Abstract
Translating the insight gained through numerical simulations of microscopic models into information and predictions useful for engineering applications is a formidable task for complex and amorphous materials. Here we propose a strategy that builds on distinct dedicated approaches at different length scales and transfers the relevant information across them, to bridge from an atomistic description to a mesoscale mechanical model. We provide an overview of the fundamental concepts that underlie such strategy and two examples for engineering-relevant materials such as clays and cement hydrates.
References
Agoritsas E, Martens K (2017) Non-trivial rheological exponents in sheared yield stress fluids. Soft Matter 13(26):4653–4660
Agoritsas E, Bertin E, Martens K, Barrat JL (2015) On the relevance of disorder in athermal amorphous materials under shear. Eur Phys J E 38(7):71
Allen MP, Tildesley DJ (1987) Computer simulations of liquids. Oxford University Press, Clarendon
Argon A, Kuo H (1979) Plastic flow in a disordered bubble raft (an analog of a metallic glass). Mater Sci Eng 39(1):101–109
Attard P (2007) Electrolytes and the electric double layer. Wiley, pp 1–159. https://doi.org/10.1002/9780470141519.ch1
Baret JC, Vandembroucq D, Roux S (2002) Extremal model for amorphous media plasticity. Phys Rev Lett 89(19):195506
Bocquet L, Colin A, Ajdari A (2009) Kinetic theory of plastic flow in soft glassy materials. Phys Rev Lett 103(3):036001
Bonnaud PA, Labbez C, Miura R, Suzuki A, Miyamoto N, Hatakeyama N, Miyamoto A, Van Vliet KJ (2016) Interaction grand potential between calcium-silicate-hydrate nanoparticles at the molecular level. Nanoscale 8:4160–4172. https://doi.org/10.1039/C5NR08142D
Bulatov V, Argon A (1994a) A stochastic model for continuum elasto-plastic behavior. I. Numerical approach and strain localization. Model Simul Mater Sci Eng 2(2):167
Bulatov V, Argon A (1994b) A stochastic model for continuum elasto-plastic behavior. III. Plasticity in ordered versus disordered solids. Model Simul Mater Sci Eng 2(2):203
Carrier B (2013) PhD thesis. Ecole Nationale des Ponts et Chaussées, Marne-la-Vallée, France
Colombo J, Del Gado E (2014) Self-assembly and cooperative dynamics of a model colloidal gel network. Soft Matter 10(22):4003–4015
Colombo J, Widmer-Cooper A, Del Gado E (2013) Microscopic picture of cooperative processes in restructuring gel networks. Phys Rev Lett 110(19):198301
de Candia A, Del Gado E, Fierro A, Sator N, Tarzia M, Coniglio A (2006) Columnar and lamellar phases in attractive colloidal systems. Phys Rev E 74:010403. https://doi.org/10.1103/PhysRevE.74.010403
Del Gado E, Ioannidou K, Masoero E, Baronnet A, Pellenq RM, Ulm FJ, Yip S (2014) A soft matter in construction – statistical physics approach to formation and mechanics of c–s–h gels in cement. Eur Phys J-Spec Top 223(11):2285–2295. https://doi.org/10.1140/epjst/e2014-02264-1
Doi M (2013) Soft matter physics. Oxford University Press, Oxford
Dormieux L, Kondo D, Ulm FJ (2006) Microporomechanics. Wiley, Chichester
Ebrahimi D, Pellenq RJM, Whittle AJ (2012) Nanoscale elastic properties of montmorillonite upon water adsorption. Langmuir 28(49):16855–16863. https://doi.org/10.1021/la302997g
Ebrahimi D, Whittle AJ, Pellenq RJM (2014) Mesoscale properties of clay aggregates from potential of mean force representation of interactions between nanoplatelets. J Chem Phys 140(15):154309
Eshelby JD (1957) The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc R Soc Lond A 241(1226):376–396
Falk ML, Langer JS (1998) Dynamics of viscoplastic deformation in amorphous solids. Phys Rev E 57(6):7192
Frenkel D, Smit B (2001) Understanding molecular simulation: from algorithms to applications. Access Online via Elsevier, London
Garrault S, Finot E, Lesniewska E, Nonat A (2005) Study of C-S-H growth on C3S surface during its early hydration. Mater Struct 38(4):435–442. https://doi.org/10.1007/BF02482139
Hébraud P, Lequeux F (1998) Mode-coupling theory for the pasty rheology of soft glassy materials. Phys Rev Lett 81(14):2934
Homer ER, Schuh CA (2009) Mesoscale modeling of amorphous metals by shear transformation zone dynamics. Acta Materialia 57(9):2823–2833
