Abstract
Granular materials are among the materials which do not fall within the traditional definition of matter. The behavior of granular materials is of great importance in fields such as chemical and agronomical industries, since many of the materials used are prepared from powders or grains, or in geotechnical engineering due to discrete nature of soils. Extensive research has been done to study and quantify the contact force network on various granular systems, specifically the contact force distribution in terms of magnitudes and orientations. However, the stress magnitudes in the contact zones have always been a challenge, regardless of the full-field method used in the analysis. The objective of the work presented here is to determine the stresses in two-dimensional granular materials from a thermoelastic stress analysis (TSA) test using an inverse approach. The inverse approach relies on both the TSA values in the vicinity of the interparticle contacts, an extension of superposed Flamant solutions for concentrated forces on surfaces, as well as static equilibrium equations. Preliminary results on a periodic stacking of cylinders show promising perspectives for granular materials.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
H.M. Jaeger, S.R. Nagel, Granular solids, liquids, and gases. Rev. Mod. Phys. 68, 1259–1272 (1996)
S. Ostojic, E. Somfai, B. Nienhuis, Scale invariance and universality of force networks in static granular matter. Nature 439, 828–830 (2006)
D.H. Nguyen, E. Azéma, F. Radjai, P. Sornay, Effect of size polydispersity versus particle shape in dense granular media. Phys. Rev. E 90, 012202 (2014)
A.A. Peña, R. García-Rojo, H.J. Herrmann, Influence of particle shape on sheared dense granular media. Granul. Matter 9, 279–291 (2007)
C. Nouguier-Lehon, B. Cambou, E. Vincens, Influence of particle shape and angularity on the behaviour of granular materials: a numerical analysis. Int. J. Numer. Anal. Methods Geomech. 27, 1207–1226 (2003)
S.G. Bardenhagen, J.U. Brackbill, D. Sulsky, Numerical study of stress distribution in sheared granular material in two dimensions. Phys. Rev. E 62, 3882–3890 (2000)
I. Preechawuttipong, R. Peyroux, F. Radjai, W. Rangsri, Static states of cohesive granular media. J. Mech. Sci. Technol. 21, 1957–1963 (2007)
P. Jongchansitto, I. Preechawuttipong, X. Balandraud, M. Grédiac, Numerical investigation of the influence of particle size and particle number ratios on texture and force transmission in binary granular composites. Powder Technol. 308, 324–333 (2017)
H. Wolf, D. Konig, T. Triantafyllidis, Experimental investigation of shear band patterns in granular material. J. Struct. Geol. 25, 1229–1240 (2003)
S.A. Hall, M. Bornert, J. Desrues, Y. Pannier, N. Lenoir, G. Viggiani, P. Besuelle, Discrete and continuum analysis of localised deformation in sand using X-ray μCT and volumetric digital image correlation. Geotechnique 60, 315–322 (2010)
G. Schneebeli, Une analogie mécanique pour les terres sans cohésion. C. R. Hebd. Acad. Sci. 243, 125–126 (1956)
C. Slominski, M. Niedostatkiewicz, J. Tejchman, Application of particle image velocimetry (PIV) for deformation measurement during granular silo flow. Powder Technol. 173, 1–18 (2007)
S.A. Hall, D.M. Wood, E. Ibraim, G. Viggiani, Localised deformation patterning in 2D granular materials revealed by digital image correlation. Granul. Matter 12, 1–14 (2010)
V. Richefeu, G. Combe, G. Viggiani, An experimental assessment of displacement fluctuations in a 2D granular material subjected to shear. Geotech. Lett. 2, 113–118 (2012)
E. Marteau, J.E. Andrade, A novel experimental device for investigating the multiscale behavior of granular materials under shear. Granul. Matter 19, 77 (2017)
