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\i\f40\fs20\lang2057\langfe1040\langnp2057\insrsid1128859\charrsid1128859 Aerospace Engineering, {\*\xmlopen\xmlns2{\factoidname PlaceName}}New Mexico{\*\xmlclose} {\*\xmlopen\xmlns2{\factoidname PlaceType}}State{\*\xmlclose} 
{\*\xmlopen\xmlns2{\factoidname PlaceType}}University}{\rtlch\fcs1 \ai\af40\afs20 \ltrch\fcs0 \i\f40\fs20\lang2057\langfe1040\langnp2057\insrsid4346792 {\*\xmlclose}, }{\rtlch\fcs1 \ai\af40\afs20 \ltrch\fcs0 
\i\f40\fs20\lang2057\langfe1040\langnp2057\insrsid12012335 {\*\xmlopen\xmlns2{\factoidname place}}{\*\xmlopen\xmlns2{\factoidname City}}Las Cruces{\*\xmlclose}{\*\xmlclose},
\par }{\rtlch\fcs1 \ai\af40\afs20 \ltrch\fcs0 \i\f40\fs20\insrsid4346792\charrsid12012335 NM 88001, USA. 
\par }\pard \ltrpar\qj \li0\ri-8\nowidctlpar\wrapdefault\faauto\rin-8\lin0\itap0\pararsid4346792 {\rtlch\fcs1 \ai\af40\afs20 \ltrch\fcs0 \i\f40\fs20\insrsid4346792\charrsid12012335 E-mail: igor@nmsu.edu}{\rtlch\fcs1 \ai\af40\afs20 \ltrch\fcs0 
\i\f40\fs20\insrsid1128859\charrsid12012335 
\par }\pard \ltrpar\qj \li0\ri-7\nowidctlpar\wrapdefault\faauto\rin-7\lin0\itap0 {\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\insrsid15466923\charrsid12012335 
\par }{\rtlch\fcs1 \ai\af40\afs20 \ltrch\fcs0 \i\f40\fs20\lang2057\langfe1040\langnp2057\insrsid15466923\charrsid16190858 Keywords:  }{\rtlch\fcs1 \ai\af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid13196179 
stiffness contribution tensor; stress functions;}{\rtlch\fcs1 \ai\af40\afs20 \ltrch\fcs0 \i\f40\fs20\lang2057\langfe1040\langnp2057\insrsid14488959  }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid14488959 
bipolar coordinates}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid15466923\charrsid16190858 .}{\rtlch\fcs1 \af39\afs20 \ltrch\fcs0 \f39\fs20\lang2057\langfe1040\langnp2057\insrsid15466923\charrsid16190858 
\par }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid15466923\charrsid16190858 
\par }\pard \ltrpar\qj \fi284\li0\ri-7\nowidctlpar\wrapdefault\faauto\rin-7\lin0\itap0\pararsid8481820 {\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid14488959 
The present works deals with the stiffness properties of an infinite 2D }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid13194663 isotropic }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f40\fs20\lang2057\langfe1040\langnp2057\insrsid14488959 elastic system}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid15466923\charrsid16190858  }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f40\fs20\lang2057\langfe1040\langnp2057\insrsid14488959 containing inhomogeneities }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid8481820 hav}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f40\fs20\lang2057\langfe1040\langnp2057\insrsid668546 ing}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid8481820  a }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid668546 contour
}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid8481820  }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid8481820\charrsid6295551 formed by union}{\rtlch\fcs1 \af40\afs20 
\ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid8481820  }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid8481820\charrsid6295551 of two overlapping circles}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f40\fs20\lang2057\langfe1040\langnp2057\insrsid8481820  of generally different}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid8481820\charrsid6295551  radii}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f40\fs20\lang2057\langfe1040\langnp2057\insrsid8481820 . }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid4269005 Starting from this general layout, t}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f40\fs20\lang2057\langfe1040\langnp2057\insrsid8481820 he cases of a matrix with lenticular, perfectly circular, semi-circular, \'93C-shaped\'94 and thin straight inclusions can be obtained as limit cases. }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f40\fs20\lang2057\langfe1040\langnp2057\insrsid8481820\charrsid8013220 Owing to the geometry of the system, }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid8481820 reference}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f40\fs20\lang2057\langfe1040\langnp2057\insrsid668546  is made}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid8481820  }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f40\fs20\lang2057\langfe1040\langnp2057\insrsid8481820\charrsid8013220 to bipolar cylindrical coordinates}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid1013284  }{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 
\f0\fs20\lang2057\langfe1040\langnp2057\insrsid1013284\charrsid9523302 (}{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 \f3\fs20\lang2057\langfe1040\langnp2057\insrsid1013284\charrsid9523302 \'61\'2c}{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 
