In this paper, a general numerical homogenisation scheme coupled with an efficient modelling strategy for predicting the effective thermoelastic properties of cork-based agglomerates is presented. In order to generate a realistic representation of the geometry and distribution of particles for the representative volume element of the agglomerate at the mesoscopic scale, a general parametric model based on the Voronoi’s tesselation has been developed. However, the classical algorithm for Voronoi’s tesselation has been enhanced by adding a full parametrisation of the representative volume element. The grains composing the representative volume element are generated by considering the full set of design variables involved at this scale, i.e. the material properties of the constitutive phases (grains and matrix) and the main geometric parameters related to the grain (volume fraction, average diameter, geometric and material orientations). Numerical results show that the macroscopic effective thermoelastic properties of the cork-based agglomerate are strongly affected by the previous parameters in perfect agreement with experimental results available in literature.
PereiraH.The rationale behind cork properties: a review of structure and chemistry. BioResources2015;
10: 1–23.
2.
PereiraH.Cork: biology, production and uses. Amsterdam: Elsevier.
3.
PereiraH.Chemical composition and variability of cork from Quercus suber L. Wood Scitechnol1988;
22: 211–218.
4.
ArteiroAJC.State-of-the-art: sandwich structures applications in impact situations. Research Initiation Scholarship Report, Technical Report. Porto: Department of Mechanical Engineering, Faculty of Engineering, University of Porto, 2010.
5.
SilvaSPSabinoMAFernandesEM, et al.
Cork: properties, capabilities and applications. Int Mater Rev2008;
53: 256–256.
6.
GibsonLJEasterlingKEAshbyMF.The structure and mechanics of cork. Proc Roy Soc A Math Phys Eng Sci1981;
377: 99–117.
7.
ManoJF.Creep-recovery behaviour of cork. Mater Lett2007;
61: 2473–2477.
8.
OliveiraVRosaMEPereiraH.Variability of the compression properties of cork. Wood Sci Technol2014;
48: 937–948.
9.
FortesMAEmília RosaM.Boletim Do Instituto Dos Produtos Florestais Cortiça. Densidade da cortiça: factores que a influenciam1988;
593: 65–68.
10.
GilL.Cortiça: produção, tecnologia e aplicação.
Lisbon, 1998.
11.
FortesMANogueiraMT. The poison effect in cork. Mater Sci Eng1989;
A122: 272–232.
12.
MedeirosH.Boletim da Junta Nacional de Cortiça.
APCOR, Associacao Portuguesa da Cortica, 1945, pp. 165–170.
13.
JardinRFernandesFPereiraA, et al.
Static and dynamic mechanical response of different cork agglomerates. Mater Des2015;
68: 121–126.
14.
KimS.A study on cork-based plastic composite material.
Cambridge:
Massachusetts Institute of Technology, 2011.
15.
MoreiraRASDe MeloFJQDias RodriguesJF.Static and dynamic characterization of composition cork for sandwich beam cores. J Mater Sci2010;
45: 3350–3366.
16.
GilL.Cork composites: a review.Materials2009;
2: 776–789.
17.
AnjosOPereiraHRosaME.Effect of quality, porosity and density on the compression properties of cork. Holz Roh Werkst2008;
66: 295–301.
18.
AnjosOPereiraHRosaME.Tensile properties of cork in the tangential direction: variation with quality, porosity, density and radial position in the cork plank. Mater Des2010;
31: 2085–2090.
19.
AnjosOPereiraHRosaME.Characterization of radial bending properties of cork. Eur J Wood Prod2011;
69: 557–563.
20.
AnjosORodriguesCMoraisJ, et al.
Effect of density on the compression behaviour of cork. Mater Des2014;
53: 1089–1096.
21.
SantosPTPintoSMarquesPA, et al.
Agglomerated cork: a way to tailor its mechanical properties. Compos Struct2017;
178: 277–287.
22.
SantosTAmaralJCostaV, et al.
Thermal conductivity of agglomerate cork.Mater Res Proceed2017;
3: 1–10.
23.
CastroOSilvaJMDevezasT, et al.
Cork agglomerates as an ideal core material in lightweight structures. Mater Des2010;
31: 425–432.
24.
RiedingerRHabarMOelhafenP, et al.
About the Delaunay-Voronoi tesselation. J Comput Phys1988;
74: 61–72.
CatapanoAJumelJ.A numerical approach for determining the effective elastic symmetries of particulate-polymer composites. Compos Part B Eng2015;
78: 227–243.
