The mechanical behavior of monolithic cementitious materials is known to be significantly affected by their granular nature. This paper describes an approach to incorporate the effects of granularity for cementitious material based upon the granular micromechanics paradigm and thermomechanics. As a result, macro-scale constitutive equations that utilize grain-scale force–displacement relationships have been derived. In this derivation, the connections between grain-scale free energy and dissipation and the macro-scale behavior are established based upon the thermomechanics framework. Expression for Cauchy stress tensor is obtained in terms of the free energy of grain-pair interactions. In addition, the free energy and dissipation potential of grain-pair interactions are used to find a grain-scale Clausius–Duhem type inequality. Thus, inter-granular constitutive equations are obtained in the usual manner with the exception that these are based upon simple physically motivated free energy and dissipation functions formulated in terms of grain-pair interactions. The derived model is used to simulate a wide variety of experimental tests that have been reported in the literature to evaluate material response under multi-axial conditions. The results are analyzed with the aim to reveal the connections between grain-scale mechanisms and the macro-scale behavior.
GreeneMSLiYChenW, et al. The archetype-genome exemplar in molecular dynamics and continuum mechanics. Comput Mech2013; 53(4): 687–737.
11.
SolarMMeyerHGauthierC, et al. Mechanical behavior of linear amorphous polymers: comparison between molecular dynamics and finite-element simulations. Phys Rev E2012; 85: 1–14.
12.
NavierCL. Sur les lois de l’equilibre et du mouvement des corps solides elastiques. Memoire de l’Academie Royale de Sciences1827; 7: 375–393.
13.
CauchyA-L. Sur l’equilibre et le mouvement d’un systeme de points materiels sollicites par des forces d’attraction ou de repulsion mutuelle. Excercises de Mathematiques1826–1830; 3: 188–212.
14.
dell’IsolaFAndreausUPlacidiL. At the origins and in the vanguard of peri-dynamics, non-local and higher gradient continuum mechanics. An underestimated and still topical contribution of Gabrio Piola. Mech Math Solid2014; 20: 887–928.
15.
AuffrayNdell’IsolaF.EremeyevV, et al. Analytical continuum mechanics á la Hamilton-Piola: least action principle for second gradient continua and capillary fluids. Math Mech Solid Epub ahead of print 28 August 2013. DOI:10.1177/1081286513497616
16.
ChangCSMisraA. Theoretical and experimental-study of regular packings of granules. J Eng Mech-ASCE1989; 115: 704–720.
17.
ChangCSMisraA. Packing structure and mechanical-properties of granulates. J Eng Mech-ASCE1990; 116: 1077–1093.
18.
DigbyPJ. The effective elastic moduli of porous granular rocks. J Appl Mech1981; 48: 803–808.
19.
WaltonK. The effective elastic moduli of a random packing of spheres. J MechPhysSolids1987; 35: 213–226.
20.
DeresiewiczH. Stress-strain relations for a simple model of a granular medium. J Appl Mech1958; 25: 402–406.
21.
DuffyJMindlinRD. Stress-strain relations of a granular medium. J Appl Mech1957; 24: 585–593.
22.
MisraAYangY. Micromechanical model for cohesive materials based upon pseudo-granular structure. Int J Solids Struct2010; 47: 2970–2981.
23.
MisraASinghV. Micromechanical model for viscoelastic materials undergoing damage. Continuum Mech Thermodyn2013; 25: 343–358.
24.
ZieglerH. An introduction to thermomechanics. 2nd ed.Amsterdam: North-Holland, 1983.
25.
MauginGA. The thermomechanics of plasticity and fracture. Cambridge: Cambridge University Press, 1992.
26.
PlacidiLHutterK. Thermodynamics of polycrystalline materials treated by the theory of mixtures with continuous diversity. Continuum Mech Thermodyn2006; 17: 409–451.
27.
PuzrinAMRabaiottiC. A thermomechanical framework for non-linear hyperviscoelastic materials. J Rheol2010; 54: 619–642.
28.
dell’IsolaFSeppecherPMadeoA. How contact interactions may depend on the shape of Cauchy cuts in Nth gradient continua: approach “à la D’Alembert”. Zeitschrift für angewandte Mathematik und Physik2012; 63: 1119–1141.
PlacidiL. A variational approach for a nonlinear 1-dimensional second gradient continuum damage model. Continuum Mech Thermodyn2015; 27: 623–638.
31.
SciarraGdell’IsolaFCoussyO. Second gradient poromechanics. Int J Solids Struct2007; 44: 6607–6629.
32.