\f0\fs20\lang2057\langfe1040\langnp2057\insrsid1013284\charrsid9523302  }{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 \f3\fs20\lang2057\langfe1040\langnp2057\insrsid1013284\charrsid9523302 \'62}{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 
\f0\fs20\lang2057\langfe1040\langnp2057\insrsid1013284\charrsid9523302 )}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid8481820 , which are }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f40\fs20\lang2057\langfe1040\langnp2057\insrsid8481820\charrsid8013220 linked to the Cartesian }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid8481820 ones}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f40\fs20\lang2057\langfe1040\langnp2057\insrsid8481820\charrsid8013220  }{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 \f0\fs20\lang2057\langfe1040\langnp2057\insrsid1013284\charrsid9523302 (}{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 
\i\f0\fs20\lang2057\langfe1040\langnp2057\insrsid1013284\charrsid9523302 x}{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 \f0\fs20\lang2057\langfe1040\sub\langnp2057\insrsid1013284\charrsid9523302 1}{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 
\f0\fs20\lang2057\langfe1040\langnp2057\insrsid1013284\charrsid9523302 , }{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 \i\f0\fs20\lang2057\langfe1040\langnp2057\insrsid1013284\charrsid9523302 x}{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 
\f0\fs20\lang2057\langfe1040\sub\langnp2057\insrsid1013284\charrsid9523302 2}{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 \f0\fs20\lang2057\langfe1040\langnp2057\insrsid1013284\charrsid9523302 ) }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f40\fs20\lang2057\langfe1040\langnp2057\insrsid8481820\charrsid8013220 through }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid1013284 the}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f40\fs20\lang2057\langfe1040\langnp2057\insrsid8481820  conformal }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid8481820\charrsid8013220 map}{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 
\f0\fs20\lang2057\langfe1040\langnp2057\insrsid8481820\charrsid9523302  [}{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 \f0\fs20\lang2057\langfe1040\langnp2057\insrsid8481820 2}{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 
\f0\fs20\lang2057\langfe1040\langnp2057\insrsid8481820\charrsid9523302 ]}{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 \f0\fs20\lang2057\langfe1040\langnp2057\insrsid1013284 :}{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 
\f0\fs20\lang2057\langfe1040\langnp2057\insrsid8481820\charrsid9523302 
\par }\pard \ltrpar\qj \li0\ri-7\nowidctlpar\wrapdefault\faauto\rin-7\lin0\itap0 {\pard\plain \ltrpar\qj \li0\ri-7\nowidctlpar\wrapdefault\faauto\rin-7\lin0\itap0 \rtlch\fcs1 \af0\afs20\alang1025 \ltrch\fcs0 
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{\sp{\sn fillShape}{\sv 1}}{\sp{\sn fillUseRect}{\sv 0}}{\sp{\sn fNoFillHitTest}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fPreferRelativeResize}{\sv 1}}{\sp{\sn fLayoutInCell}{\sv 1}}
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1c000000fb021000070000000000bc02000000000102022253797374656d0000d61c662e00000a0038008a0100000000ffffffff78e41800040000002d01030004000000f0010100030000000000}}}}}\sectd \ltrsect\linex0\sectdefaultcl\sftnbj {\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 
\fs20\lang2057\langfe1040\langnp2057\insrsid1013284\charrsid9523302 \tab \tab \tab            }{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 \fs20\lang2057\langfe1040\langnp2057\insrsid1013284   }{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 
\f0\fs20\lang2057\langfe1040\langnp2057\insrsid1013284\charrsid9523302 (1)}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid8481820 
\par }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid14488959 The effective }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid668546 elastic}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f40\fs20\lang2057\langfe1040\langnp2057\insrsid14488959  }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid75497 properties }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f40\fs20\lang2057\langfe1040\langnp2057\insrsid14488959 of }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid15466923\charrsid16190858 the}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f40\fs20\lang2057\langfe1040\langnp2057\insrsid14488959  system is }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid8481820 analytically investigated }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f40\fs20\lang2057\langfe1040\langnp2057\insrsid14488959 by introducing a }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid13196179 fourth}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f40\fs20\lang2057\langfe1040\langnp2057\insrsid14488959 -order compliance contribution tensor}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid8656856  }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\b\i\f40\fs20\lang2057\langfe1040\langnp2057\insrsid8656856\charrsid668546 H}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid13196179 
