FEA Based on 3D Micro-CT Images of Mesoporous Engineered Hydrogels


  • L. Siad University of Champagne, France
  • J. Jing University of Champagne, France
  • J. Braux University of Champagne, France
  • M. Dubus University of Champagne, France
  • F. Velard University of Champagne, France
  • D. Laurent-Maquin University of Champagne, France
  • S. C. Gangloff University of Champagne, France
  • H. Kerdjoudj University of Champagne, France
  • R. Rahouadj University of Lorraine, France
  • J. -F. Schmidt University of Lorraine, France
  • J. -F. Ganghoffer University of Lorraine, France
Volume: 5 | Issue: 6 | Pages: 885-890 | December 2015 | https://doi.org/10.48084/etasr.606


The objective of this computational study was to propose a rapid procedure in obtaining an estimation of elastic moduli of solid phases of porous natural-polymeric biomaterials used for bone tissue engineering. This procedure was based on the comparison of experimental results to finite element (FE) responses of parallelepiped so-called representative volume elements (rev) of the material at hand. To address this issue a series of quasi-static unconfined compression tests were designed and performed on three prepared cylindrical biopolymer samples. Subsequently, a computed tomography scan was performed on fabricated specimens and two 3D images were reconstructed. Various parallelepiped revs of different sizes and located at distinct places within both constructs were isolated and then analyzed under unconfined compressive loads using FE modelling. In this preliminary study, for the sake of simplicity, the dried biopolymer solid is assumed to be linear elastic.


Porous biomaterials, finite elements, microtomography, elasticity.


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ABAQUS/Standard, SIMULIA, Providence, RI, 2013

E. M. Ahmed, “Hydrogel: Preparation, characterization, and applications: A review”, Journal of Advanced Research, Vol. 6, pp. 105-121, 2015 DOI: https://doi.org/10.1016/j.jare.2013.07.006

V. Brun, C. Guillaume, S. Mechiche Alami, J. Josse, J. Jing, F. Draux, S. Bouthors, D. Laurent-Maquin, S. C. Gangloff, H. Kerdjoudj, F. Velard, “Chitosan/hydroxyapatite hybrid scaffold for bone tissue engineering”,

Biomed. Mater. Eng., Vol. 24, pp. 63-73, 2014

S. Baek, A. R. Srinivasa, “Diffusion of a fluid through an elastic solid undergoing large deformation”, Int. J. Non-linear Mech., Vol. 39, pp. 201-218, 2004 DOI: https://doi.org/10.1016/S0020-7462(02)00153-1

S. Baek, T. J. Pence, “Inhomogeneous deformation of elastomer gels in equilibrium under saturated and unsaturated conditions”, J. Mech. Phys. Solids, Vol. 59, pp. 561-582, 2011 DOI: https://doi.org/10.1016/j.jmps.2010.12.013

M. A. Biot, “General theory of three-dimensional consolidation”, J. Appl. Phys., Vol. 12, pp. 155-164, 1941 DOI: https://doi.org/10.1063/1.1712886

S. K. Boyd, "Image-Based Finite Element Analysis" in C. W. Sensen, B. Hallgrimson, editors, Advanced Imaging in Biology and medecine, pp. 3-25, Springer, Berlin, 2009

S. A. Chester, L. Anand, “A coupled theory of fluid permeation and large deformations for elastomeric materials”, J. Mech. Phys. Solids, Vol. 58, pp. 1879-1919, 2010 DOI: https://doi.org/10.1016/j.jmps.2010.07.020

S.C. Cowin, S.B. Doty, Tissue mechanics, Springer, Berlin, 2007. DOI: https://doi.org/10.1007/978-0-387-49985-7

J. Delbow, E. Fried, H. Ji, "Chemically induced swelling of hydrogels", J. Mech. Phys. Solids, Vol. 52, pp. 51-84, 2004 DOI: https://doi.org/10.1016/S0022-5096(03)00091-7

M. Djabourov, K. Nishinari, E. Schacht, Physical Gels from Biological and Synthetic Polymers, Cambridge University Press, 2013 DOI: https://doi.org/10.1017/CBO9781139024136

P. J. Flory, J. Rehner, “Statistical mechanics of cross-linked polymer networks I. Rubberlike elasticity”, J. Chem. Phys., Vol. 11, pp. 512-520, 1943 DOI: https://doi.org/10.1063/1.1723791

P. J. Flory, J. Rehner, “Statistical mechanics of cross-linked polymer networks II. Swelling”, J. Chem. Phys., Vol. 11, pp. 521-526, 1943 DOI: https://doi.org/10.1063/1.1723792

P. J. Flory, Principles of Polymer Chemistry, Cornell University Press, Ithaca, 1953

J. W. Gibbs, The Scientific papers of J. Willard Gibbs, Dover Publication, New York, 1961. Digital copy of the book is freely available at http://books.google.com/

F. Horkay, G. B. McKenna, “Polymer network and gels”, in J. E. Mark, editor, Physical properties of polymers handbook, pp. 497-523, Springer, Berlin, 2007 DOI: https://doi.org/10.1007/978-0-387-69002-5_29

