2D Gel Network

A mesoscale model for the micromechanical study of gels

Abstract Gels are comprised of polymer networks swelled by some interstitial solvent. They are under... Read more
Rate dependent damage

Rate-Dependent Damage Mechanics of Polymer Networks with Reversible Bonds

Brief Description In this work, we develop a statistical theory of damage for transient networks... Read more
Ant Raft Treadmilling

Computational exploration of treadmilling and protrusion growth observed in fire ant rafts

Brief Description Cooperative behavior in organisms often permits groups to achieve collective tasks that are... Read more



109. Xu L., Lamont, S.C., Li T., Zhang Y., Pan W., Gao C., Zhu C., Chen, S., Hu H., Ding J. and Vernerey F.J.*, Nonlinear Viscoelasticity and Toughening Mechanisms in Nanoclay-PNIPAAm Double Network Hydrogels, ACS Macro Letters

108.  Lamont S.C, Weishaar K., Bruns C. and Vernerey F.J.*, Micromechanics and damage in slide-ring networks, Physical Review E

107. Wagner R.J. and Vernerey F.J.*, Coupled bond dynamics alters relaxation in polymers with multiple intrinsic dissociation rates, Soft Matter     

106. Crespo-Cuevas V.,Ferguson  V.L. and Vernerey F.J.*, Poroviscoelasto-plasticity of agarose-based hydrogels, Soft Matter

105. Lamont S., Fropier J., Abadie J., Piat E., Constantinescu A., Roux C.and Vernerey F.J.*, Profiling oocytes with neural networks from images and mechanical data, Journal of the Mechanical Behavior of Biomedical Materials 138, 105640   


104. Mwaffo V.* and Vernerey F.J., Analysis of Group of Fish Response to Startle Reaction, Journal of Nonlinear Science 32 (6), 96        

103. Xu L., Fu Y., Wagner R.J., Zou X., He Q., Li T., Pan W., Ding J. and Vernerey F.J.*, Thermosensitive P (AAc‐co‐NIPAm) Hydrogels Display Enhanced Toughness and Self‐Healing via Ion–Ligand Interactions, Macromolecular Rapid Communications 43 (19), 2200320, 3    

102. Wagner R.J., Dai J., Su X. and Vernerey F.J.*, A mesoscale model for the micromechanical study of gels, Journal of the Mechanics and Physics of Solids 167, 104982, 5    

101. Xu L., Wagner R.J., Liu S., He Q., Li T., Pan W., Feng Y., Feng H., Meng Q. and Vernerey F.J.*, Locomotion of an untethered, worm-inspired soft robot driven by a shape-memory alloy skeleton, Scientific Reports 12 (1), 12392

100. Wagner R.J and Vernerey F.J.*, Computational exploration of treadmilling and protrusion growth observed in fire ant rafts, PLoS Computational Biology 18 (2), e1009869

99. Vernerey F.J. Mechanics of transient semi-flexible networks: soft-elasticity, stress relaxation and remodeling (2022), Journal of the Mechanics and Physics of Solids, in press


98. Lamont S.C, Mulderrig J., Bouklas N., and Vernerey F.J., (2021) Rate-Dependent Damage Mechanics of Polymer Networks with Reversible Bond, Macromolecules, 54, 23, 10801–10813

97. Hui C.Y., Cui F., Zehnder A. and Vernerey F.J.*, (2021), Physically-motivated models of polymer networks with dynamic cross-links: comparative study and future outlook, Proceedings of the Royal Society A, https://doi.org/10.1098/rspa.2021.0608

96. Lamont, S. and Vernerey F.J. (2021) A Transient Microsphere Model for nonlinear viscoelasticity in dynamic polymer networks, Journal of Applied Mechanics, In press

95. Vernerey F.J, Sridhar S.L., Muralidharan A, and Bryant S. (2021). Mechanics of 3D cell-hydrogel interactions: Experiments, mechanisms and modelsChemical Reviews (Invited paper). https://doi.org/10.1021/acs.chemrev.1c00046 

