<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0035-001X</journal-id>
<journal-title><![CDATA[Revista mexicana de física]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. mex. fis.]]></abbrev-journal-title>
<issn>0035-001X</issn>
<publisher>
<publisher-name><![CDATA[Sociedad Mexicana de Física]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0035-001X2022000300019</article-id>
<article-id pub-id-type="doi">10.31349/revmexfis.68.031401</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Effect of the orientation distribution of thin highly conductive inhomogeneities on the overall electrical conductivity of heterogeneous material]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Levin]]></surname>
<given-names><![CDATA[V.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Markov]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Ronquillo Jarillo]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Instituto Mexicano del Petroleo  ]]></institution>
<addr-line><![CDATA[ Ciudad de México]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2022</year>
</pub-date>
<volume>68</volume>
<numero>3</numero>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0035-001X2022000300019&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0035-001X2022000300019&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0035-001X2022000300019&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract Many natural composite materials contain systems of partially oriented thin low-resistivity inclusions (for example, water-saturated microcracks in a double porosity sedimentary formation). We have calculated the components of the electrical conductivity tensor of such materials as a function of crack density. The results were obtained for thin ellipsoidal inclusions with conductivity (electrical or thermal) much larger than the matrix conductivity. To calculate the effective conductivity, we have used the effective field method (EFM). We have obtained the explicit expressions for the effective parameters of inhomogeneous materials. The application of the EFM allows one to describe the influence of the peculiarities in the spatial distribution of inclusions on the effective properties of the medium. General explicit expressions, obtained in this work, are illustrated by calculating examples for inclusions, homogeneously distributed in the sector [-&#946;,&#946;], where &#946; is the disorientation angle, and some continuous angle distribution functions. The calculations have shown that the spatial distribution of the crack-like inclusions strongly affects the conductive properties of the effective medium and the symmetry of their tensor.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Heterogeneous medium]]></kwd>
<kwd lng="en"><![CDATA[highly conductive inhomogeneities]]></kwd>
<kwd lng="en"><![CDATA[homogenization problem]]></kwd>
<kwd lng="en"><![CDATA[effective field method]]></kwd>
<kwd lng="en"><![CDATA[influence of the inclusion orientations]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<label>[1]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Aguilera]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<source><![CDATA[Naturally Fractured Reservoirs]]></source>
<year>1995</year>
<publisher-name><![CDATA[PennWell Books]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B2">
<label>[2]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Benveniste]]></surname>
<given-names><![CDATA[Ya.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On the effective thermal conductivity of multiphase composites]]></article-title>
<source><![CDATA[ZAMP]]></source>
<year>1986</year>
<volume>37</volume>
<page-range>696</page-range></nlm-citation>
</ref>
<ref id="B3">
<label>[3]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bergman]]></surname>
<given-names><![CDATA[D.J.]]></given-names>
</name>
<name>
<surname><![CDATA[Stroud]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The physical properties of macroscopically inhomogeneous media]]></article-title>
<source><![CDATA[Solid State Phys]]></source>
<year>1992</year>
<volume>46</volume>
</nlm-citation>
</ref>
<ref id="B4">
<label>[4]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Brosseau]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Modeling and simulation of dielectric heterostructures: a physical survey from an historical perspective]]></article-title>
<source><![CDATA[J. of Physics. D: Appl. Phys]]></source>
<year>2006</year>
<volume>39</volume>
<page-range>1277</page-range></nlm-citation>
</ref>
<ref id="B5">
<label>[5]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bruggeman]]></surname>
<given-names><![CDATA[D.A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Berechnung Verschidener Physikalischer Konstanten von Heterogenen Substanzen]]></article-title>
<source><![CDATA[Ann. Phys. Lpz]]></source>
<year>1935</year>
<volume>24</volume>
<page-range>636</page-range></nlm-citation>
</ref>
<ref id="B6">
<label>[6]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Fricke]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A mathematical treatment of the electric conductivity and capacity of disperse systems]]></article-title>
<source><![CDATA[Phys. Rev.]]></source>
<year>1924</year>
<volume>24</volume>
<page-range>575</page-range></nlm-citation>
</ref>
<ref id="B7">
<label>[7]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Giordano]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Effective medium theories of dielectric ellipsoids]]></article-title>
<source><![CDATA[J. of Electrostatics]]></source>
<year>2003</year>
<volume>58</volume>
<page-range>59</page-range></nlm-citation>
</ref>
<ref id="B8">