AndreausUGiorgioILekszyckiT. A 2-D continuum model of a mixture of bone tissue and bio-resorbable material for simulating mass density redistribution under load slowly variable in time. Zamm-Z Angew Math Me2014; 94: 978–1000.
33.
PlacidiL. A variational approach for a nonlinear one-dimensional damage-elasto-plastic second-gradient continuum model. Continuum Mech Thermodyn2016; 28: 119–137.
34.
HoulsbyGTPuzrinAM. Principles of hyperplasticity: an approach to plasticity theory based on thermodynamic principles. London: Springer, 2006.
35.
PlacidiLGreveRSeddikH, et al. Continuum-mechanical, anisotropic flow model for polar ice masses, based on an anisotropic flow enhancement factor. Continuum Mech Thermodyn2010; 22: 221–237.
36.
MisraAChangCS. Effective elastic moduli of heterogeneous granular solids. Int J Solids Struct1993; 30: 2547–2566.
37.
Abu Al-RubRKVoyiadjisGZ. On the coupling of anisotropic damage and plasticity models for ductile materials. Int J Solids Struct2003; 40: 2611–2643.
38.
EinavIHoulsbyGTNguyenGD. Coupled damage and plasticity models derived from energy and dissipation potentials. Int J Solids Struct2007; 44: 2487–2508.
39.
VoyiadjisGZAbu Al-RubRKPalazottoAN. Thermodynamic framework for coupling of non-local viscoplasticity and non-local anisotropic viscodamage for dynamic localization problems using gradient theory. Int J Plast2004; 20: 981–1038.
40.
CarcaterraA. Ensemble energy average and energy flow relationships for nonstationary vibrating systems. J Sound Vib2005; 288: 751–790.
41.
CarcaterraAAkayA. Theoretical foundations of apparent-damping phenomena and nearly irreversible energy exchange in linear conservative systems. J Acoust Soc Am2007; 121: 1971–1982.
42.
CullaASestieriACarcaterraA. Energy flow uncertainties in vibrating systems: definition of a statistical confidence factor. Mech Syst Signal Process2003; 17: 635–663.
43.
RinaldiAKrajcinovicDPeraltaP, et al. Lattice models of polycrystalline micro structures: a quantitative approach. Mech Mater2008; 40: 17–36.
44.
RinaldiALaiYC. Statistical damage theory of 2D lattices: energetics and physical foundations of damage parameter. Int J Plast2007; 23: 1796–1825.
45.
RinaldiA. Bottom-up modeling of damage in heterogeneous quasi-brittle solids. Continuum Mech Thermodyn2013; 25: 359–373.
46.
ScerratoDGiorgioIMadeoA, et al. A simple non-linear model for internal friction in modified concrete. Int J Eng Sci2014; 80: 136–152.
MisraAHuangSP. Micromechanical stress-displacement model for rough interfaces: effect of asperity contact orientation on closure and shear behavior. Int J Solids Struct2012; 49: 111–120.
49.
ChangCSMisraAAcheampongK. Elastoplastic deformation for particulates with frictional contacts. J Eng Mech-ASCE1992; 118: 1692–1707.
50.
MagoariecHDanescuACambouB. Nonlocal orientational distribution of contact forces in granular samples containing elongated particles. Acta Geotech2008; 3: 49–60.
51.
ClausiusR XVI. On a mechanical theorem applicable to heat. London Edinburgh Dublin Philos Mag J Sci1870; 40: 122–127.
52.
SwensonRJ. Comments on virial theorems for bounded systems. Am J Phys1983; 51: 940–942.
53.
IrvingJHKirkwoodJG. The statistical mechanical theory of transport processes. 4. The equations of hydrodynamics. J Chem Phys. 1950; 18: 817–829.
54.
TsaiDH. Virial theorem and stress calculation in molecular-dynamics. J Chem Phys. 1979; 70: 1375–1382.
55.
SubramaniyanAKSunCT. Continuum interpretation of virial stress in molecular simulations. Int J Solids Struct2008; 45: 4340–4346.
56.
ZhouM. A new look at the atomic level virial stress: on continuum-molecular system equivalence. Proc R Soc London Ser A2003; 459: 2347–2392.
57.
BazantZPXiangYYAdleyMD, et al. Microplane model for concrete. 2. Data delocalization and verification. J Eng Mech-ASCE1996; 122: 255–262.
58.
Van MierJG. Fracture processes of concrete. Boca Raton, FL: CRC Press, 1996.
59.
ContrafattoLCuomoA. A globally convergent numerical algorithm for damaging elasto-plasti city based on the multiplier method. Int J Numer Methods Eng2005; 63: 1089–1125.