94. Wagner R.J., Hobbs E. and Vernerey F.J. (2021). A network model of transient polymers: Exploring the micromechanics of nonlinear viscoelasticity. Soft Matter. In press

93. Wagner R., Such K., Hobbs E. and Vernerey F.J. (2021). Treadmilling and dynamic protrusions in fire ant raftsJournal of the Royal Society Interface. Link

92. Barthold J.E., St. Martin B.M., Sridhar S.L., Vernerey F.J., Schneider S.E., Wacquez A., Ferguson V.L., Calve S., and Neu C.P. (2021). Recellularization and Integration of Dense Extracellular Matrix by Percolation of Tissue Microparticles. Advanced Functional Materials. Link

91. Shen T., Song Z., Cai S. and Vernerey F.J. (2021). Nonsteady fracture of transient networks: the case of vitrimer. PNAS. Link

90. Song Z., Shen T., Vernerey F.J. and Cai S. (2021). Force-dependent bond dissociation explains the rate-dependent fracture of vitrimers. Soft Matter. Link

89. Ortega, J.K.E., Mohan R., Munoz C., Sridhar S.L. and Vernerey F.J. (2021). Phycomyces: Helical growth during the phototropic and avoidance responses, and in stiff mutantsScientific Reports. Link

88. Sridhar, L.S., Dunagin, J., Koo, K., Hough L. and Vernerey, F.J. (2021). Enhanced diffusion by reversible binding to active polymers. Macromolecules. Link

87. Koo K., Sridhar, L.S., Clark N., Vernerey F.J., and Loren Hough (2021). Moving while you’re stuck: A macroscopic demonstration of an active system inspired by binding-mediated transport in biology. Soft Matter. Link

86. Vernerey, F. J. & Lamont, S. (2021). Transient mechanics of slide-ring networks, a continuum modelJournal of the Mechanics and Physics of Solids. Link


85. Shen, T & Vernerey, F. J. (2020). Rate-dependent Fracture of Transient NetworksJournal of the Mechanics and Physics of Solids. Link

84. Brighenti, R, Li, Y, & Vernerey, F. J. (2020). Smart polymers for advanced applications: a mechanical perspective reviewFrontiers in Materials. Link

83. Sridhar, S & Vernerey, F. J. (2020). Mechanics of transiently crosslinked nematic networks. Journal of the Mechanics and Physics of Solids. Link

82.Schneider, M., Sridhar, S.L., Vernerey, F.J., Bryant, S. (2020). Spatiotemporal Neocartilage Growth in Matrix-Metalloproteinase-Sensitive Poly(Ethylene Glycol) Hydrogels Under Dynamic Compressive Loading: An Experimental and Computational Approach. Journal of Material Chemistry B. Link

81.  Vernerey, F. J., & Bryant, S. (2020). The role of Percolation in hydrogel-based tissue engineering and bioprinting. Current Opinion in Biomedical Engineering, Link


80. Benet, E., & Vernerey, F. J. (2019). Dynamic competition of inflation and delamination in the finite deformation of thin membranes. Soft matter, Link

79. Shen, T., Kan, J., Benet, E., & Vernerey, F. J. (2019). On the blistering of thermo-sensitive hydrogel: the volume phase transition and mechanical instability. Soft Matter, Link.

78. White, Z., Shen, T., Volk, E. M., & Vernerey, F. J. (2019). The role of surface properties on the penetration resistance of scaled skins. Mechanics Research Communications98, 1-8. Link.

77. Benet, E., Zhu, H., & Vernerey, F. J. (2019). Interplay of elastic instabilities and viscoelasticity in the finite deformation of thin membranes. Physical Review E99(4), 042502. Link.