<label>[8]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Giordano]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Order and disorder in heterogeneous material microstructure: electric and elastic characterization of dispersions of pseudo oriented spheroids]]></article-title>
<source><![CDATA[International Journal of Engineering Science]]></source>
<year>2005</year>
<volume>43</volume>
<page-range>1033</page-range></nlm-citation>
</ref>
<ref id="B9">
<label>[9]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Giordano]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Colombo]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Effects of the orientation distribution of cracks in isotropic solids]]></article-title>
<source><![CDATA[Engineering Fracture Mechanics]]></source>
<year>2007</year>
<volume>74</volume>
<page-range>1983</page-range></nlm-citation>
</ref>
<ref id="B10">
<label>[10]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kanaun]]></surname>
<given-names><![CDATA[S.K.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Elastic medium with random fields of inhomogeneities]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Kunin]]></surname>
<given-names><![CDATA[I.A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Elastic Media with Microstructure II, Three-dimensional Models]]></source>
<year>1983</year>
<page-range>165</page-range><publisher-loc><![CDATA[Berlin ]]></publisher-loc>
<publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B11">
<label>[11]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kachanov]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Sevostianov]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Effective Properties of Heterogeneous Materials]]></article-title>
<source><![CDATA[Solid Mechanics and Its Applications]]></source>
<year>2013</year>
<volume>193</volume>
</nlm-citation>
</ref>
<ref id="B12">
<label>[12]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kanaun]]></surname>
<given-names><![CDATA[S.K.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The thin defect in a homogeneous elastic medium]]></article-title>
<source><![CDATA[Mech. Solids]]></source>
<year>1984</year>
<volume>3</volume>
<page-range>74</page-range></nlm-citation>
</ref>
<ref id="B13">
<label>[13]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kanaun]]></surname>
<given-names><![CDATA[S. K.]]></given-names>
</name>
<name>
<surname><![CDATA[Levin]]></surname>
<given-names><![CDATA[V. M.]]></given-names>
</name>
</person-group>
<source><![CDATA[Self-Consistent Methods for Composites V.I Static Problems]]></source>
<year>2008</year>
<page-range>386</page-range><publisher-loc><![CDATA[Dordrecht ]]></publisher-loc>
<publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B14">
<label>[14]</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kanaun]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Levin]]></surname>
<given-names><![CDATA[V.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Effective field method in the theory of heterogeneous media]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Kachanov M.]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Sevostianov]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
</person-group>
<source><![CDATA[Effective Properties of Heterogeneous Materials. Solid Mechanics and Its Applications]]></source>
<year>2013</year>
<volume>193</volume>
<page-range>199</page-range></nlm-citation>
</ref>
<ref id="B15">
<label>[15]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kushch]]></surname>
<given-names><![CDATA[V.]]></given-names>
</name>
<name>
<surname><![CDATA[Sevostianov]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
<name>
<surname><![CDATA[Mishnaevsky]]></surname>
<given-names><![CDATA[Jr.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Effect of crack orientation statistics on effective stiffness of microcracked solid]]></article-title>
<source><![CDATA[Int. J. of Solids and Structures]]></source>
<year>2008</year>
<volume>46</volume>
<page-range>2574</page-range></nlm-citation>
</ref>
<ref id="B16">
<label>[16]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Levin]]></surname>
<given-names><![CDATA[V.]]></given-names>
</name>
<name>
<surname><![CDATA[Markov]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Electroconductivity of a medium with thin low-resistivity inclusions]]></article-title>
<source><![CDATA[Journal of Electrostatics]]></source>
<year>2004</year>
<volume>61</volume>
<page-range>129</page-range></nlm-citation>
</ref>
<ref id="B17">
<label>[17]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Markov]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Mousatov]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Kazatchenko]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Conductivity of carbonate formations with microfracture systems]]></article-title>
<source><![CDATA[J. of Petr. Sci. and Eng.]]></source>
<year>2009</year>
<volume>69</volume>
<page-range>247</page-range></nlm-citation>
</ref>
<ref id="B18">
<label>[18]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Mavko]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Mukerji]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Dvorkin]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[The rock physics handbook. Tools for seismic analysis in porous media]]></source>
<year>2009</year>
<page-range>330</page-range><publisher-name><![CDATA[Cambridge university press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B19">
<label>[19]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Maxwell]]></surname>
<given-names><![CDATA[J. C.]]></given-names>
</name>
</person-group>
<source><![CDATA[A treatise on electricity and magnetism]]></source>
<year>1892</year>
<edition>3rd</edition>
<publisher-name><![CDATA[Clarendon Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B20">