, which represents the effect induced by the inhomogeneity on the compliance of the system according to}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid8656856  [1]}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f40\fs20\lang2057\langfe1040\langnp2057\insrsid13196179 
\par }\pard \ltrpar\qj \li0\ri-6\nowidctlpar\wrapdefault\faauto\rin-6\lin0\itap0\pararsid6295551 {\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f3\fs20\lang2057\langfe1040\langnp2057\insrsid13196179\charrsid13196179 \'65}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f40\fs20\lang2057\langfe1040\sub\langnp2057\insrsid13196179\charrsid13196179 ij}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid13196179  = }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\i\f40\fs20\lang2057\langfe1040\langnp2057\insrsid13196179\charrsid13196179 S}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\sub\langnp2057\insrsid13196179\charrsid13196179 ijkl}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f3\fs20\lang2057\langfe1040\langnp2057\insrsid13196179\charrsid13196179 \'73}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\sub\langnp2057\insrsid13196179\charrsid13196179 kl}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f40\fs20\lang2057\langfe1040\langnp2057\insrsid13196179  }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid8656856 + }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \i\f40\fs20\lang2057\langfe1040\langnp2057\insrsid8656856 H}{
\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\sub\langnp2057\insrsid8656856\charrsid13196179 ijkl}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f3\fs20\lang2057\langfe1040\langnp2057\insrsid8656856\charrsid13196179 \'73}{\rtlch\fcs1 
\af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\sub\langnp2057\insrsid8656856\charrsid13196179 kl}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid8013220 ,}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f40\fs20\lang2057\langfe1040\langnp2057\insrsid13196179 \tab \tab \tab \tab \tab \tab \tab \tab      }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid8013220        }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f40\fs20\lang2057\langfe1040\langnp2057\insrsid13196179 (}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid1013284 2}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid13196179 )}{
\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid14488959 
\par }\pard \ltrpar\qj \li0\ri-7\nowidctlpar\wrapdefault\faauto\rin-7\lin0\itap0\pararsid11340341 {\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid8013220 being }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\b\i\f40\fs20\lang2057\langfe1040\langnp2057\insrsid8013220\charrsid668546 S}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid8013220  the compliance tensor for the homogeneous elastic matrix and }{\rtlch\fcs1 
\af40\afs20 \ltrch\fcs0 \b\f3\fs20\lang2057\langfe1040\langnp2057\insrsid8013220\charrsid8013220 \'73}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid8013220  the stress field.}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f40\fs20\lang2057\langfe1040\langnp2057\insrsid8481820  I}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid1013284 t is remarked that the last term in eq (1) }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f40\fs20\lang2057\langfe1040\langnp2057\insrsid8481820 denotes the correction}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid668546  }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f3\fs20\lang2057\langfe1040\langnp2057\insrsid668546\charrsid668546 \'44}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \b\f3\fs20\lang2057\langfe1040\langnp2057\insrsid668546\charrsid668546 \'65}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f40\fs20\lang2057\langfe1040\langnp2057\insrsid8481820  acting on the strain field owing to the presence of the inclusions. }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid8013220 