76. Shen, T., Benet, E., Sridhar, S. L., Abadie, J., Piat, E., & Vernerey, F. J. (2019). Separating the contributions of zona pellucida and cytoplasm in the viscoelastic response of human oocytes. Acta biomaterialia85, 253-262. Link.


75. Vernerey, F. J., E. Benet, L. Blue, A. K. Fajrial, S. Lalitha Sridhar, J. Lum, G. Shakya, K. H. Song, A. N. Thomas, and M. A. Borden, (2018). Biological active matter aggregates: Inspiration for smart colloidal materialsAdvances in Colloid and Interface Science . Link.

74. Sridhar, S.L., Ortega, J. K. E., & Vernerey, F. J., (2018). A statistical model of expansive growth in plant and fungal cells: The case of Phycomyces. The Biophysical Journal. In Press. Link

73. Vernerey, F. J., Shen, T., Sridhar, S.L., & Wagner, R.J., (2018). How do fire ants control the rheology of their aggregations? -A statistical mechanics approach-. Journal of Royal Society Interface. Link.  

72. Vernerey, F. J., Brighenti, R., Long, R., & Shen, T. (2018). Statistical Damage Mechanics of Polymer NetworksMacromolecules. Link. PDF

71. Shen, T., Long, R., & Vernerey, F. (2018). Computational modeling of the large deformation and flow of viscoelastic polymersComputational Mechanics, 1-21. Link. PDF

​70. Sridhar, S.L., and Vernerey, F.J (2018), The Chain Distribution Tensor: Linking Nonlinear Rheology and Chain Anistropy in Transient Polymers. Polymers10(8), 848. Link. PDF

69. Brighenti, R., Menzel, A., & Vernerey, F. J. (2018). A physics-based micromechanical model for electroactive viscoelastic polymersJournal of Intelligent Material Systems and Structures29(14), 2902-2918. Link. PDF

68. White, Z. W., & Vernerey, F. J. (2018). Armours for soft bodies: how far can bioinspiration take us?Bioinspiration & biomimetics13(4), 041004. Link. PDF

67. Benet E., Lostec G., Pellegrino J. and Vernerey, F.J.* (2018), Mechanical instability and percolation of deformable particles through porous networks, Physical Review E. 97, 042607. Link. PDF

66. Vernerey, F. J. (2018). Transient response of nonlinear polymer networks: A kinetic theoryJournal of the Mechanics and Physics of Solids115, 230-247. LinkPDF

65.  Sridhar, S. L., & Vernerey, F. (2018). Localized Enzymatic Degradation of Polymers: Physics and Scaling LawsPhysical Review Applied9(3), 031001. Link. PDF

64.  Brighenti, R., Artoni, F., Vernerey, F., Torelli, M., Pedrini, A., Domenichelli, I., & Dalcanale, E. (2018). Mechanics of responsive polymers via conformationally switchable moleculesJournal of the Mechanics and Physics of Solids113, 65-81. Link. PDF


 63. Shen, T.; Font, M, Jung, S.; Gabriel, M.; Stoykovich, M.; Vernerey, F.;  (2017),  Remotely Triggered Locomotion of Hydrogel Mag-bots in Confined Spaces,  Scientific Reports 7.1 (2017): 16178. Link. PDF

62. Vernerey, F., & Shen, T. (2017). The mechanics of hydrogel crawlers in confined environment. Journal of The Royal Society Interface14(132), 20170242. Link PDF

61.   Schneider, M. C., Chu, S., Sridhar, S. L., De Roucy, G., Vernerey, F. J., & Bryant, S. J. (2017). Local Heterogeneities Improve Matrix Connectivity in Degradable and Photoclickable Poly (ethylene glycol) Hydrogels for Applications in Tissue Engineering. ACS Biomaterials Science & Engineering3(10), 2480-2492. PDF

60. Stefferson, M. W., Norris, S. L., Vernerey, F. J., Betterton, M. D., & Hough, L. E. (2017). Effects of soft interactions and bound mobility on diffusion in crowded environments: a model of sticky and slippery obstacles. Physical biology14(4), 045008.   Link. PDF