R. Hurley, E. Marteau, G. Ravichandran, J.E. Andrade, Extracting inter-particle forces in opaque granular materials: beyond photoelasticity. J. Mech. Phys. Solids 63, 154–166 (2014)
R.C. Hurley, K.W. Lim, G. Ravichandran, J.E. Andrade, Dynamic inter-particle force inference in granular materials: method and application. Exp. Mech. 56, 217–229 (2016)
N. Karanjgaokar, Evaluation of energy contributions using inter-particle forces in granular materials under impact loading. Granul. Matter 19, 36 (2017)
A. Shukla, C. Damania, Experimental investigation of wave velocity and dynamic contact stresses in an assembly of disks. Exp. Mech. 27, 268–281 (1987)
K.M. Roessig, J.C. Foster, S.G. Bardenhagen, Dynamic stress chain formation in a two-dimensional particle bed. Exp. Mech. 42, 329–337 (2002)
S.A. Mirbagheri, E. Ceniceros, M. Jabbarzadeh, et al., Sensitively photoelastic biocompatible gelatin spheres for investigation of locomotion in granular media. Exp. Mech. 55, 427–438 (2015)
C. Chaiamarit, X. Balandraud, I. Preechawuttipong, M. Grédiac, Stress network analysis of 2D non-cohesive polydisperse granular materials using infrared thermography. Exp. Mech. 39, 761–769 (2015)
P. Jongchansitto, X. Balandraud, M. Grédiac, C. Beitone, I. Preechawuttipong, Using infrared thermography to study hydrostatic stress networks in granular materials. Soft Matter 10, 8603–8607 (2014)
T.S. Majmudar, R.P. Behringer, Contact force measurements and stress-induced anisotropy in granular materials. Nature 435, 1079–1082 (2005)
M. Yousefi, X. Balandraud, W.A. Samad, Thermographic stress field investigation of a multiply-loaded disk, in Residual Stress Thermomechanics & Infrared Imaging, Hybrid Techniques and Inverse Problems, vol. 7 (Springer, Cham, 2019), pp. 115–117
S. Lin, D. Matthys, R.E. Rowlands, Separating stresses thermoelastically in a central circularly perforated plate using an airy stress function. Strain 45, 516–526 (2009)
A.A. Khaja, R.E. Rowlands, Experimentally determined stresses associated with elliptical holes using polar coordinates. Strain 49, 116–124 (2013)
W.A. Samad, R.E. Rowlands, Full-field thermoelastic stress analysis of a finite structure containing an irregularly-shaped hole. Exp. Mech. 54, 457–469 (2014)
W.A. Samad, A.A. Khaja, A. Kaliyanda, R.E. Rowlands, Hybrid thermoelastic stress analysis of a pinned joint. Exp. Mech. 54, 515–525 (2014)
B. Foust, R.E. Rowlands, Thermoelastic determination of individual stresses in a diametrally loaded disk. Strain 47, 146–153 (2011)
S. Lin, W.A. Samad, A.A. Khaja, R.E. Rowlands, Hybrid thermoelastic stress analysis. Exp. Mech. 55, 653–665 (2015)
Acknowledgements
The authors gratefully acknowledge Dr. Chanwit Chaiamarit, Dr. Pawarut Jongchansitto and Prof. Itthichai Preechawuttipong from Chiang Mai University, Thailand for the discussions about the mechanical response of granular materials. Ms. Rym Boufayed, Université Clermont-Auvergne, France is also acknowledged for the help in image processing.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Society for Experimental Mechanics, Inc.
About this paper
Cite this paper
Yousefi, M., Balandraud, X., Samad, W.A. (2020). Stress Determination for Granular Materials Using TSA: An Inverse Approach. In: Baldi, A., Kramer, S., Pierron, F., Considine, J., Bossuyt, S., Hoefnagels, J. (eds) Residual Stress, Thermomechanics & Infrared Imaging and Inverse Problems, Volume 6. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-030-30098-2_17
Download citation
DOI: https://doi.org/10.1007/978-3-030-30098-2_17
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-30097-5
Online ISBN: 978-3-030-30098-2
eBook Packages: EngineeringEngineering (R0)