. Wang, “Stability evaluation of the underground gas storage in rock salts based on new partitions of the surrounding rock,” Environ. Earth Sci. 73(11), 6911–6925 (2015).
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V. S. Prasad, K. R. Madhu, and K. Ramesh, “Towards effective phase unwrapping in digital photo-elasticity,” Opt. Lasers Eng. 42(4), 421–436 (2004).
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Magalhães, C. A.

Makhnenko, R. Y.

R. Y. Makhnenko, J. Harvieux, and J. F. Labuz, “Paul-Mohr-Coulomb failure surface of rock in the brittle regime,” Geophys. Res. Lett. 42(17), 6975–6981 (2015).
[Crossref]

Mao, L.

Y. Ju, L. Wang, H. Xie, G. Ma, Z. Zheng, and L. Mao, “Visualization and transparentization of the structure and stress field of aggregated geomaterials through 3D printing and photoelastic techniques,” Rock Mech. Rock Eng. 50(6), 1383–1407 (2017).
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L. Wang, Y. Ju, H. Xie, G. Ma, L. Mao, and K. He, “The mechanical and photoelastic properties of 3D printable stress-visualized materials,” Sci. Rep. 7(1), 10918 (2017).
[Crossref] [PubMed]

Y. Ju, H. Xie, Z. Zheng, J. Lu, L. Mao, F. Gao, and R. Peng, “Visualization of the complex structure and stress field inside rock by means of 3D printing technology,” Chin. Sci. Bull. 59(36), 5354–5365 (2014).
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Matsui, K.

M. Zhang, H. Shimada, T. Sasaoka, K. Matsui, and L. Dou, “Evolution and effect of the stress concentration and rock failure in the deep multi-seam coal mining,” Environ. Earth Sci. 72(3), 629–643 (2014).
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A. Mazaira and P. Konicek, “Intense rockburst impacts in deep underground construction and their prevention,” Can. Geotech. J. 52(10), 1426–1439 (2015).
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J. T. Pinto, F. Touchard, S. Castagnet, C. Nadot-Martin, and D. Mellier, “DIC strain measurements at the micro-scale in a semi-crystalline polymer,” Exp. Mech. 53(8), 1311–1321 (2013).
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P. Bénézeth, B. Ménez, and C. Noiriel, “CO2 geological storage: Integrating geochemical, hydro-dynamical, mechanical and biological processes from the pore to the reservoir scale,” Chem. Geol. 265(1–2), 1–2 (2009).
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J. T. Pinto, F. Touchard, S. Castagnet, C. Nadot-Martin, and D. Mellier, “DIC strain measurements at the micro-scale in a semi-crystalline polymer,” Exp. Mech. 53(8), 1311–1321 (2013).
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R. Ikeda, Y. Iio, and K. Omura, “In situ stress measurements in NIED boreholes in and around the fault zone near the 1995 Hyogo-ken Nanbu earthquake Japan,” Isl. Arc 10(3–4), 252–260 (2010).

Paoli, A.

P. Forte, A. Paoli, and A. V. Razionale, “A CAE approach for the stress analysis of gear models by 3D digital photoelasticity,” Int. J. Interact. Des. Manuf. 9(1), 31–43 (2015).
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Pawlak, A.

A. Pawlak and A. Galeski, “Determination of stresses around beads in stressed epoxy resin by photoelasticity,” J. Appl. Polym. Sci. 86(7), 1436–1444 (2002).
[Crossref]

Peng, R.

Y. Ju, H. Xie, Z. Zheng, J. Lu, L. Mao, F. Gao, and R. Peng, “Visualization of the complex structure and stress field inside rock by means of 3D printing technology,” Chin. Sci. Bull. 59(36), 5354–5365 (2014).
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Petrucci, G.

A. Ajovalasit, G. Petrucci, and M. Scafidi, “Review of RGB photoelasticity,” Opt. Lasers Eng. 68, 58–73 (2015).
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A. Ajovalasit, G. Petrucci, and M. Scafidi, “RGB photoelasticity: review and improvements,” Strain 46(2), 137–147 (2010).
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A. Ajovalasit and G. Petrucci, “Developments in RGB photoelasticity,” Appl. Mech. Mater. 3–4, 205–210 (2005).
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Pinto, J. T.