59. Bryant, S. J., & Vernerey, F. J. (2018). Programmable hydrogels for cell encapsulation and neo‐tissue growth to enable personalized tissue engineering. Advanced healthcare materials7(1), 1700605. Link. PDF

58. Vernerey, F. J., Long, R., & Brighenti, R. (2017). A statistically-based continuum theory for polymers with transient networks. Journal of the Mechanics and Physics of Solids107, 1-20. Link . PDF

57. Sridhar, S. L., Schneider, M. C., Chu, S., de Roucy, G., Bryant, S. J., & Vernerey, F. J. (2017). Heterogeneity is key to hydrogel-based cartilage tissue regeneration. Soft matter13(28), 4841-4855. Link. PDF

56. A. C. Sullivan, S. Lalitha Sridhar, A. Resman, D. J. Glugla, M. D. Alim, F.J Vernerey, R. R. McLeod (2017) Mechanical response of holographic photopolymers, Proc. SPIE 10233, Holography: Advances and Modern Trends V, 102330O; doi: 10.1117/12.2265878;  Link. PDF

55.Brighenti, R., Vernerey, F. J., & Artoni, F. (2017). Rate-dependent failure mechanism of elastomers. International Journal of Mechanical Sciences130, 448-457.  Link. PDF

54. Benet, E., Badran, A., Pellegrino, J., & Vernerey, F. (2017). The porous media's effect on the permeation of elastic (soft) particles. Journal of Membrane Science535, 10-19. Link. PDF

53. Chu, S., Sridhar, S. L., Akalp, U., Skaalure, S. C., Vernerey, F. J., & Bryant, S. J. (2017). Understanding the Spatiotemporal Degradation Behavior of Aggrecanase-Sensitive Poly (ethylene glycol) Hydrogels for Use in Cartilage Tissue Engineering. Tissue Engineering Part A23(15-16), 795-810. Link. PDF

52.   Shen, T., & Vernerey, F. (2017). Phoretic motion of soft vesicles and droplets: an XFEM/particle-based numerical solution. Computational mechanics60(1), 143-161. Link. PDF

51. Akalp, U., Schnatwinkel, C., Stoykovich, M. P., Bryant, S. J., & Vernerey, F. J. (2017). Structural modeling of mechanosensitivity in non-muscle cells: multiscale approach to understand cell sensingACS biomaterials science & engineering3(11), 2934-2942. Link. PDF


 50. Benet, E., & Vernerey, F. J.* (2016). “Mechanics and stability of vesicles and droplets in confined spaces”, Physical Review E94(6), 062613.    Link. PDF

49.  Brighenti, R.∗ and Vernerey, F. J.∗ (2016) A simple statistical approach to model the time dependent response of polymers with reversible cross-links, Composites Part B: Engineering, Volume 115, 15 April 2017, Pages 257–265   Link. PDF

48. Akalp U., Bryant S. and Vernerey, F. J.*  (2016) “Tuning Tissue Growth with Scaffold degradation in Enzyme-sensitive Hydrogels: a Mathematical Model”, Soft Matter, 12, 7505-7520     Link. PDF

47. Vernerey, F. J.* and Akalp U. (2016) “Role of catch bonds in actomyosin mechanics and cell mechanosensitivity”, Physical Review E,94, 012403     Link. PDF

46.  Musiket, K, Vernerey, F.J. and Xi Y. (2016) “Numeral Modeling of Fracture Failure of Recycled Aggregate Concrete Beams under High Loading Rates”, International Journal of Fracture, January 2017, Volume 203, Issue 1, pp 263–276  Link. PDF


45. Foucard, L. and Vernerey, F. J.* (2016) “A Particle-based Moving Interface Method (PMIM) for modeling the large deformation of boundaries in soft matter systems.”, International Journal for Numerical Methods in Engineering, 107 (11), 923–946. 2015     Link. PDF