<label>[20]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Mishurova]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Evaluation of the probability density of orientations of inhomogeneities by computed tomography and its application to the calculation of the effective properties of a fiber reinforced concrete]]></article-title>
<source><![CDATA[International Journal of Engineering Science]]></source>
<year>2018</year>
<volume>122</volume>
<page-range>14</page-range></nlm-citation>
</ref>
<ref id="B21">
<label>[21]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Mori]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Tanaka]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Average stress in matrix and average energy of materials with misfitting inclusions]]></article-title>
<source><![CDATA[Acta Metallurgia]]></source>
<year>1973</year>
<volume>21</volume>
<page-range>571</page-range></nlm-citation>
</ref>
<ref id="B22">
<label>[22]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Phan-Thien]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
<name>
<surname><![CDATA[Pham]]></surname>
<given-names><![CDATA[D. C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Differential multiphase models for polydispersed spheroidal inclusions: thermal conductivity and effective viscosity]]></article-title>
<source><![CDATA[International Journal of Engineering Science]]></source>
<year>2000</year>
<volume>38</volume>
<page-range>73</page-range></nlm-citation>
</ref>
<ref id="B23">
<label>[23]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Robinson]]></surname>
<given-names><![CDATA[D. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Friedman]]></surname>
<given-names><![CDATA[S. P.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Observations of the effects of particle shape and particle size distribution on avalanching of granular media]]></article-title>
<source><![CDATA[Physica A: Statistical Mechanics and its Applications]]></source>
<year>2002</year>
<volume>311</volume>
<page-range>97</page-range></nlm-citation>
</ref>
<ref id="B24">
<label>[24]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Shafiro]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
<name>
<surname><![CDATA[Kachanov]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Anisotropic effective conductivity of materials with nonrandomly oriented inclusions of diverse ellipsoidal shapes]]></article-title>
<source><![CDATA[J. Appl. Phys.]]></source>
<year>2000</year>
<volume>87</volume>
<page-range>8561</page-range></nlm-citation>
</ref>
<ref id="B25">
<label>[25]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Sen]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Scala]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Cohen]]></surname>
<given-names><![CDATA[M.H.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A self-similar model for sedimentary rocks with application to the dielectric constant of fused glass beard]]></article-title>
<source><![CDATA[Geophysics]]></source>
<year>1981</year>
<volume>46</volume>
<page-range>781</page-range></nlm-citation>
</ref>
<ref id="B26">
<label>[26]</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Shvidler]]></surname>
<given-names><![CDATA[M.I.]]></given-names>
</name>
</person-group>
<source><![CDATA[Statistical hydrodynamics of porous media]]></source>
<year>1985</year>
<page-range>228</page-range><publisher-loc><![CDATA[Moscow ]]></publisher-loc>
<publisher-name><![CDATA[Nedra]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B27">
<label>[27]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Sevostianov]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
<name>
<surname><![CDATA[Giraud]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On the compliance contribution tensor for a concave superspherical pore]]></article-title>
<source><![CDATA[International Journal of Fracture]]></source>
<year>2012</year>
<volume>177</volume>
<page-range>199</page-range></nlm-citation>
</ref>
<ref id="B28">
<label>[28]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Sevostianov]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
<name>
<surname><![CDATA[Kachanov]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Modeling of the anisotropic elastic properties of plasma-sprayed coatings in relation to their micro-structure]]></article-title>
<source><![CDATA[Acta Mater]]></source>
<year>2000</year>
<volume>48</volume>
<page-range>1361</page-range></nlm-citation>
</ref>
<ref id="B29">
<label>[29]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Sihvola]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Electromagnetic Mixing Formulae and Applications]]></article-title>
<source><![CDATA[IEEE Electromagnetic Waves Series]]></source>
<year>1999</year>
<volume>47</volume>
<page-range>296</page-range></nlm-citation>
</ref>
<ref id="B30">
<label>[30]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Beek]]></surname>
<given-names><![CDATA[L.K.H. Van]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Dielectric behavior of heterogeneous systems]]></article-title>
<source><![CDATA[Prog. Dielectr]]></source>
<year>1976</year>
<volume>7</volume>
<page-range>71</page-range></nlm-citation>
</ref>
<ref id="B31">
<label>[31]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Zeng]]></surname>
<given-names><![CDATA[X.]]></given-names>
</name>
<name>
<surname><![CDATA[Wei]]></surname>
<given-names><![CDATA[Y.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The influence of crack-orientation distribution on the mechanical properties of pre-cracked brittle media]]></article-title>
<source><![CDATA[Int. J. of Solids and Structures]]></source>
<year>2016</year>
<volume>90</volume>
<page-range>64</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
