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From Microscopic Insight to Constitutive Models: Bridging Length Scales in Soft and Hard Materials

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Handbook of Materials Modeling

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.

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References

  • Agoritsas E, Martens K (2017) Non-trivial rheological exponents in sheared yield stress fluids. Soft Matter 13(26):4653–4660

    Article  ADS  Google Scholar 

  • 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

    Article  Google Scholar 

  • Allen MP, Tildesley DJ (1987) Computer simulations of liquids. Oxford University Press, Clarendon

    MATH  Google Scholar 

  • 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

    Article  Google Scholar 

  • Attard P (2007) Electrolytes and the electric double layer. Wiley, pp 1–159. https://doi.org/10.1002/9780470141519.ch1

    Google Scholar 

  • Baret JC, Vandembroucq D, Roux S (2002) Extremal model for amorphous media plasticity. Phys Rev Lett 89(19):195506

    Article  ADS  Google Scholar 

  • Bocquet L, Colin A, Ajdari A (2009) Kinetic theory of plastic flow in soft glassy materials. Phys Rev Lett 103(3):036001

    Article  ADS  Google Scholar 

  • 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

    Article  ADS  Google Scholar 

  • 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

    Article  ADS  Google Scholar 

  • 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

    Article  ADS  Google Scholar 

  • Carrier B (2013) PhD thesis. Ecole Nationale des Ponts et Chaussées, Marne-la-Vallée, France

    Google Scholar 

  • Colombo J, Del Gado E (2014) Self-assembly and cooperative dynamics of a model colloidal gel network. Soft Matter 10(22):4003–4015

    Article  ADS  Google Scholar 

  • Colombo J, Widmer-Cooper A, Del Gado E (2013) Microscopic picture of cooperative processes in restructuring gel networks. Phys Rev Lett 110(19):198301

    Article  ADS  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Doi M (2013) Soft matter physics. Oxford University Press, Oxford

    Book  MATH  Google Scholar 

  • Dormieux L, Kondo D, Ulm FJ (2006) Microporomechanics. Wiley, Chichester

    Book  MATH  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  ADS  Google Scholar 

  • 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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Falk ML, Langer JS (1998) Dynamics of viscoplastic deformation in amorphous solids. Phys Rev E 57(6):7192

    Article  ADS  Google Scholar 

  • Frenkel D, Smit B (2001) Understanding molecular simulation: from algorithms to applications. Access Online via Elsevier, London

    MATH  Google Scholar 

  • 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

    Article  Google Scholar 

  • Hébraud P, Lequeux F (1998) Mode-coupling theory for the pasty rheology of soft glassy materials. Phys Rev Lett 81(14):2934

    Article  ADS  Google Scholar 

  • Homer ER, Schuh CA (2009) Mesoscale modeling of amorphous metals by shear transformation zone dynamics. Acta Materialia 57(9):2823–2833

    Article  Google Scholar 

  • Ioannidou K, Pellenq RJM, Del Gado E (2014) Controlling local packing and growth in calcium–silicate–hydrate gels. Soft Matter 10:1121–1133

    Article  ADS  Google Scholar 

  • 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

    Article  ADS  Google Scholar 

  • 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

    Article  ADS  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  ADS  Google Scholar 

  • 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

    Article  ADS  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  ADS  Google Scholar 

  • Lin J, Wyart M (2016) Mean-field description of plastic flow in amorphous solids. Phys Rev X 6(1):011005

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  ADS  Google Scholar 

  • 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

    Article  ADS  Google Scholar 

  • 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

    Article  ADS  Google Scholar 

  • 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

    Article  ADS  Google Scholar 

  • Merabia S, Detcheverry F (2016) Thermally activated creep and fluidization in flowing disordered materials. EPL (Europhysics Letters) 116(4):46003

    Article  ADS  Google Scholar 

  • Morriss GP, Evans DJ (2013) Statistical mechanics of nonequilbrium liquids. ANU Press, Cambridge

    Google Scholar 

  • 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

    Article  ADS  Google Scholar 

  • 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

    Article  ADS  Google Scholar 

  • Olivier J, Renardy M (2011) Glass transition seen through asymptotic expansions. SIAM J Appl Math 71(4):1144–1167

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  ADS  Google Scholar 

  • 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

    Article  ADS  Google Scholar 

  • 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

    Article  ADS  Google Scholar 

  • Schall P, Weitz DA, Spaepen F (2007) Structural rearrangements that govern flow in colloidal glasses. Science 318(5858):1895–1899

    Article  ADS  Google Scholar 

  • Sollich P, Lequeux F, Hébraud P, Cates ME (1997) Rheology of soft glassy materials. Phys Rev Lett 78(10):2020

    Article  ADS  Google Scholar 

  • Su C, Anand L (2006) Plane strain indentation of a zr-based metallic glass: experiments and numerical simulation. Acta Materialia 54(1):179–189

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  ADS  Google Scholar 

  • 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

    Article  ADS  Google Scholar 

  • 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

    Article  ADS  Google Scholar 

  • 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

    Article  ADS  Google Scholar 

  • 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

    Article  ADS  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  ADS  Google Scholar 

  • 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

    Article  ADS  Google Scholar 

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Acknowledgements

EDG and KM acknowledge the support from the National Science Foundation under Grant No. NSF PHY-1748958. RP thanks for support AMIDEX, 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.

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Correspondence to Kirsten Martens or Roland J. -M. Pellenq .

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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

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  • DOI: https://doi.org/10.1007/978-3-319-50257-1_130-2

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  • Online ISBN: 978-3-319-50257-1

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Chapter history

  1. 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

  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