Ioannidou K, Pellenq RJM, Del Gado E (2014) Controlling local packing and growth in calcium–silicate–hydrate gels. Soft Matter 10:1121–1133
Ioannidou K, Kanduc M, Li L, Frenkel D, Dobnikar J, Del Gado E (2016a) The crucial effect of early-stage gelation on the mechanical properties of cement hydrates. Nat Commun 7:12106
Ioannidou K, Krakowiak KJ, Bauchy M, Hoover CG, Masoero E, Yip S, Ulm FJ, Levitz P, Pellenq RJM, Del Gado E (2016b) Mesoscale texture of cement hydrates. Proc Natl Acad Sci 113(8):2029–2034. https://doi.org/10.1073/pnas.1520487113
Ioannidou K, Carrier B, Vandamme M, Pellenq R (2017a) The potential of mean force concept for bridging (length and time) scales in the modeling of complex porous materials. In: EPJ web of conferences, EDP sciences, vol 140, p 01009
Ioannidou K, Del Gado E, Ulm FJ, Pellenq RJM (2017b) Inhomogeneity in cement hydrates: linking local packing to local pressure. J Nanomech Micromech 7(2):04017003
Israelachvili JN (1992) Intermolecular and surface forces: with applications to colloidal and biological systems (Colloid Science), 2nd edn. Academic. http://www.amazon.com/exec/obidos/redirect?tag=citeulike07-20&path=ASIN/0123751810
Kumar S, Rosenberg JM, Bouzida D, Swendsen RH, Kollman PA (1992) The weighted histogram analysis method for free-energy calculations on biomolecules. I. The method. J Comput Chem 13(8):1011–1021
Laubie H, Radjai F, Pellenq R, Ulm FJ (2017) Stress transmission and failure in disordered porous media. Phys Rev Lett 119:075501. https://link.aps.org/doi/10.1103/PhysRevLett.119.075501
Lerner E, Düring G, Wyart M (2012) A unified framework for non-brownian suspension flows and soft amorphous solids. Proc Natl Acad Sci 109(13):4798–4803
Lesko S, Lesniewska E, Nonat A, Mutin JC, Goudonnet JP (2001) Investigation by atomic force microscopy of forces at the origin of cement cohesion. Ultramicroscopy 86(1–2):11–21. http://www.ncbi.nlm.nih.gov/pubmed/11215612
Lin J, Lerner E, Rosso A, Wyart M (2014) Scaling description of the yielding transition in soft amorphous solids at zero temperature. Proc Natl Acad Sci 111(40):14382–14387
Lin J, Wyart M (2016) Mean-field description of plastic flow in amorphous solids. Phys Rev X 6(1):011005
Liu C, Martens K, Barrat JL (2018) Mean-field scenario for the athermal creep dynamics of yield-stress fluids. Phys Rev Lett. APS 120(2):028004
Martens K, Bocquet L, Barrat JL (2011) Connecting Diffusion and Dynamical Heterogeneities in Actively Deformed Amorphous Systems. Phys Rev Lett 106(15):156001. http://link.aps.org/doi/10.1103/PhysRevLett.106.156001
Martens K, Bocquet L, Barrat JL (2012) Spontaneous formation of permanent shear bands in a mesoscopic model of flowing disordered matter. Soft Matter 8(15):4197–4205
Masoero E, Del Gado E, Pellenq RJM, Ulm FJ, Yip S (2012) Nanostructure and nanomechanics of cement: polydisperse colloidal packing. Phys Rev Lett 109(15):155503
Masoero E, Del Gado E, Pellenq RJM, Yip S, Ulm FJ (2014) Nano-scale mechanics of colloidal C–S–H gels. Soft Matter 10:491–499. https://doi.org/10.1039/C3SM51815A
Merabia S, Detcheverry F (2016) Thermally activated creep and fluidization in flowing disordered materials. EPL (Europhysics Letters) 116(4):46003
Morriss GP, Evans DJ (2013) Statistical mechanics of nonequilbrium liquids. ANU Press, Cambridge
Mosayebi M, Ilg P, Widmer-Cooper A, Del Gado E (2014) Soft modes and nonaffine rearrangements in the inherent structures of supercooled liquids. Phys Rev Lett 112(10):105503
Nicolas A, Ferrero EE, Martens K, Barrat JL (2018) Deformation and flow of amorphous solids: a review of mesoscale elastoplastic models. Rev Mod Phys 90:045001
Olivier J, Renardy M (2011) Glass transition seen through asymptotic expansions. SIAM J Appl Math 71(4):1144–1167
Pellenq RJM, Van Damme H (2004) Why does concrete set? The nature of cohesion forces in hardened cement-based materials. MRS Bull 29(5):319–323
Pellenq RJM, Caillol JM, Delville A (1997) Electrostatic attraction between two charged surfaces: a (n,v,t) monte carlo simulation. J Phys Chem B 101(42):8584–8594. https://doi.org/10.1021/jp971273s
Pellenq RJM, Lequeux N, van Damme H (2008) Engineering the bonding scheme in C-S-H: the iono-covalent framework. Cem Concr Res 38(2):159–174. https://doi.org/10.1016/j.cemconres.2007.09.026; http://www.sciencedirect.com/science/article/pii/S0008884607002372