\par }\pard \ltrpar\qj \fi284\li0\ri-7\nowidctlpar\wrapdefault\faauto\rin-7\lin0\itap0\pararsid75497 {\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid8013220  }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f40\fs20\lang2057\langfe1040\langnp2057\insrsid13196179 The system without }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid8013220 inhomogeneities}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f40\fs20\lang2057\langfe1040\langnp2057\insrsid13196179  and subjected to a remote}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid668546  }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f40\fs20\lang2057\langfe1040\langnp2057\insrsid13196179 stress field}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid8013220  }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f40\fs20\lang2057\langfe1040\langnp2057\insrsid13196179 is considered }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\highlight7\langnp2057\insrsid2717736\charrsid2717736 first}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f40\fs20\lang2057\langfe1040\highlight7\langnp2057\insrsid13196179\charrsid2717736 . }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\highlight7\langnp2057\insrsid2717736\charrsid2717736 The }{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 
\f0\fs20\lang2057\langfe1040\highlight7\langnp2057\insrsid2717736\charrsid2717736 corresponding }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\highlight7\langnp2057\insrsid668546\charrsid2717736 fundamental stress field }{\rtlch\fcs1 
\af40\afs20 \ltrch\fcs0 \b\f3\fs20\lang2057\langfe1040\highlight7\langnp2057\insrsid668546\charrsid2717736 \'73}{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 \b\f0\fs20\lang2057\langfe1040\super\highlight7\langnp2057\insrsid668546\charrsid2717736 (0) }{\rtlch\fcs1 
\af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\highlight7\langnp2057\insrsid2717736\charrsid2717736 within}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\highlight7\langnp2057\insrsid11340341\charrsid2717736  }{\rtlch\fcs1 
\af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\highlight7\langnp2057\insrsid668546\charrsid2717736 the matrix}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid668546  }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f40\fs20\lang2057\langfe1040\langnp2057\insrsid13196179 does not accomplish the }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid668546 BC}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f40\fs20\lang2057\langfe1040\langnp2057\insrsid13196179 s at the contour}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid668546  of the }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f40\fs20\lang2057\langfe1040\langnp2057\insrsid13196179 inhomogeneities. Th}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid668546 us}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f40\fs20\lang2057\langfe1040\langnp2057\insrsid13196179 ,}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid75497  following the Jeffery approach,}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f40\fs20\lang2057\langfe1040\langnp2057\insrsid13196179  }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid8013220 an auxiliary stress field }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\b\f3\fs20\lang2057\langfe1040\langnp2057\insrsid8481820\charrsid8013220 \'73}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \b\f3\fs20\lang2057\langfe1040\super\langnp2057\insrsid8481820\charrsid8481820 \'28}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\b\f3\fs20\lang2057\langfe1040\super\langnp2057\insrsid8481820 \'31\'29\'20}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid11340341 deduced}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f40\fs20\lang2057\langfe1040\langnp2057\insrsid8013220  by a biharmonic stress }{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 \f0\fs20\lang2057\langfe1040\langnp2057\insrsid8013220\charrsid2717736 function}{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 
\f0\fs20\lang2057\langfe1040\langnp2057\insrsid2717736  }{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 \f0\fs20\lang2057\langfe1040\langnp2057\insrsid2717736\charrsid2717736 in bipolar co}{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 
\f0\fs20\lang2057\langfe1040\langnp2057\insrsid2717736 o}{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 \f0\fs20\lang2057\langfe1040\langnp2057\insrsid2717736\charrsid2717736 rdinates }{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 
\f0\fs20\lang2057\langfe1040\langnp2057\insrsid8013220\charrsid2717736 is}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid8013220  introduced}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f40\fs20\lang2057\langfe1040\langnp2057\insrsid668546  and tensor }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \b\i\f40\fs20\lang2057\langfe1040\langnp2057\insrsid668546\charrsid668546 H}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\f40\fs20\lang2057\langfe1040\langnp2057\insrsid668546  is then evaluated by performing proper contour integrals involving the total stress distribution }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 
\b\f3\fs20\lang2057\langfe1040\highlight7\langnp2057\insrsid668546\charrsid2717736 \'73}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \b\f3\fs20\lang2057\langfe1040\super\highlight7\langnp2057\insrsid668546\charrsid2717736 \'28}{\rtlch\fcs1 \af40\afs20 