44. Skaalure, S., Akalp, U., Vernerey, F. J.* and Bryant, S.* (2015) “Tuning Reaction and Diffusion Mediated Degradation of Enzyme-Sensitive Hydrogels”, Advanced Healthcare Materials. 5: 432–438.   Link. PDF

43.  Vernerey, F. J.* (2016) “A Mixture Approach to Investigate Interstitial Growth in Engineering Scaffolds”, Biomechanics and Modeling in Mechanobiology, 15(2):259-78    Link. PDF

42.  Akalp, U., Chu, S., Skaalure, S., Bryant, S.J., Doostan, A. and Vernerey, F. J.* (2015) “Determination of the Polymer-Solvent Interaction Parameter for PEG Hydrogels in Water: Application of a Self Learning Algorithm”, Polymer., Volume 66, 1 June 2015, Pages 135147     Link. PDF

41. Funk, N., Vera, M., Szewciw, L., Barthelat, F., Stoykovich*, M., and Vernerey, F. J*. (2015), Bio-inspired fabrication and characterization of a synthetic fish skin for soft materials protection, ACS Applied Materials and Interfaces, 7 (10), pp 5972–5983    Link. PDF
Highlighted in Science: p 1434 in vol 347 issue 6229 (27 MARCH 2015)

40. Foucard, L., Aryal A., Duddu*, R. and Vernerey F. J.*(2015), A coupled Eulerian-Lagrangian extended finite element formulation for simulating large deformations in hyperelastic media with moving free boundaries. Computer Methods in Applied Mechanics and Engineering, Volume 283, 1 January 2015, Pages 280–302  Link. PDF


39.  Foucard, L. and Vernerey, F. J.* (2014) An X-FEM numerical asymptotic expansion for simulating a Stokes flow near a sharp corner, International Journal of Numerical Methods in Engineering, 102, 79–98.  Link. PDF

38. Foucard, L. and Vernerey, F. J.* (2014) Particle-based Moving Interface Method for the study of the interaction between soft colloid particles and immersed fibrous network, Computer Modeling in Engineering and Science, 98(1), pp 101-127.  Link. PDF

37. Vernerey, F. J.* and Kabiri, M (2014) Adaptive Concurrent Multiscale Model for Fracture and Crack Propagation in Heterogeneous Media, Computer Methods in Applied Mechanics and Engineering, 276, pp 566-588.  Link. PDF

36. Vernerey, F.J.*, and Barthelat, F. (2014)  Skin and scales of teleost fish: simple structure but high performance and multiple functions, Journal of the Mechanics and Physics of Solids, 68, pp 66-76.  Link. PDF

35. Vernerey, F.J.∗ (2014). A Microstructure-based Continuum Model for Multiphase Solids, Mechanics of Advanced Materials and Structures, 21(6), 441-456  Link. PDF


34. Vernerey, F. J.*, Musiket K. and Barthelat, F. (2013) Mechanics of Fish skin: A computational approach for bio-inspired flexible composites, International Journal of Solids and Structures, 51 (1), pp 274-283  Link. PDF

33. Zhu, D., Barthelat, F. and Vernerey, F.J.∗ (2013). The intricate multiscale mechanical response of natural fish-scale composites, Handbook of Micromechanics and Nanomechanics, Pan Stanford Publishing Co.     Link. PDF

32. Liang, Y.C, Ye, Z. Vernerey, F.J. and Xi, Y. (2013) Development of Processing Methods to Improve Strength of Concrete with 100% Recycled Coarse Aggregate, Journal of the Materials in Civil Engineering, 10.1061/(ASCE)MT.1943-5533.0000909  Link. PDF

31. Zhu, D., Szewciw, L. Vernerey, F.J. and Barthelat, F. (2013) Puncture resistance of the scaled skin from striped bass: collective mechanisms and inspiration for new flexible armor designs, Journal of the Mechanical Behavior of Biomedical Materials, 24, pp 30–40.  Link. PDF  