J. T. Pinto, F. Touchard, S. Castagnet, C. Nadot-Martin, and D. Mellier, “DIC strain measurements at the micro-scale in a semi-crystalline polymer,” Exp. Mech. 53(8), 1311–1321 (2013).
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Prasad, V. S.

V. S. Prasad, K. R. Madhu, and K. Ramesh, “Towards effective phase unwrapping in digital photo-elasticity,” Opt. Lasers Eng. 42(4), 421–436 (2004).
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Qiu, W.

Z. K. Lei, R. X. Bai, W. Qiu, L. B. Deng, and B. C. Huang, “Flexural effects of sandwich beam with a plate insert under in-plane bending,” Opt. Laser Technol. 44(5), 1223–1231 (2012).
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Quiroga, J. A.

Ramesh, K.

K. Ramesh, M. P. Hariprasad, and S. Bhuvanewari, “Digital photoelastic analysis applied to implant dentistry,” Opt. Lasers Eng. 87, 204–213 (2016).
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M. Ramji and K. Ramesh, “Whole field evaluation of stress components in digital photoelasticity-Issues, implementation and application,” Opt. Lasers Eng. 46(3), 257–271 (2008).
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V. S. Prasad, K. R. Madhu, and K. Ramesh, “Towards effective phase unwrapping in digital photo-elasticity,” Opt. Lasers Eng. 42(4), 421–436 (2004).
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M. Ramji and K. Ramesh, “Whole field evaluation of stress components in digital photoelasticity-Issues, implementation and application,” Opt. Lasers Eng. 46(3), 257–271 (2008).
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J. G. Ramsay, “The crack-seal mechanism of rock deformation,” Nature 284(5752), 135–139 (1980).
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P. Forte, A. Paoli, and A. V. Razionale, “A CAE approach for the stress analysis of gear models by 3D digital photoelasticity,” Int. J. Interact. Des. Manuf. 9(1), 31–43 (2015).
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Rios, I. G.