S. Hazanov, C. Huet, “Order relationships for BCs effect”, J. Mech. Phys. Solids, Vol. 42, pp. 1995–2011, 1994 DOI: https://doi.org/10.1016/0022-5096(94)90022-1

W. Hong, “Continuum models of stimuli-responsive gels”, in S. Li, B. Sun, editors, Advances in Soft Matter Mechanics, pp. 165-196, Springer, Berlin, 2012 DOI: https://doi.org/10.1007/978-3-642-19373-6_6

W. Hong, X. Zhao, J. Zhou, Z. Suo, “A theory of coupled diffusion and large deformation in polymeric gels”, J. Mech. Phys. Solids, Vol. 56, pp. 1779-1793, 2008 DOI: https://doi.org/10.1016/j.jmps.2007.11.010

W. Hong, Z. Liu, Z. G. Suo, “Inhomogeneous swelling of a gel in equilibrium with a solvent and mechanical load”, Int. J. Solids Struct., Vol. 46, pp. 3282-3289, 2009 DOI: https://doi.org/10.1016/j.ijsolstr.2009.04.022

C. Huet, “Application of variational concepts to size effects”, J. Mech. Phys. Solids, Vol. 38, pp. 815–831, 1990 DOI: https://doi.org/10.1016/0022-5096(90)90041-2

I.-Y. Kim, S.J. Seo, H.S. Moon, M. K. Yoo, In-Y. Park, B.-C. Kim, C. S. Cho, “Chitosan and its derivatives for tissue engineering applications”, Biotechnology Advances, Vol. 26, pp 1-21, 2008. DOI: https://doi.org/10.1016/j.biotechadv.2007.07.009

R. Jin, P.J. Dijstra, “Hydrogels for Tissue Engineering Applications”, in R. M. Ottenbrite, K. Park, T. Okano, editors, Biomedical applications of hydrogels handbook, pp. 203-225 , Springer, Berlin, 2010

T. Kanit, S. Forest, I. Galliet, V. Mounoury, D. Jeulin, "Determination of the size of the representative volume element for random composites: statistical and numerical approach", Int. J. Solids Struct, Vol. 40, pp. 3647–3679, 2003 DOI: https://doi.org/10.1016/S0020-7683(03)00143-4

D. Lacroix, A. Chateau, M. P. Ginebra, J. A. Planell, “Micro-finite element models of bone tissue engineering scaffold”, Biomaterials, Vol. 27, pp. 5326-5334, 2006 DOI: https://doi.org/10.1016/j.biomaterials.2006.06.009

H. Li, Smart Hydrogel Modelling, Springer, Berlin, 2009 DOI: https://doi.org/10.1007/978-3-642-02368-2

E. Maire, P. J. Withers, "Quantitative X-ray tomography", International Materials Reviews, Vol. 59, pp. 1-43, 2014 DOI: https://doi.org/10.1179/1743280413Y.0000000023

M. A. Meyer, P.-Y. Chen, Biological Materials Science, Cambridge University Press, 2014

H. Omidian, K. Park, “Introduction to hydrogels”, in R. M. Ottenbrite, K. Park, T. Okano, editors, Biomedical applications of hydrogels handbook, pp. 1-16, Springer, Berlin, 2010 DOI: https://doi.org/10.1007/978-1-4419-5919-5_1

M. L. Oyen, "Mechanical characterisation of hydrogel materials", International Materials Reviews, Vol. 59, pp. 44-58, 2014 DOI: https://doi.org/10.1179/1743280413Y.0000000022

N. A. Peppas, Hydrogels in medicine and pharmacy, vol. 1, CRC Press, Florida, 1987

B. D. Ratner, A. S. Hoffman, F. J. Schoen, J. E. Lemons, Biomaterials Sciences, 3rd edition, App. 8: Properties of Soft Materials by M. C. L. Martins, Elsevier Inc., 2013

B. van Rietbergen, R. Huiskes, F. Eckstein, P. Rüegsegger, “Trabecular Bone Tissue Strains in the Healthy and Osteoporotic Human Femur”, J. Bone Miner. Res., Vol. 18, pp. 1781-1788, 2003 DOI: https://doi.org/10.1359/jbmr.2003.18.10.1781

H. Shen, L. C. Brinson, “Representative volume element size for porous titanium”, J. Mech. Mater. Structures, Vol. 1, pp. 1179–1204, 2006 DOI: https://doi.org/10.2140/jomms.2006.1.1179

Simpleware Ltd., Exeter, UK, http://www.simpleware.com, 2014

Suo, http://imechanica.org/node/987, http://imechanica.org/node/538

A. Steinbuchel, editor, Biopolymers, Vols. 5-6, Wiley, Weinheim, 2006

S. K. Wang, J. Li, F. Yao, "Application of Chitosan-Based Biomaterials in Tissue Engineering", in K. Yao, J. Li, F. Yao, Y. Yin, editors, Chitosan-based hydrogels. Functions and Applications, pp. 407-468, SCRC Press, 2012 DOI: https://doi.org/10.1201/b11048-10


How to Cite

L. Siad, “FEA Based on 3D Micro-CT Images of Mesoporous Engineered Hydrogels”, Eng. Technol. Appl. Sci. Res., vol. 5, no. 6, pp. 885–890, Dec. 2015.


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