The work is focused on the mechanical behavior description of porous filled composites that is not based on simulations or exact physical models, including different assumptions and simplifications with further comparison with real behavior of materials with different extents of accordance. The proposed process begins by measurement and further fitting of data by spatial exponential function zc = zm · p1b · p2c, where zc/zm is mechanical property value for composite/nonporous matrix, p1/p2 are suitable dimensionless structural parameters (equal to 1 for nonporous matrix) and b/c are exponents ensuring the best fitting. The fitting is followed by interpolation of b and c, which are logarithmic variables based on the observed mechanical property value of nonporous matrix with additions of further properties of matrix in some cases. The work is dedicated to the utilization of further suitable pairs of structural parameters to one pair published earlier. The proposed mathematical approach was demonstrated for PUR/rubber composites with a wide range of rubber filling, various porosity, and different polyurethane matrices. The mechanical properties derived from tensile testing included elastic modulus, ultimate strength and strain, and energy need for ultimate strain achievement. The proposed relationships between structure/composition and mechanical behavior seem to be suitable for materials containing randomly shaped filler particles and voids and, therefore, could be universal (and also hold materials with less complicated microstructure) after potential following and more exact research.

Central European Institute of Technology Brno University of Technology Purkyňova 656 123 612 00 Brno Czech Republic

Faculty of Chemistry Institute of Materials Science Brno University of Technology Purkyňova 464 118 612 00 Brno Czech Republic

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Choren J.A., Heinrich S.M., Silver-Thorn M.B. Young’s modulus and volume porosity relationships for additive manufacturing applications. J. Mater. Sci. 2013;48:5103–5112. doi: 10.1007/s10853-013-7237-5. DOI

Krishna V., Bose S., Bandyopadhyay A. Low stiffness porous Ti structures for load-bearing implants. Acta Biomater. 2007;3:997–1006. doi: 10.1016/j.actbio.2007.03.008. PubMed DOI

Rubshtein A.P., Trakhtenberg I.S., Makarova E.B., Triphonova E.B., Bliznets D.G., Yakovenkova L.I., Vladimirov A.B. Porous material based on spongy titanium granules: Structure, mechanical properties, and osseointegration. Mat. Sci. Eng. C-Mater. 2014;35:363–369. doi: 10.1016/j.msec.2013.11.020. PubMed DOI

Kovacik J. Correlation between shear modulus and porosity in porous materials. J. Mater. Sci. Lett. 2001;20:1953–1955. doi: 10.1023/A:1013186702962. DOI

Lian C., Zhuge Y., Beecham S. The relationship between porosity and strength for porous concrete. Constr. Build. Mater. 2011;25:4294–4298. doi: 10.1016/j.conbuildmat.2011.05.005. DOI

Fan X., Case E.D., Ren F., Shu Y., Baumann M.J. Part II: Fracture strength and elastic modulus as a function of porosity for hydroxyapatite and other brittle materials. J. Mech. Behav. Biomed. 2012;8:99–110. doi: 10.1016/j.jmbbm.2011.12.014. PubMed DOI

Karthikeyan S., Balasubramanian V., Rajendran R. Developing empirical relationships to estimate porosity and Young’s modulus of plasma sprayed YSZ coatings. Appl. Surf. Sci. 2014;296:31–46. doi: 10.1016/j.apsusc.2014.01.021. DOI

Kovacik J. Correlation between Young’s modulus and porosity in porous materials. J. Mater. Sci. Lett. 1999;18:1007–1010. doi: 10.1023/A:1006669914946. DOI

Kovacik J. Correlation between elastic modulus, shear modulus, Poisson’s ratio and porosity in porous materials. Adv. Eng. Mater. 2008;10:250–252. doi: 10.1002/adem.200700266. DOI

Smolin L.Y., Eremin M.O., Makarov M.P., Evtushenko E.P., Kulkov S.N., Buyakova S.P. Brittle Porous Material Mesovolume Structure Models and Simulation of their Mechanical Properties. AIP Conf. Proc. 2014;1623:595–598. doi: 10.1063/1.4899015. DOI