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A. J. Desbarats, D. R. Boyle, M. Stapinsky, and M. J. Robin, “A dual‐porosity model for water level response to atmospheric loading in wells tapping fractured rock aquifers,” Water Resour. Res. 35(5), 1495–1505 (1999).
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M. Zhang, H. Shimada, T. Sasaoka, K. Matsui, and L. Dou, “Evolution and effect of the stress concentration and rock failure in the deep multi-seam coal mining,” Environ. Earth Sci. 72(3), 629–643 (2014).
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A. Ajovalasit, G. Petrucci, and M. Scafidi, “Review of RGB photoelasticity,” Opt. Lasers Eng. 68, 58–73 (2015).
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A. Ajovalasit, G. Petrucci, and M. Scafidi, “RGB photoelasticity: review and improvements,” Strain 46(2), 137–147 (2010).
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R. Katsman, E. Aharonov, and H. Scher, “Numerical simulation of compaction bands in high-porosity sedimentary rock,” Mech. Mater. 37(1), 143–162 (2005).
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C. Lempp, K. M. Shams, and N. Jahr, “Approaches to stress monitoring in deep boreholes for future CCS projects,” Environ. Earth Sci. 67(2), 435–445 (2012).
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H. Ma, C. Yang, Y. Li, X. Shi, J. Liu, and T. Wang, “Stability evaluation of the underground gas storage in rock salts based on new partitions of the surrounding rock,” Environ. Earth Sci. 73(11), 6911–6925 (2015).
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M. Zhang, H. Shimada, T. Sasaoka, K. Matsui, and L. Dou, “Evolution and effect of the stress concentration and rock failure in the deep multi-seam coal mining,” Environ. Earth Sci. 72(3), 629–643 (2014).
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R. P. Singh, J. Lambros, A. Shukla, and A. J. Rosakis, “Investigation of the mechanics of intersonic crack propagation along a bimaterial interface using coherent gradient sensing and photoelasticity,” P. Roy Soc. A-Math. Phys. 453 (1967), 2649–2667 (1997).
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R. P. Singh, J. Lambros, A. Shukla, and A. J. Rosakis, “Investigation of the mechanics of intersonic crack propagation along a bimaterial interface using coherent gradient sensing and photoelasticity,” P. Roy Soc. A-Math. Phys. 453 (1967), 2649–2667 (1997).
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L. Yang, J. Zhao, W. Liu, Y. Li, M. Yang, and Y. Song, “Microstructure observations of natural gas hydrate occurrence in porous media using microfocus X-ray computed tomography,” Energy Fuels 29(8), 4835–4841 (2015).
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D. A. Demer, M. A. Soule, and R. P. Hewitt, “A multiple-frequency method for potentially improving the accuracy and precision of in situ target strength measurements,” J. Acoust. Soc. Am. 105(4), 2359–2376 (1999).
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A. J. Desbarats, D. R. Boyle, M. Stapinsky, and M. J. Robin, “A dual‐porosity model for water level response to atmospheric loading in wells tapping fractured rock aquifers,” Water Resour. Res. 35(5), 1495–1505 (1999).
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K. Sakaguchi, Y. Obara, T. Nakayama, and K. Sugawara, “Accuracy of rock stress measurement by means of conical-ended borehole technique,” Shigen-to-Sozai 108(6), 455–460 (1992).
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J. H. Yang, F. Q. Wu, and J. Z. Sun, “Estimation of the tensile elastic modulus using Brazilian disc by applying diametrically opposed concentrated loads,” Int. J. Rock Mech. Min. Sci. 46(3), 568–576 (2009).
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S. Takao, S. Yoneyama, and M. Takashi, “Minute displacement and strain analysis using lensless Fourier transformed holographic interferometry,” Opt. Lasers Eng. 38(5), 233–244 (2002).
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J. T. Pinto, F. Touchard, S. Castagnet, C. Nadot-Martin, and D. Mellier, “DIC strain measurements at the micro-scale in a semi-crystalline polymer,” Exp. Mech. 53(8), 1311–1321 (2013).
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B. Zuccarello and G. Tripoli, “Photoelastic stress pattern analysis using Fourier transform with carrier fringes: influence of quarter-wave plate error,” Opt. Lasers Eng. 37(4), 401–416 (2002).
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B. C. Haimson, L. W. Tunbridge, M. Y. Lee, and C. M. Cooling, “Measurement of rock stress using the hydraulic fracturing method in Cornwall, U.K.-Part II. Data reduction and stress calculation,” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 26(5), 361–372 (1989).
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V. Vajdova, P. Baud, L. Wu, and T. F. Wong, “Micromechanics of inelastic compaction in two allochemical limestones,” J. Struct. Geol. 43(7), 100–117 (2012).
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V. Vajdova, W. Zhu, T. M. N. Chen, and T. F. Wong, “Micromechanics of brittle faulting and cataclastic flow in Tavel limestone,” J. Struct. Geol. 32(8), 1158–1169 (2010).
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Y. Ju, Z. Zheng, H. Xie, J. Lu, L. Wang, and K. He, “Experimental visualisation methods for three-dimensional stress fields of porous solids,” Exp. Tech. 41(4), 331–344 (2017).
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L. Wang, Y. Ju, H. Xie, G. Ma, L. Mao, and K. He, “The mechanical and photoelastic properties of 3D printable stress-visualized materials,” Sci. Rep. 7(1), 10918 (2017).
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H. Ma, C. Yang, Y. Li, X. Shi, J. Liu, and T. Wang, “Stability evaluation of the underground gas storage in rock salts based on new partitions of the surrounding rock,” Environ. Earth Sci. 73(11), 6911–6925 (2015).
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K. Sun, J. Tan, and D. Wu, “The research on dynamic rules of crack extension during hydraulic fracturing for oil shale in-situ exploitation,” Procedia Environ. Sci. 12, 736–743 (2012).
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J. H. Yang, F. Q. Wu, and J. Z. Sun, “Estimation of the tensile elastic modulus using Brazilian disc by applying diametrically opposed concentrated loads,” Int. J. Rock Mech. Min. Sci. 46(3), 568–576 (2009).