30. Dhote, V. and Vernerey, F.J.∗ (2013). Mathematical model of the role of degradation on matrix development in hydrogel scaffold, Biomechanics and Modeling in Mechanobiology, doi 10.1007/s10237-013-0493-0     Link. PDF

29. Vernerey, F.J.∗ and Farsad, M. (2013). A mathematical model of the coupled mechanisms of cell adhesion, contraction and spreading, Journal of Mathematical Biology, doi 10.1007/s00285-013-0656-8  Link. PDF

28.  Kabiri, M. and Vernerey, F. J.∗ (2013). “An XFEM based multiscale approach to fracture of heterogeneous media, International Journal of Multiscale Computational Engineering, DOI: 10.1615/IntJMultCompEng.2013005569.     Link. PDF

27.  Foucard, L., Espinet, X. Benet, E. M. and Vernerey, F. J. ∗(2013). The role of the cortical membrane in cell mechanics: model and simulation, Multiscale Simulations and Mechanics of Biological Materials, Wiley, DOI: 10.1002/9781118402955. ch13.     Link. PDF


26.  Dhote, V., Skaalure, S. Akalp, U., Robert, J., Bryant, S. and Vernerey, F.J.∗ (2012). On the role of hydrogel structure and degradation in controlling the transport of cell-secreted matrix molecules for engineered cartilage, Journal of the Mechanical Behavior of Biomedical Materials, doi: 10.1016/j.jmbbm.2012.10.016  Link. PDF

25. Vernerey, F.J. Preface, Multiscale Modeling of inelastic and localization behavior in heterogeneous media, International Journal for Multiscale Computational Engineering 10 (5)     Link. PDF

24.  Vernerey, F.J.∗ and Kabiri, M. (2012). An adaptive concurrent multiscale method for microstructured elastic solids, Computer Methods in Applied Mechanics and Engineering, 241-244, pp. 52-64  Link. PDF

23. Farsad, M. and Vernerey, F.J.∗ (2012). An XFEM-based numerical strategy to model mechanical interactions between biological cells and a deformable substrate, International Journal of Numerical Methods in Engineering, 92,(3), pp 238-267     Link. PDF

22. Foucard, L. and Vernerey, F.J.∗ (2012). On the dynamics of Stress Fibers turnover in contractile cells, Journal of Engineering Mechanics, v138(10), pp 1282-1287  Link. PDF

21. Vernerey, F.J.∗ (2012). The effective permeability of cracks and interfaces in porous media, Transport in Porous Media, 93,(3), pp815-829  Link. PDF

20. Foucard, L. and Vernerey, F.J.∗ (2012). A thermodynamical model for stress-fiber organization in contractile cells, Applied Physics Letters, 100(1), 013702 1-4.  Link. PDF

19. Vernerey, F. J.∗, Chevalier, T. (2012). A multiscale micro-continuum model to capture strain localization in composite materials, International Journal of Multiscale Computational Engineering, 10(5), 487-501     Link. PDF


18.  Vernerey, F.J.∗ (2011). A theoretical treatment on the mechanics of interfaces in deformable porous media, International Journal of Solids and Structures, 48(22-23), 3129-3141  Link. PDF

17.  Zhu, D, Ortega, C, Motamedi, R, Szewciw, L, Vernerey, F.J. and Barthelat, F. (2011). Structure and mechanical performance of a modern fish scale, Advanced Biomaterials, 14(4), B185-B194     Link. PDF

16.  Vernerey, F.J.∗ , Foucard, L. and Farsad, M. (2011). Bridging the scales to explore cellular adaptation and remodeling, BionanoScience, 1(3),110-115     Link. PDF