60.
BažantZPCedolinL. Stability of structures: elastic, inelastic, fracture and damage theories. Singapore: World Scientific, 2010.
61.
HillR. A general theory of uniqueness and stability in elastic-plastic solids. J Mech Phys Solids1958; 6: 236–249.
62.
RudnickiJWRiceJ. Conditions for the localization of deformation in pressure-sensitive dilatant materials. J Mech Phys Solids1975; 23: 371–394.
63.
SulemJVardoulakisI. Bifurcation analysis in geomechanics. London: Taylor & Francis, 1995.
64.
AltenbachHEremeyevVALebedevLP, et al. Acceleration waves and ellipticity in thermoelastic micropolar media. Arch Appl Mech2010; 80: 217–227.
YeremeyevVAFreidinABSharipovaLL. The stability of the equilibrium of two-phase elastic solids. Pmm J Appl Math Mech2007; 71: 61–84.
67.
dell’isolaFRomanoA. On the derivation of thermomechanical balance-equations for continuous systems with a nonmaterial interface. Int J Eng Sci1987; 25: 1459–1468.
68.
dell’isolaFRomanoA. A phenomenological approach to phase-transition in classical field-theory. Int J Eng Sci1987; 25: 1469–1475.
69.
MadeoAdell’IsolaFDarveF. A continuum model for deformable, second gradient porous media partially saturated with compressible fluids. J Mech Phys Solids2013; 61: 2196–2211.
70.
YangYMisraA. Micromechanics based second gradient continuum theory for shear band modeling in cohesive granular materials following damage elasticity. Int J Solids Struct2012; 49: 2500–2514.
71.
LuongoA. Mode localization in dynamics and buckling of linear imperfect continuous structures. Nonlinear Dynam2001; 25: 133–156.
72.
LuongoAPaoloneAPiccardoG. Postcritical behavior of cables undergoing two simultaneous galloping modes. Meccanica1998; 33: 229–242.
73.
LuongoAZulliDPiccardoG. A linear curved-beam model for the analysis of galloping in suspended cables. J Mech Mater Struct2007; 2: 675–694.
MehrabadiMMCowinSC. Eigentensors of linear anisotropic elastic-materials. Q J Mech Appl Math1990; 43: 15–41.
76.
LuX. Uniaxial and triaxial behavior of high strength concrete with and without steel fibers. Newark, NJ: New Jersey Institute of Technology, Department of Civil and Environmental Engineering, 2005.
77.
BiarezJHicherPY. Mechanisms of soil deformation. In: HicherP-YShaoJ-F (eds) Constitutive modeling of soils and rocks. Hoboken, NJ: Wiley, pp. 31–76.
78.
HanJ. Experimental study on the mechanical behavior of a stiff clay subjected to monotonic and cyclic loading. Nantes, France: Ecole Centrale de Nantes, 2014.
79.
CuomoMContrafattoLGrecoL. A variational model based on isogeometric interpolation for the analysis of cracked bodies. Int J Eng Sci2014; 80: 173–188.
80.
BilottaAFormicaGTurcoE. Performance of a high-continuity finite element in three-dimensional elasticity. Int J Numer Meth Bio2010; 26: 1155–1175.
81.
CazzaniAMalagùMTurcoE. Isogeometric analysis of plane-curved beams. Math Mech Solid2016; 21: 562–577.
82.
YangYMisraA. Higher-order stress-strain theory for damage modeling implemented in an element-free Galerkin formulation. Comput Model Eng Sci2010; 64: 1–36.
83.
ChabocheJL. A review of some plasticity and viscoplasticity constitutive theories. Int J Plast2008; 24: 1642–1693.
84.
HorstemeyerMFBammannDJ. Historical review of internal state variable theory for inelasticity. Int J Plast2010; 26: 1310–1334.
85.
AltenbachHEremeyevV. Strain rate tensors and constitutive equations of inelastic micropolar materials. Int J Plast2014; 63: 3–17.
86.
ChallamelNLanosCCasandjianC. Creep damage modelling for quasi-brittle materials. Eur J Mech A Solid2005; 24: 593–613.
87.
ChallamelNLanosCCasandjianC. Strain-based anisotropic damage modelling and unilateral effects. Int J Mech Sci2005; 47: 459–473.
88.
ContrafattoLCuomoM. A new thermodynamically consistent continuum model for hardening plasticity coupled with damage. Int J Solids Struct2002; 39: 6241–6271.
89.
ContrafattoLCuomoM. A framework of elastic-plastic damaging model for concrete under multiaxial stress states. Int J Plast2006; 22: 2272–2300.