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V. Vajdova, P. Baud, L. Wu, and T. F. Wong, “Micromechanics of inelastic compaction in two allochemical limestones,” J. Struct. Geol. 43(7), 100–117 (2012).
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Y. Ju, L. Wang, H. Xie, G. Ma, Z. Zheng, and L. Mao, “Visualization and transparentization of the structure and stress field of aggregated geomaterials through 3D printing and photoelastic techniques,” Rock Mech. Rock Eng. 50(6), 1383–1407 (2017).
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Y. Ju, Z. Zheng, H. Xie, J. Lu, L. Wang, and K. He, “Experimental visualisation methods for three-dimensional stress fields of porous solids,” Exp. Tech. 41(4), 331–344 (2017).
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L. Wang, Y. Ju, H. Xie, G. Ma, L. Mao, and K. He, “The mechanical and photoelastic properties of 3D printable stress-visualized materials,” Sci. Rep. 7(1), 10918 (2017).
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Y. Ju, H. Xie, Z. Zheng, J. Lu, L. Mao, F. Gao, and R. Peng, “Visualization of the complex structure and stress field inside rock by means of 3D printing technology,” Chin. Sci. Bull. 59(36), 5354–5365 (2014).
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H. Ma, C. Yang, Y. Li, X. Shi, J. Liu, and T. Wang, “Stability evaluation of the underground gas storage in rock salts based on new partitions of the surrounding rock,” Environ. Earth Sci. 73(11), 6911–6925 (2015).
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J. H. Yang, F. Q. Wu, and J. Z. Sun, “Estimation of the tensile elastic modulus using Brazilian disc by applying diametrically opposed concentrated loads,” Int. J. Rock Mech. Min. Sci. 46(3), 568–576 (2009).
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L. Yang, J. Zhao, W. Liu, Y. Li, M. Yang, and Y. Song, “Microstructure observations of natural gas hydrate occurrence in porous media using microfocus X-ray computed tomography,” Energy Fuels 29(8), 4835–4841 (2015).
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L. Yang, J. Zhao, W. Liu, Y. Li, M. Yang, and Y. Song, “Microstructure observations of natural gas hydrate occurrence in porous media using microfocus X-ray computed tomography,” Energy Fuels 29(8), 4835–4841 (2015).
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S. Takao, S. Yoneyama, and M. Takashi, “Minute displacement and strain analysis using lensless Fourier transformed holographic interferometry,” Opt. Lasers Eng. 38(5), 233–244 (2002).
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Z. Lei, M. Fu, and H. Yun, “Experimental study on interfacial shear transfer in partially-debonded aluminum/ epoxy joint,” Int. J. Adhes. 31(2), 104–111 (2011).
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Y. Liu, F. J. H. G. Kessels, W. D. V. Driel, J. A. S. V. Driel, F. L. Sun, and G. Q. Zhang, “Comparing drop impact test method using strain gauge measurements,” Microelectron. Reliab. 49(9–11), 1299–1303 (2009).
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M. Zhang, H. Shimada, T. Sasaoka, K. Matsui, and L. Dou, “Evolution and effect of the stress concentration and rock failure in the deep multi-seam coal mining,” Environ. Earth Sci. 72(3), 629–643 (2014).
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L. Yang, J. Zhao, W. Liu, Y. Li, M. Yang, and Y. Song, “Microstructure observations of natural gas hydrate occurrence in porous media using microfocus X-ray computed tomography,” Energy Fuels 29(8), 4835–4841 (2015).
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Y. Ju, Z. Zheng, H. Xie, J. Lu, L. Wang, and K. He, “Experimental visualisation methods for three-dimensional stress fields of porous solids,” Exp. Tech. 41(4), 331–344 (2017).
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Y. Ju, L. Wang, H. Xie, G. Ma, Z. Zheng, and L. Mao, “Visualization and transparentization of the structure and stress field of aggregated geomaterials through 3D printing and photoelastic techniques,” Rock Mech. Rock Eng. 50(6), 1383–1407 (2017).
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Y. Ju, H. Xie, Z. Zheng, J. Lu, L. Mao, F. Gao, and R. Peng, “Visualization of the complex structure and stress field inside rock by means of 3D printing technology,” Chin. Sci. Bull. 59(36), 5354–5365 (2014).
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V. Vajdova, W. Zhu, T. M. N. Chen, and T. F. Wong, “Micromechanics of brittle faulting and cataclastic flow in Tavel limestone,” J. Struct. Geol. 32(8), 1158–1169 (2010).
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B. Zuccarello and G. Tripoli, “Photoelastic stress pattern analysis using Fourier transform with carrier fringes: influence of quarter-wave plate error,” Opt. Lasers Eng. 37(4), 401–416 (2002).
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L. Yang, J. Zhao, W. Liu, Y. Li, M. Yang, and Y. Song, “Microstructure observations of natural gas hydrate occurrence in porous media using microfocus X-ray computed tomography,” Energy Fuels 29(8), 4835–4841 (2015).
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A. S. Voloshin and T. Leng-Tsun, “Investigation of the stress singularities by enhanced moiré interferometry,” Eng. Fract. Mech. 43(4), 477–486 (1992).
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M. Zhang, H. Shimada, T. Sasaoka, K. Matsui, and L. Dou, “Evolution and effect of the stress concentration and rock failure in the deep multi-seam coal mining,” Environ. Earth Sci. 72(3), 629–643 (2014).
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R. Zhang, T. Ai, H. W. Zhou, Y. Ju, and Z. T. Zhang, “Fractal and volume characteristics of 3D mining-induced fractures under typical mining layouts,” Environ. Earth Sci. 73(10), 6069–6080 (2015).
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J. T. Pinto, F. Touchard, S. Castagnet, C. Nadot-Martin, and D. Mellier, “DIC strain measurements at the micro-scale in a semi-crystalline polymer,” Exp. Mech. 53(8), 1311–1321 (2013).
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Y. Ju, Z. Zheng, H. Xie, J. Lu, L. Wang, and K. He, “Experimental visualisation methods for three-dimensional stress fields of porous solids,” Exp. Tech. 41(4), 331–344 (2017).
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Z. Lei, M. Fu, and H. Yun, “Experimental study on interfacial shear transfer in partially-debonded aluminum/ epoxy joint,” Int. J. Adhes. 31(2), 104–111 (2011).
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Int. J. Interact. Des. Manuf. (1)

