{"id":10721,"date":"2021-03-12T14:00:22","date_gmt":"2021-03-12T12:00:22","guid":{"rendered":"http:\/\/www2.mie.uth.gr\/?page_id=10721"},"modified":"2025-09-26T09:21:48","modified_gmt":"2025-09-26T06:21:48","slug":"%ce%bc%cf%851100-%cf%83%cf%85%ce%bd%ce%b8%ce%b5%cf%84%ce%b1-%cf%85%ce%bb%ce%b9%ce%ba%ce%b1-%ce%b5%ce%ba2","status":"publish","type":"page","link":"https:\/\/mie.uth.gr\/?page_id=10721","title":{"rendered":"\u039c\u03a51100 \u03a3\u03a5\u039d\u0398\u0395\u03a4\u0391 \u03a5\u039b\u0399\u039a\u0391 (\u0395\u039a2)"},"content":{"rendered":"\t\t
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\u039c\u03a51100 \u03a3\u03a5\u039d\u0398\u0395\u03a4\u0391 \u03a5\u039b\u0399\u039a\u0391 (\u0395\u039a2)<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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\u039c\u03a51100 \u03a3\u03a5\u039d\u0398\u0395\u03a4\u0391 \u03a5\u039b\u0399\u039a\u0391 (\u0395\u039a2)<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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\u03a0\u03bb\u03b7\u03c1\u03bf\u03c6\u03bf\u03c1\u03af\u03b5\u03c2 \u039c\u03b1\u03b8\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t
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\u03a0\u03b5\u03c1\u03af\u03b3\u03c1\u03b1\u03bc\u03bc\u03b1 \u039c\u03b1\u03b8\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2<\/strong><\/span><\/a><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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\u039a\u03b1\u03c4\u03b7\u03b3\u03bf\u03c1\u03af\u03b1 \u039c\u03b1\u03b8\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2<\/strong>
\u03a4\u03cd\u03c0\u03bf\u03c2 \u039c\u03b1\u03b8\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2<\/strong>
\u039a\u03c9\u03b4\u03b9\u03ba\u03cc\u03c2 \u0393\u03c1\u03b1\u03bc\u03bc\u03b1\u03c4\u03b5\u03af\u03b1\u03c2<\/strong>
\u0395\u03be\u03ac\u03bc\u03b7\u03bd\u03bf<\/strong>
\u0394\u03b9\u03ac\u03c1\u03ba\u03b5\u03b9\u03b1<\/strong>
ECTS Units
\u03a4\u03bf\u03bc\u03ad\u03b1\u03c2
<\/strong>\u039a\u03b1\u03c4\u03b5\u03cd\u03b8\u03c5\u03bd\u03c3\u03b7<\/strong>
\u0394\u03b9\u03b4\u03ac\u03c3\u03ba\u03c9\u03bd<\/strong><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t

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\u03a0\u03c1\u03bf\u03c0\u03c4\u03c5\u03c7\u03b9\u03b1\u03ba\u03cc
\u0395\u039a2
\u039c\u03a51100
8\u03bf (\u0395\u03b1\u03c1\u03b9\u03bd\u03cc)
5 \u03ce\u03c1\u03b5\u03c2\/\u03b5\u03b2\u03b4\u03bf\u03bc\u03ac\u03b4\u03b1
6
\u039c\u03b7\u03c7\u03b1\u03bd\u03b9\u03ba\u03ae\u03c2, \u03a5\u03bb\u03b9\u03ba\u03ce\u03bd & \u039a\u03b1\u03c4\u03b5\u03c1\u03b3\u03b1\u03c3\u03b9\u03ce\u03bd