Werner J., Aneziris C.G., Schaffoner S. Influence of porosity on Young’s modulus of carbon-bonded alumina from room temperature up to 1450 °C. Ceram. Int. 2014;40:14439–14445. doi: 10.1016/j.ceramint.2014.07.013. DOI

Zhang L., Gao K.W., Elias A., Dong Z.G., Chen W.X. Porosity dependence of elastic modulus of porous Cr3C2 ceramics. Ceram. Int. 2014;40:191–198. doi: 10.1016/j.ceramint.2013.05.122. DOI

Sapozhnikov S.B., Kudryavtsev O.A., Dolganina N.Y. Experimental and numerical estimation of strength and fragmentation of different porosity alumina ceramics. Mater. Design. 2015;88:1042–1048. doi: 10.1016/j.matdes.2015.08.117. DOI

Wu Z., Sun L.C., Wang J.Y. Synthesis and characterization of porous Y2SiO5 with low linear shrinkage, high porosity and high strength. Ceram. Int. 2016;42:14894–14902. doi: 10.1016/j.ceramint.2016.06.128. DOI

Sonnenschein M.F. Porosity-Dependent Young’s Modulus of Membranes from Polyetherether Ketone. J. Polym. Sci. Pol. Phys. 2003;41:1168–1174. doi: 10.1002/polb.10473. DOI

Palchik V. Influence of porosity and elastic modulus on uniaxial compressive strength in soft brittle porous sandstones. Rock Mech. Rock Eng. 1999;32:303–309. doi: 10.1007/s006030050050. DOI

Gibson L.J., Ashby M.F., Easterling K.E. Structure and mechanics of the iris leaf. J. Mater. Sci. 1988;23:3041–3048. doi: 10.1007/BF00551271. DOI

Nielsen L.F. Elasticity and damping of porous materials and impregnated materials. J. Am. Ceram. Soc. 1984;67:93–98. doi: 10.1111/j.1151-2916.1984.tb09622.x. DOI

Huiru X., Quizhen S. Deformation mechanisms and mechanical properties of porous magnesium/carbon nanofiber composites with different porosities. J. Mater. Sci. 2018;53:14375–14385. doi: 10.1007/s10853-018-2649-x. DOI

Wagh A.S., Poeppel R.B., Singh J.P. Open pore description of mechanical properties of ceramics. J. Mater. Sci. 1991;26:3862–3868. doi: 10.1007/BF01184983. DOI

Chen Y., Xu Y.F. Compressive Strength of Fractal-Textured Foamed Concrete. Fractals. 2019;27:1940003. doi: 10.1142/S0218348X19400036. DOI

Bruck H.A., Rabin B.H. Evaluating microstructural and damage effects in rule-of-mixtures predictions of the mechanical properties of Ni-Al2O3 composites. J. Mater. Sci. 1999;34:2241–2251. doi: 10.1023/A:1004509220648. DOI

Chao X.J., Tian W.L., Xu F., Shou D.H. A fractal model of effective mechanical properties of porous composites. Compos. Sci. Technol. 2021;213:108957. doi: 10.1016/j.compscitech.2021.108957. DOI

Katsube N., Wu Y.N. A constitutive theory for porous composite materials. Int. J. Solids Struct. 1998;35:4587–4596. doi: 10.1016/S0020-7683(98)00085-7. DOI

Xu H., Li Q. Effect of carbon nanofiber concentration on mechanical properties of porous magnesium composites: Experimental and theoretical analysis. Mater. Sci. Eng. A. 2017;706:249–255. doi: 10.1016/j.msea.2017.09.024. DOI

Odhiambo J.O., Yoshida M., Otsu A., Yi L.-F., Onda T., Chen Z.-C. Microstructure and tensile properties of in-situ synthesized and hot-extruded aluminum-matrix composites reinforced with hybrid submicron-sized ceramic particles. J. Compos. Mater. 2022;56:1987–2001. doi: 10.1177/00219983221087334. DOI