P. Forte, A. Paoli, and A. V. Razionale, “A CAE approach for the stress analysis of gear models by 3D digital photoelasticity,” Int. J. Interact. Des. Manuf. 9(1), 31–43 (2015).
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B. C. Haimson, L. W. Tunbridge, M. Y. Lee, and C. M. Cooling, “Measurement of rock stress using the hydraulic fracturing method in Cornwall, U.K.-Part II. Data reduction and stress calculation,” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 26(5), 361–372 (1989).
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J. Acoust. Soc. Am. (1)

D. A. Demer, M. A. Soule, and R. P. Hewitt, “A multiple-frequency method for potentially improving the accuracy and precision of in situ target strength measurements,” J. Acoust. Soc. Am. 105(4), 2359–2376 (1999).
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M. Bai, J. C. Roegiers, and D. Elsworth, “Poromechanical response of fractured-porous rock masses,” J. Petrol. Sci. Eng. 13(3–4), 155–168 (1995).
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J. Struct. Geol. (2)

V. Vajdova, P. Baud, L. Wu, and T. F. Wong, “Micromechanics of inelastic compaction in two allochemical limestones,” J. Struct. Geol. 43(7), 100–117 (2012).
[Crossref]

V. Vajdova, W. Zhu, T. M. N. Chen, and T. F. Wong, “Micromechanics of brittle faulting and cataclastic flow in Tavel limestone,” J. Struct. Geol. 32(8), 1158–1169 (2010).
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Mech. Mater. (1)

R. Katsman, E. Aharonov, and H. Scher, “Numerical simulation of compaction bands in high-porosity sedimentary rock,” Mech. Mater. 37(1), 143–162 (2005).
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Microelectron. Reliab. (1)

Y. Liu, F. J. H. G. Kessels, W. D. V. Driel, J. A. S. V. Driel, F. L. Sun, and G. Q. Zhang, “Comparing drop impact test method using strain gauge measurements,” Microelectron. Reliab. 49(9–11), 1299–1303 (2009).
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J. G. Ramsay, “The crack-seal mechanism of rock deformation,” Nature 284(5752), 135–139 (1980).
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V. S. Prasad, K. R. Madhu, and K. Ramesh, “Towards effective phase unwrapping in digital photo-elasticity,” Opt. Lasers Eng. 42(4), 421–436 (2004).
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A. Ajovalasit, G. Petrucci, and M. Scafidi, “Review of RGB photoelasticity,” Opt. Lasers Eng. 68, 58–73 (2015).
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M. Ramji and K. Ramesh, “Whole field evaluation of stress components in digital photoelasticity-Issues, implementation and application,” Opt. Lasers Eng. 46(3), 257–271 (2008).
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K. Ramesh, M. P. Hariprasad, and S. Bhuvanewari, “Digital photoelastic analysis applied to implant dentistry,” Opt. Lasers Eng. 87, 204–213 (2016).
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B. Zuccarello and G. Tripoli, “Photoelastic stress pattern analysis using Fourier transform with carrier fringes: influence of quarter-wave plate error,” Opt. Lasers Eng. 37(4), 401–416 (2002).
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P. Roy Soc. A-Math. Phys. (1)