Pellenq RJM, Kushima A, Shahsavari R, Van Vliet KJ, Buehler MJ, Yip S, Ulm FJ (2009) A realistic molecular model of cement hydrates. Proc Nat Acad Sci USA 106(38):16102–16107. https://doi.org/10.1073/pnas.0902180106; http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2739865&tool=pmcentrez&rendertype=abstract
Puosi F, Rottler J, Barrat JL (2014) Time-dependent elastic response to a local shear transformation in amorphous solids. Phys Rev E 89(4):042302
Rodney D, Tanguy A, Vandembroucq D (2011) Modeling the mechanics of amorphous solids at different length scale and time scale. Model Simul Mater Sci Eng 19(8):083001
Schall P, Weitz DA, Spaepen F (2007) Structural rearrangements that govern flow in colloidal glasses. Science 318(5858):1895–1899
Sollich P, Lequeux F, Hébraud P, Cates ME (1997) Rheology of soft glassy materials. Phys Rev Lett 78(10):2020
Su C, Anand L (2006) Plane strain indentation of a zr-based metallic glass: experiments and numerical simulation. Acta Materialia 54(1):179–189
Tanguy A, Leonforte F, Barrat JL (2006) Plastic response of a 2d lennard-jones amorphous solid: detailed analysis of the local rearrangements at very slow strain rate. Eur Phys J E 20(3):355–364
Talamali M, Petäjä V, Vandembroucq D, Roux S (2011) Avalanches, precursors, and finite-size fluctuations in a mesoscopic model of amorphous plasticity. Phys Rev E 84:016115
Tsamados M, Tanguy A, Goldenberg C, Barrat JL (2009) Local elasticity map and plasticity in a model lennard-jones glass. Phys Rev E 80(2):026112
Vasisht VV, Dutta SK, Del Gado E, Blair DL (2018) Rate dependence of elementary rearrangements and spatiotemporal correlations in the 3d flow of soft solids. Phys Rev Lett 120(1):018001
Widmer-Cooper A, Harrowell P (2006) Predicting the long-time dynamic heterogeneity in a supercooled liquid on the basis of short-time heterogeneities. Phys Rev Lett 96:185701
Widmer-Cooper A, Harrowell P (2007) On the study of collective dynamics in supercooled liquids through the statistics of the isoconfigurational ensemble. J Chem Phys 126(15):154503
Widmer-Cooper A, Perry H, Harrowell P, Reichman DR (2008) Irreversible reorganization in a supercooled liquid originates from localized soft modes. Nat Phys 4:711–715
Widmer-Cooper A, Perry H, Harrowell P, Reichman DR (2009) Localized soft modes and the supercooled liquid’s irreversible passage through its configuration space. J Chem Phys 131(19):194508
Zhuang Y, Zhang K, Charbonneau P (2016) Equilibrium phase behavior of a continuous-space microphase former. Phys Rev Lett 116:098301. https://link.aps.org/doi/10.1103/PhysRevLett.116.098301
Acknowledgements
EDG and KM acknowledge the support from the National Science Foundation under Grant No. NSF PHY-1748958. RP thanks for support A∗MIDEX, the Aix-Marseille University Idex Foundation, the CSHub@MIT (thanks to the Portland Cement Association (PCA) and the Ready Mixed Concrete (RMC) Research & Education Foundation), and the National Science Foundation under Grant No. 1562066.
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Section Editor information
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this entry
Cite this entry
Del Gado, E., Martens, K., Pellenq, R.J.M. (2020). From Microscopic Insight to Constitutive Models: Bridging Length Scales in Soft and Hard Materials. In: Andreoni, W., Yip, S. (eds) Handbook of Materials Modeling. Springer, Cham. https://doi.org/10.1007/978-3-319-50257-1_130-2
Download citation
DOI: https://doi.org/10.1007/978-3-319-50257-1_130-2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-50257-1
Online ISBN: 978-3-319-50257-1
eBook Packages: Springer Reference Physics and AstronomyReference Module Physical and Materials ScienceReference Module Chemistry, Materials and Physics
Publish with us
Chapter history
-
Latest
From Microscopic Insight to Constitutive Models: Bridging Length Scales in Soft and Hard Materials- Published:
- 28 December 2019
DOI: https://doi.org/10.1007/978-3-319-50257-1_130-2
-
Original
From Microscopic Insight to Constitutive Models: Bridging Length Scales in Soft and Hard Materials- Published:
- 11 August 2018
DOI: https://doi.org/10.1007/978-3-319-50257-1_130-1