\ltrch\fcs0 \b\f3\fs20\lang2057\langfe1040\super\highlight7\langnp2057\insrsid2717736\charrsid2717736 \'30}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \b\f3\fs20\lang2057\langfe1040\super\highlight7\langnp2057\insrsid668546\charrsid2717736 \'29\'20}{\rtlch\fcs1 
\af40\afs20 \ltrch\fcs0 \f3\fs20\lang2057\langfe1040\highlight7\langnp2057\insrsid668546\charrsid2717736 \'2b\'20}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \b\f3\fs20\lang2057\langfe1040\highlight7\langnp2057\insrsid668546\charrsid2717736 \'73}{\rtlch\fcs1 
\af40\afs20 \ltrch\fcs0 \b\f3\fs20\lang2057\langfe1040\super\highlight7\langnp2057\insrsid668546\charrsid2717736 \'28\'31\'29}{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 \f0\fs20\lang2057\langfe1040\highlight7\langnp2057\insrsid668546\charrsid2717736  }{
\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 \f0\fs20\lang2057\langfe1040\highlight7\langnp2057\insrsid2717736\charrsid2717736 along the contour}{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 \f0\fs20\lang2057\langfe1040\langnp2057\insrsid668546\charrsid668546 
 of the inclusions.}{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 \f0\fs20\lang2057\langfe1040\langnp2057\insrsid75497  }{\rtlch\fcs1 \af0\afs20 \ltrch\fcs0 \f0\fs20\lang2057\langfe1040\langnp2057\insrsid75497\charrsid75497 
\par }\pard \ltrpar\qj \fi284\li0\ri-7\nowidctlpar\wrapdefault\faauto\rin-7\lin0\itap0\pararsid8481820 {\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid15739037 
The study allows evaluating the effective elastic properties of a wide class of inhomogeneous materials, with pa}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid14490967 rticular reference to composites }{\rtlch\fcs1 
\af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid15739037 reinforced with natural or synthetic fibres having optimized }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid14490967 cross sections}{
\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid15466923\charrsid16190858 .}{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid8481820 
\par }{\rtlch\fcs1 \af40\afs20 \ltrch\fcs0 \f40\fs20\lang2057\langfe1040\langnp2057\insrsid1013284\charrsid16190858 
\par }\pard \ltrpar\ql \fi240\li0\ri-7\nowidctlpar\wrapdefault\faauto\rin-7\lin0\itap0 {\rtlch\fcs1 \ai\af39\afs20 \ltrch\fcs0 \i\f39\fs20\lang2057\langfe1040\langnp2057\insrsid15466923\charrsid16190858 References
\par }\pard \ltrpar\qj \fi-360\li360\ri-7\nowidctlpar\wrapdefault\faauto\rin-7\lin360\itap0\pararsid6295551 {\rtlch\fcs1 \ai\af39\afs20 \ltrch\fcs0 \f39\fs20\lang2057\langfe1040\langnp2057\insrsid15466923\charrsid14122708 [1]}{\rtlch\fcs1 \ai\af39\afs20 
\ltrch\fcs0 \i\f39\fs20\lang2057\langfe1040\langnp2057\insrsid15466923\charrsid16190858 \tab }{\rtlch\fcs1 \ai\af39\afs20 \ltrch\fcs0 \i\f39\fs20\lang2057\langfe1040\langnp2057\insrsid6295551 Sevostianov}{\rtlch\fcs1 \ai\af39\afs20 \ltrch\fcs0 
\i\f39\fs20\lang2057\langfe1040\langnp2057\insrsid15466923\charrsid16190858 , }{\rtlch\fcs1 \ai\af39\afs20 \ltrch\fcs0 \i\f39\fs20\lang2057\langfe1040\langnp2057\insrsid6295551 {\*\xmlopen\xmlns2{\factoidname place}}I}{\rtlch\fcs1 \ai\af39\afs20 
\ltrch\fcs0 \i\f39\fs20\lang2057\langfe1040\langnp2057\insrsid15466923\charrsid16190858 .{\*\xmlclose}, }{\rtlch\fcs1 \ai\af39\afs20 \ltrch\fcs0 \i\f39\fs20\lang2057\langfe1040\langnp2057\insrsid14490967 and }{\rtlch\fcs1 \ai\af39\afs20 \ltrch\fcs0 
\i\f39\fs20\lang2057\langfe1040\langnp2057\insrsid6295551 Kachanov}{\rtlch\fcs1 \ai\af39\afs20 \ltrch\fcs0 \i\f39\fs20\lang2057\langfe1040\langnp2057\insrsid15466923\charrsid16190858 , }{\rtlch\fcs1 \ai\af39\afs20 \ltrch\fcs0 
\i\f39\fs20\lang2057\langfe1040\langnp2057\insrsid6295551 M}{\rtlch\fcs1 \ai\af39\afs20 \ltrch\fcs0 \i\f39\fs20\lang2057\langfe1040\langnp2057\insrsid15466923\charrsid16190858 ., \'93}{\rtlch\fcs1 \ai\af39\afs20 \ltrch\fcs0 
\i\f39\fs20\lang2057\langfe1040\langnp2057\insrsid6295551\charrsid6295551 Explicit cross-property correlations for anisotropic
\par two-phase composite materials}{\rtlch\fcs1 \ai\af39\afs20 \ltrch\fcs0 \i\f39\fs20\lang2057\langfe1040\langnp2057\insrsid15466923\charrsid16190858 \'94 }{\rtlch\fcs1 \ai\af39\afs20 \ltrch\fcs0 
\i\f39\fs20\lang2057\langfe1040\langnp2057\insrsid6295551\charrsid6295551 Journal of the Mechanics and Physics of Solids}{\rtlch\fcs1 \ai\af39\afs20 \ltrch\fcs0 \i\f39\fs20\lang2057\langfe1040\langnp2057\insrsid15739037 ,}{\rtlch\fcs1 \ai\af39\afs20 
\ltrch\fcs0 \i\f39\fs20\lang2057\langfe1040\langnp2057\insrsid6295551  }{\rtlch\fcs1 \ai\af39\afs20 \ltrch\fcs0 \b\i\f39\fs20\lang2057\langfe1040\langnp2057\insrsid6295551\charrsid15739037 50}{\rtlch\fcs1 \ai\af39\afs20 \ltrch\fcs0 
\i\f39\fs20\lang2057\langfe1040\langnp2057\insrsid6295551 , 253-282 (2002)}{\rtlch\fcs1 \ai\af39\afs20 \ltrch\fcs0 \i\f39\fs20\lang2057\langfe1040\langnp2057\insrsid15466923\charrsid16190858 .