R. P. Singh, J. Lambros, A. Shukla, and A. J. Rosakis, “Investigation of the mechanics of intersonic crack propagation along a bimaterial interface using coherent gradient sensing and photoelasticity,” P. Roy Soc. A-Math. Phys. 453 (1967), 2649–2667 (1997).
[Crossref]

Procedia Environ. Sci. (1)

K. Sun, J. Tan, and D. Wu, “The research on dynamic rules of crack extension during hydraulic fracturing for oil shale in-situ exploitation,” Procedia Environ. Sci. 12, 736–743 (2012).
[Crossref]

Procedia Technol. (1)

I. A. Takacs, A. I. Botean, M. Hardau, and S. Chindris, “Displacement-stress distribution in a femoral bone by optical methods,” Procedia Technol. 19, 901–908 (2015).
[Crossref]

Rock Mech. Rock Eng. (2)

Y. Ju, L. Wang, H. Xie, G. Ma, Z. Zheng, and L. Mao, “Visualization and transparentization of the structure and stress field of aggregated geomaterials through 3D printing and photoelastic techniques,” Rock Mech. Rock Eng. 50(6), 1383–1407 (2017).
[Crossref]

D. Li and L. N. Y. Wong, “The Brazilian disc test for rock mechanics applications: review and new insights,” Rock Mech. Rock Eng. 46(2), 269–287 (2013).
[Crossref]

Sci. Rep. (1)

L. Wang, Y. Ju, H. Xie, G. Ma, L. Mao, and K. He, “The mechanical and photoelastic properties of 3D printable stress-visualized materials,” Sci. Rep. 7(1), 10918 (2017).
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[Crossref] [PubMed]

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[Crossref]

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A. Ajovalasit, G. Petrucci, and M. Scafidi, “RGB photoelasticity: review and improvements,” Strain 46(2), 137–147 (2010).
[Crossref]

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A. J. Desbarats, D. R. Boyle, M. Stapinsky, and M. J. Robin, “A dual‐porosity model for water level response to atmospheric loading in wells tapping fractured rock aquifers,” Water Resour. Res. 35(5), 1495–1505 (1999).
[Crossref]

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S. P. Timoshenko, Theory of Elastic Stability (McGraw-Hill, 1961).

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Figures (17)