Poh L., Della C., Ying S., Goh C., Li Y. Micromechanics model for predicting effective elastic moduli of porous ceramic matrices with randomly oriented carbon nanotube reinforcements. AIP Adv. 2015;5:097153. doi: 10.1063/1.4931453. DOI

Alam P. A mixtures model for porous particle-polymer composites. Mech. Res. Commun. 2010;37:389–393. doi: 10.1016/j.mechrescom.2010.04.002. DOI

Choi H.K., Son M.J., Shin E.S., Yu J. Prediction of thermos-poro-elastic properties of porous composites using an expanded unmixing-mixing model. Compos. Struct. 2018;188:387–393. doi: 10.1016/j.compstruct.2018.01.003. DOI

Chan C., Naguib H.E. Development and Characterization of Polypyrrole-Polylactide Conductive Open-Porous Composites. J. Appl. Polym. Sci. 2010;117:3187–3195. doi: 10.1002/app.32197. DOI

Tran A.T., Le Quang H., He Q.-C. Computation of the size-dependent elastic moduli of nano-fibrous and nano-porous composites by FFT. Compos. Sci. Technol. 2016;135:159–171. doi: 10.1016/j.compscitech.2016.09.012. DOI

Khoroshun L.P., Shikula E.N. Nonlinear Straining of Porous Composite Materials. Int. Appl. Mech. 1993;29:983–988. doi: 10.1007/BF00862495. DOI

Cerny M., Petrus J., Kucera F., Pavlinakova V., Kupka V., Polacek P., Chamradova I. A new approach to the structure-properties relationship evaluation for porous polymer composites. SN Appl. Sci. 2020;2:640. doi: 10.1007/s42452-020-2479-8. DOI

Keleş Ö., Anderson E.H., Huynh J., Gelb J., Freund J., Karakoç A. Stochastic fracture of additively manufactured porous composites. Sci. Rep. 2018;8:15437. doi: 10.1038/s41598-018-33863-4. PubMed DOI PMC

Teng J., Yang B., Zhang L.-Q., Lin S.-Q., Xu L., Zhong G.-J., Tang J.-H., Li Z.-M. Ultra-high mechanical properties of porous composites based on regenerated cellulose and cross-linked poly(ethylene glycole) Carbohydr. Polym. 2018;179:244–251. doi: 10.1016/j.carbpol.2017.09.090. PubMed DOI

Węgrzyk S., Herman D. Strengthening of Al2O3 porous composites with a glass-ceramic binder doped with nanocopper. J. Eur. Ceram. 2021;41:5558–5569. doi: 10.1016/j.jeurceramsoc.2021.04.057. DOI

Olmos L., Gonzalés-Pedraza A.S., Vergara-Hernández H.J., Chávez J., Jimenez O., Mihalcea E., Arteaga D., Ruiz-Mondragón J.J. Ti64/20Ag Porous Composites Fabricated by Powder Metallurgy for Biomedical Applications. Materials. 2022;15:5956. doi: 10.3390/ma15175956. PubMed DOI PMC

Seuba J., Maire E., Adrien J., Meille S., Deville S. Mechanical properties of unidirectional porous polymer/ceramic composites for biomedical applications. Open Ceram. 2021;8:100195. doi: 10.1016/j.oceram.2021.100195. DOI

Yeboah A., Ying S., Lu J., Xie Y., Amoanimaa-Dede H., Boateng K.G.A., Chen M., Yin X. Castor oil (Ricinus communis): A review on the chemical composition and physicochemical properties. Food. Sci. Technol. 2021;41:399–413. doi: 10.1590/fst.19620. DOI

Vereshchagin A.G., Novitskaya G.V. The triglyceride composition of linseed oil. J. Am. Oil Chem. Soc. 1965;42:970–974. doi: 10.1007/BF02632457. PubMed DOI