\par }\pard \ltrpar\qj \fi-360\li360\ri-7\nowidctlpar\wrapdefault\faauto\rin-7\lin360\itap0 {\rtlch\fcs1 \ai\af39\afs20 \ltrch\fcs0 \f39\fs20\lang2057\langfe1040\langnp2057\insrsid15466923\charrsid14122708 [2]}{\rtlch\fcs1 \ai\af39\afs20 \ltrch\fcs0 
\i\f39\fs20\lang2057\langfe1040\langnp2057\insrsid15466923\charrsid16190858 \tab }{\rtlch\fcs1 \ai\af0\afs20 \ltrch\fcs0 \i\f0\fs20\lang2057\langfe1040\langnp2057\insrsid15739037 Korn, G.A. }{\rtlch\fcs1 \ai\af0\afs20 \ltrch\fcs0 
\i\f0\fs20\lang2057\langfe1040\langnp2057\insrsid15739037\charrsid11207973 and }{\rtlch\fcs1 \ai\af0\afs20 \ltrch\fcs0 \i\f0\fs20\lang2057\langfe1040\langnp2057\insrsid15739037 Korn, T.M.}{\rtlch\fcs1 \ai\af0\afs20 \ltrch\fcs0 
\i\f0\fs20\lang2057\langfe1040\langnp2057\insrsid15739037\charrsid11207973 , }{\rtlch\fcs1 \ai\af0\afs20 \ltrch\fcs0 \i\f0\fs20\lang2057\langfe1040\langnp2057\insrsid15739037 
Mathematical handbook for scientists and engineers. Definitions, Theorems and Formulas for Reference and Review, {\*\xmlopen\xmlns2{\factoidname State}}{\*\xmlopen\xmlns2{\factoidname State}}Dover}{\rtlch\fcs1 \ai\af0\afs20 \ltrch\fcs0 
\i\f0\fs20\lang2057\langfe1040\langnp2057\insrsid15739037\charrsid11207973 {\*\xmlclose}, }{\rtlch\fcs1 \ai\af0\afs20 \ltrch\fcs0 \i\f0\fs20\lang2057\langfe1040\langnp2057\insrsid15739037 {\*\xmlopen\xmlns2{\factoidname State}}New York}{\rtlch\fcs1 
\ai\af0\afs20 \ltrch\fcs0 \i\f0\fs20\lang2057\langfe1040\langnp2057\insrsid15739037\charrsid11207973 {\*\xmlclose}{\*\xmlclose} (}{\rtlch\fcs1 \ai\af0\afs20 \ltrch\fcs0 \i\f0\fs20\lang2057\langfe1040\langnp2057\insrsid15739037 1968}{\rtlch\fcs1 
\ai\af0\afs20 \ltrch\fcs0 \i\f0\fs20\lang2057\langfe1040\langnp2057\insrsid15739037\charrsid11207973 )}{\rtlch\fcs1 \ai\af0\afs20 \ltrch\fcs0 \i\f0\fs20\lang2057\langfe1040\langnp2057\insrsid15739037 .}{\rtlch\fcs1 \ai\af39\afs20 \ltrch\fcs0 
\i\f39\fs20\lang2057\langfe1040\langnp2057\insrsid15466923\charrsid16190858 
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