Fig. 1
Fig. 1 Micro-porous structure of the Berea sandstone
Fig. 2
Fig. 2 3D-printed model with micro-porous structure of a local part from a section of the Berea sandstone samples.
Fig. 3
Fig. 3 Arrangement of dark-field circular polariscopes: (a) Experimental setup; (b) Angles of the optical axes of the polarizer and analyser, and the fast axes of the two quarter wave plates to the vertical direction.
Fig. 4
Fig. 4 Analytical photoelasticity patterns with continuous load increment.
Fig. 5
Fig. 5 Description of the method used to determine the fringe orders based on the light intensity changes of point P in Fig. 4.
Fig. 6
Fig. 6 The flow chart of the process to determine the integral fringe orders, where I refers to the continuous light intensity in the whole loading process.
Fig. 7
Fig. 7 Influence of the incoherent superposition in the interference of lights with two different wave lengths.
Fig. 8
Fig. 8 Illustration of the effectiveness of this method through comparison of experimental and theoretical results. (a) Comparison in horizontal direction. (b) Comparison in vertical direction.
Fig. 9
Fig. 9 Comparison of the experimental and calculated results of two different models under the diametrical pressures: (a) the photoelastic pattern of a circular disk under the load of 3 kN, (b) the unwrapped result under the same load, (c) the photoelastic pattern of a cubic plate with a circular hole under the load of 8 kN, and (d) the unwrapped results under the same load.
Fig. 10
Fig. 10 Relative errors with the increment of the fringe orders: (a) the errors in the disk model and (b) the errors in the plate model containing a circular hole.
Fig. 11
Fig. 11 Photoelastic fringe patterns selected from the stress–strain curve of the loading process: (a) the frame when the loading pressure is 7.5 MPa, (b) the frame when the loading pressure is 12.5 MPa, (c) the frame when the loading pressure is 17.5 MPa, and (d) the frame when the loading pressure is 22.5 MPa. The dark black areas in Fig. 11(a)–11(d) represent pores. Note that the stress–strain curve is the average stress and strain calculated using the load force divided by the area of the top surface and the displacement divided by the initial length of the specimen along the loading direction. Hence, it is a “nominal” stress vs strain curve that represents the continuous loading process.
Fig. 12
Fig. 12 Results calculated by the proposed method at the load pressure of 7.5 MPa: (a) photoelastic fringe pattern, (b) the wrapped contour of fringe orders, (c) the unwrapped contour of fringe orders. The dark black areas in (a) and the dark blue areas in (b) and 9(c) represent pores.
Fig. 13
Fig. 13 Principal stress difference of different loading pressures in two directions: (a) the principal stress difference in the horizontal direction and (b) the principal stress difference in the vertical direction.
Fig. 14
Fig. 14 FEM model of the complex structure model.
Fig. 15
Fig. 15 Comparison of unwrapped contours of the principal stress differences: numerical simulation results when the pressure was (a) 7.5 MPa, (b) 12.5 MPa, (c) 17.5 MPa, (d) 22.5 MPa, (e) 7.5 MPa, (f) 12.5 MPa, (g) 17.5 MPa, and (h) 17.5 MPa. The white areas in Figs. 15(a)–15(d) and the dark blue areas in Fig. 15(e)–15(h) represent pores.
Fig. 16
Fig. 16 Detailed comparison of the experimental and numerical simulation results: (a) comparison of the principal stress difference in the horizontal direction, and (b) comparison of the principal stress difference in the vertical direction.
Fig. 17
Fig. 17 Comparison of wrapped contours of fringe orders at the loading pressure of 7.5 MPa: (a) the result of the experiment, and (b) the result of the numerical simulation. The dark blue areas in (a) and the white areas in (b) represent pores.

Tables (3)

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Table 1 Basic Mechanical Properties of 3D Printing Materials.

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Table 2 Formulas for Calculating the Fractional Part Nf in the Three Simulations.

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Table 3 Comparison of mechanical parameters between printing material and conventional photoelastic materials [44, 54–57]

Equations (17)

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σ x = 2P πt { x 2 (r+y) [ x 2 + (r+y) 2 ] 2 + x 2 (ry) [ x 2 + (ry) 2 ] 2 }+ P πrt σ y = 2P πt { (r+y) 3 [ x 2 + (r+y) 2 ] 2 + (ry) 3 [ x 2 + (ry) 2 ] 2 }+ P πrt , τ xy = 2P πt { x ( r+y ) 2 [ x 2 + ( r+y ) 2 ] 2 + x ( ry ) 2 [ x 2 + ( ry ) 2 ] 2 }
σ 1 σ 2 = ( σ x σ y ) 2 +4 τ xy 2 = 4P( r 2 ( x 2 + y 2 ) ) πtr( ( x 2 + y 2 + r 2 )4y r 2 ) ,
σ 1 σ 2 = Nf t ,
δ=2π ( σ 1 σ 2 )t f .
I= 1 2 I s ( 1cosδ ).
I= 1 2 I s ( 1cos(2π ( σ 1 σ 2 )t f ) ) = 1 2 I s ( 1cos(2π 4P( r 2 ( x 2 + y 2 ) ) πfr( ( x 2 + y 2 + r 2 )4y r 2 ) ) ).
N i =n1.
I'= I p + I v 2 I p I v 2 cosδ.
δ=arccos( ( I ' I av )/( I p I av )) or δ[0,π]. δ=arccos( ( I ' I av )/( I av I v ))
I av = I p + I v 2 .
N= N i + N f ,
e= | n 2 n 1 | n 1 ,
σ 1 = σ x + σ y 2 + ( σ x σ y ) 2 4 + τ xy 2
σ 2 = σ x + σ y 2 ( σ x σ y ) 2 4 + τ xy 2
σ 1 σ 2 = ( σ x σ y ) 2 +4 τ xy 2
F N =( σ 1 σ 2 )×d/f,
δ N = F N INT( F N ),

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