15. Vernerey, F.J.∗ and Farsad, M. (2011). A Constrained Mixture Approach to Mechano- Sensing and Force Generation in Contractile Cells, Journal of the Mechanical Behavior of Biomedical Materials, 4(8), 1683-1699  Link. PDF

14.  Vernerey, F.J.∗, Greenwald, E. and Bryant, S. (2011). Triphasic mixture model of cell- mediated enzymatic degradation of hydrogels, Computer Methods in Biomechanics and Biomedical Engineering, 15(11), 1197-1210  Link. PDF

13. Vernerey, F.J.∗ (2011), On the application of multiphasic theories to the problem of cell-substrate mechanical interactions, Advances in Cell Mechanics, Springer, Li, Shaofan; Sun, Bohua (Eds.), 27-54  Link. PDF

12. Vernerey, F.J.∗, Pak, R. (2011). Analysis of Soft Fibers with Kinematic Constraints and Cross-links by Large Deformation Beam Theory, Journal of Engineering Mechanics, 137, pp 527-536.  Link. PDF

11. Vernerey, F.J.∗ and Farsad, M. (2011), An Eulerian/XFEM formulation for the large deformation of cortical cell membrane, Computer Methods in Biomechanics and Biomedical Engineering, 14(5),433-45.  Link. PDF


10. Vernerey, F. J.∗ and Bartelat, F. (2010). On the Mechanics of Fish-Scale Structures. International Journal of Solids and Structures, 47(17), 2268-2275.  Link. PDF

9. Farsad, M., Vernerey, F. J.∗, and Park, H. S. (2010). An Extended Finite Element/Level Set Method to Study Surface effects on the Mechanical Behavior and Properties of Nanoma- terials. International Journal of Numerical Methods in Engineering, 84(12),1466-1489.  Link. PDF

8. Vernerey, F. J.∗ and Moran, B. (2010). A nonlinear, large deformation finite element beam/column formulation for the study of the human spine: investigation of the role of muscle in spine stability. Journal of Engineering Mechanics, 136(11), 1319-1328.  Link. PDF

2009 & before

7. Vernerey, F. J.∗, Liu, W. K., Moran, B., Olson, G. B. (2009). Multi-length Scale Micromorphic Process Zone Model. Computational Mechanics, 44, 433-445.  Link. PDF

6. Vernerey, F. J.∗, Liu, W. K., Moran, B., and Olson, G. B. (2008). A Micromorphic Model for the Multiple Scale Failure of Heterogeneous Materials. Journal of the Mechanics and Physics of Solids, 56(4), 1320-1347  Link. PDF

5. Vernerey, F. J.∗, Liu, W. K., and Moran, B. (2007). Multi-Scale Micromorphic Theory for Hierarchical Materials. Journal of the Mechanics and Physics of Solids, 55(12), 2603-2651.  Link. PDF

4. Vernerey, F. J.∗, McVeigh, C., Liu, W. K., Moran, B., Tewari, D., Parks, D., and Olson, G. (2006). The 3D Computational Modeling of Shear Dominated Ductile Failure of Steel. JOM, The Journal of The Minerals, Metals and Materials Society, 58(12), 45-51.  Link. PDF

3. McVeigh, C., Vernerey, F. J., Liu, W. K., Moran, B., and Olson, G. B. (2006). An Interactive Microvoid Shear Localization Mechanism in High Strength Steels. Journal of the Mechanics and Physics of Solids, 55(2),225-244.  Link. PDF

2. McVeigh, C., Vernerey, F. J., Liu, W. K., and Brinson, C. (2006). Multiresolution Analysis for Material Design. Computer Methods in Applied Mechanics and Engineering, 195(37-40), 5053-5076.   Link. PDF

1.  Hao, S., Liu, W. K., Moran, B., Vernerey, F. J., and Olson, G. B. (2004). Multi-scale Constitutive Model and Computational Framework for the Design of Ultra-high Strength”. Computer Methods in Applied Mechanics and Engineering, 193, 1865.  Link. PDF