27.
MontemurroMCatapanoADoroszewskiD.A multi-scale approach for the simultaneous shape and material optimisation of sandwich panels with cellular core. Compos Part B Eng2016;
91: 458–472.
28.
GentieuTCatapanoAJumelJ, et al. Computational modelling of particulate-reinforced materials up to high volume fractions: linear elastic homogenisation. Proc Inst Mech Eng Part L J Mater Des Appl.2019; 233(6): 1101–1116.
29.
CappelliLMontemurroMDauF, et al.
Characterisation of composite elastic properties by means of a multi-scale two-level inverse approach. Compos Struct2018;
204: 767–777.
30.
RefaiKMontemurroMBruggerC, et al. Determination of the effective elastic properties of titanium lattice structures. Mech Adv Mater Struct. 2019; 16: 1–4.
31.
EinsteinA.Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. Ann Phys1905;
322: 549–560.
32.
BroadbentTAAEinsteinAHertzH, et al.
Investigations on the Theory of the Brownian Movement. Math Gazette1957;
41: 231.
33.
GuthE.Theory of filler reinforcement. J Appl Phys1945;
16: 20–25.
34.
HalpinJC.Stiffness and expansion estimates for oriented short fiber composites. J Compos Mater1969;
3: 732–734.
35.
HalpinJC.Effects of environmental factors on composite materials. Technical Report Afml-Tr-67-423, June 1969. Wright-Patterson Air Force Base, OH: Air Force Materials Laboratory, 1969.
36.
KernerEH.The elastic and thermo-elastic properties of composite media. Proc Phys Soc B1956;
69: 808–813.
37.
VoigtW.Ueber die Beziehung zwischen den beiden Elasticitatsconstanten isotroper korper. Ann Phys1889;
274: 573–587.
38.
ReussA.Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle. Z Angew Math Mech1929;
9: 49–58.
39.
HashinZShtrikmanS.A variational approach to the theory of the elastic behaviour of multiphase materials. J Mech Phys Solids1963;
11: 127–140.
40.
ChmielewskiMWeglewskiW.Comparison of experimental and modelling results of thermal properties in Cu-AlN composite materials. Bull Polish Acad Sci Tech Sci2013;
61: 507–514.
41.
EshelbyJD.The determination of the elastic field of an ellipsoidal inclution and related problems.Proc Phys Soc Lond Series A1957;
241: 376–396.
42.
MoriTTanakaK.Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metallurgica1973;
21: 571–574.
BudianskyB.On the elastic moduli of some heterogeneous materials. J Mech Phys Solids1965;
13: 223–227.
45.
LielensGPirottePCouniotA, et al.
Prediction of thermo-mechanical properties for compression moulded composites. Compos Part A Appl Sci Manuf1998;
29: 63–70.
46.
SchaperyRA.Thermal expansion coefficients of composite materials based on energy principles. J Compos Mater1968;
2: 380–404.
47.
ChamberlainNJ.Derivation of expansion coefficients for a fibre reinforced composites. Technical Report. London: British Aircraft Corporation, 1968.
48.
ChamisCC. Simplified composite micromechanics equations for hygral, thermal and mechanical properties. In: 38th Annual Conference of the Society of the Plastics Industry (SPI) Reinforced Plastics/Composites Institute, Houston, TX, 7–11 February 1983.
49.
RosenBWHashinZ.Effective thermal expansion coefficients and specific heats of composite materials. Int J Eng Sci1970;
8: 157–173.
SihnSRoyAK.Micromechanical analysis for transverse thermal conductivity of composites. J Compos Mater2011;
45: 1245–1255.
52.
KarchC.Micromechanical analysis of thermal expansion coefficients.Model Numer Simul Mater Sci2014;
4: 104–118.
53.
BowlesDETompkinsSS.Prediction of coefficients of thermal expansion for unidirectional composites. J Compos Mater1989;
23: 370–388.
54.
AshbyMCopeECebonD.Materials selection for engineering design. In: RajanK (ed) Informatics for materials science and engineering.
Oxford:
Butterworth-Heinemann, 2013, pp. 219–244.
55.
MottramJTGearyBTaylorR.Thermal expansion of phenolic resin and phenolic-fibre composites. J Mater Sci1992;
27: 5015–5026.
56.
EvansPR.Rotations and rotation matrices. Acta Crystallogr D Biol Crystallogr2001;
57: 1355–1359.