\u039c\u03b7\u03c7\u03b1\u03bd\u03b9\u03ba\u03ae, \u03a5\u03bb\u03b9\u03ba\u03ac & \u039a\u03b1\u03c4\u03b5\u03c1\u03b3\u03b1\u03c3\u03af\u03b5\u03c2\u00a0
\u0391\u03b3\u03cc\u03c1\u03b1\u03c2 \u039c\u03b9\u03c7\u03ac\u03bb\u03b7\u03c2<\/a><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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\u039a\u03b1\u03c4\u03b7\u03b3\u03bf\u03c1\u03af\u03b1 \u039c\u03b1\u03b8\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2: <\/strong>\u03a0\u03c1\u03bf\u03c0\u03c4\u03c5\u03c7\u03b9\u03b1\u03ba\u03cc
\u03a4\u03cd\u03c0\u03bf\u03c2 \u039c\u03b1\u03b8\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2: <\/strong>\u0395\u039a2
\u039a\u03c9\u03b4\u03b9\u03ba\u03cc\u03c2 \u0393\u03c1\u03b1\u03bc\u03bc\u03b1\u03c4\u03b5\u03af\u03b1\u03c2:\u00a0<\/strong>\u039c\u03a51100
\u0395\u03be\u03ac\u03bc\u03b7\u03bd\u03bf:\u00a0<\/strong>8\u03bf (\u0395\u03b1\u03c1\u03b9\u03bd\u03cc)
\u0394\u03b9\u03ac\u03c1\u03ba\u03b5\u03b9\u03b1:\u00a0<\/strong>5 \u03ce\u03c1\u03b5\u03c2\/\u03b5\u03b2\u03b4\u03bf\u03bc\u03ac\u03b4\u03b1
ECTS Units:\u00a0<\/strong>6
\u03a4\u03bf\u03bc\u03ad\u03b1\u03c2:\u00a0<\/strong>\u039c\u03b7\u03c7\u03b1\u03bd\u03b9\u03ba\u03ae\u03c2, \u03a5\u03bb\u03b9\u03ba\u03ce\u03bd & \u039a\u03b1\u03c4\u03b5\u03c1\u03b3\u03b1\u03c3\u03b9\u03ce\u03bd
\u039a\u03b1\u03c4\u03b5\u03cd\u03b8\u03c5\u03bd\u03c3\u03b7:\u00a0<\/strong>\u039c\u03b7\u03c7\u03b1\u03bd\u03b9\u03ba\u03ae, \u03a5\u03bb\u03b9\u03ba\u03ac & \u039a\u03b1\u03c4\u03b5\u03c1\u03b3\u03b1\u03c3\u03af\u03b5\u03c2
\u0394\u03b9\u03b4\u03ac\u03c3\u03ba\u03c9\u03bd:\u00a0<\/strong>\u0391\u03b3\u03cc\u03c1\u03b1\u03c2 \u039c\u03b9\u03c7\u03ac\u03bb\u03b7\u03c2<\/a><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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<\/i>\u03a3\u03ba\u03bf\u03c0\u03cc\u03c2<\/span><\/div>

\u03a4\u03bf \u03bc\u03ac\u03b8\u03b7\u03bc\u03b1 \u03b1\u03c5\u03c4\u03cc \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03b5\u03af \u03bc\u03b9\u03b1 \u03b5\u03b9\u03c3\u03b1\u03b3\u03c9\u03b3\u03ae \u03c3\u03c4\u03b9\u03c2 \u03b8\u03b5\u03bc\u03b5\u03bb\u03b9\u03ce\u03b4\u03b5\u03b9\u03c2 \u03b1\u03c1\u03c7\u03ad\u03c2 \u03ba\u03b1\u03b9 \u03bc\u03b5\u03b8\u03cc\u03b4\u03bf\u03c5\u03c2 \u03c4\u03b7\u03c2 \u0398\u03b5\u03c9\u03c1\u03af\u03b1\u03c2 \u03c4\u03c9\u03bd \u03a3\u03cd\u03bd\u03b8\u03b5\u03c4\u03c9\u03bd \u03a5\u03bb\u03b9\u03ba\u03ce\u03bd. \u0399\u03b4\u03b9\u03b1\u03af\u03c4\u03b5\u03c1\u03b7 \u03ad\u03bc\u03c6\u03b1\u03c3\u03b7 \u03b4\u03af\u03bd\u03b5\u03c4\u03b1\u03b9 \u03c3\u03c4\u03b9\u03c2 \u03b5\u03c6\u03b1\u03c1\u03bc\u03bf\u03b3\u03ad\u03c2 \u03bf\u03c1\u03b9\u03c3\u03bc\u03ad\u03bd\u03c9\u03bd \u03b5\u03c5\u03c1\u03ad\u03c9\u03c2 \u03b3\u03bd\u03c9\u03c3\u03c4\u03ce\u03bd \u03b1\u03bd\u03b1\u03bb\u03c5\u03c4\u03b9\u03ba\u03ce\u03bd \u03bb\u03cd\u03c3\u03b5\u03c9\u03bd \u03c3\u03b5 \u03c3\u03cd\u03bd\u03b8\u03b5\u03c4\u03b1 \u03c5\u03bb\u03b9\u03ba\u03ac \u03c0\u03c1\u03b1\u03ba\u03c4\u03b9\u03ba\u03bf\u03cd \u03ba\u03b1\u03b9 \u03c4\u03b5\u03c7\u03bd\u03bf\u03bb\u03bf\u03b3\u03b9\u03ba\u03bf\u03cd \u03b5\u03bd\u03b4\u03b9\u03b1\u03c6\u03ad\u03c1\u03bf\u03bd\u03c4\u03bf\u03c2, \u03c3\u03c5\u03bc\u03c0\u03b5\u03c1\u03b9\u03bb\u03b1\u03bc\u03b2\u03b1\u03bd\u03bf\u03bc\u03ad\u03bd\u03c9\u03bd \u03c4\u03c9\u03bd \u03b5\u03ba\u03c4\u03b9\u03bc\u03ae\u03c3\u03b5\u03c9\u03bd \u03c4\u03cd\u03c0\u03bf\u03c5 Hashin\ufffeShtrikman \u03b3\u03b9\u03b1 \u03c5\u03bb\u03b9\u03ba\u03ac \u03bc\u03b5 \u03c3\u03c9\u03bc\u03b1\u03c4\u03b9\u03b4\u03b9\u03b1\u03ba\u03ae \u03bc\u03b9\u03ba\u03c1\u03bf\u03b4\u03bf\u03bc\u03ae \u03ba\u03b1\u03b9 \u03c4\u03b7\u03c2 \u03b1\u03c5\u03c4\u03cc-\u03c3\u03c5\u03bd\u03b5\u03c0\u03bf\u03cd\u03c2 (self-consistent) \u03b5\u03ba\u03c4\u03b9\u03bc\u03ae\u03c3\u03b5\u03c9\u03c2 \u03b3\u03b9\u03b1 \u03c5\u03bb\u03b9\u03ba\u03ac \u03bc\u03b5 \u03ba\u03bf\u03ba\u03ba\u03ce\u03b4\u03b7 \u03bc\u03b9\u03ba\u03c1\u03bf\u03b4\u03bf\u03bc\u03ae.<\/p><\/div>\n\t\t\t\t\t<\/div>

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<\/i>\u03a0\u03b5\u03c1\u03b9\u03b5\u03c7\u03cc\u03bc\u03b5\u03bd\u03b1<\/span><\/div>
\u0395\u03b9\u03c3\u03b1\u03b3\u03c9\u03b3\u03ae<\/b>.<\/span> \u0392\u03b1\u03c3\u03b9\u03ba\u03ad\u03c2 \u03ad\u03bd\u03bd\u03bf\u03b9\u03b5\u03c2 \u03ba\u03b1\u03b9 \u03bf\u03c1\u03b9\u03c3\u03bc\u03bf\u03af. \u039a\u03b1\u03c1\u03c4\u03b5\u03c3\u03b9\u03b1\u03bd\u03bf\u03af \u03c4\u03b1\u03bd\u03c5\u03c3\u03c4\u03ad\u03c2. \u039a\u03c5\u03c1\u03c4\u03ad\u03c2 \u03c3\u03c5\u03bd\u03b1\u03c1\u03c4\u03ae\u03c3\u03b5\u03b9\u03c2 \u03ba\u03b1\u03b9 \u03bf \u03bc\u03b5\u03c4\u03b1\u03c3\u03c7\u03b7\u03bc\u03b1\u03c4\u03b9\u03c3\u03bc\u03cc\u03c2 Legendre-Fenchel.\u00a0 \u039a\u03b1\u03c4\u03b1\u03c3\u03c4\u03b1\u03c4\u03b9\u03ba\u03ad\u03c2 \u03b5\u03be\u03b9\u03c3\u03ce\u03c3\u03b5\u03b9\u03c2: \u03b3\u03c1\u03b1\u03bc\u03bc\u03b9\u03ba\u03ae \u03ba\u03b1\u03b9 \u03bc\u03b7 \u03b3\u03c1\u03b1\u03bc\u03bc\u03b9\u03ba\u03ae \u03b5\u03bb\u03b1\u03c3\u03c4\u03b9\u03ba\u03cc\u03c4\u03b7\u03c4\u03b1, \u03b9\u03be\u03c9\u03b4\u03bf\u03c0\u03bb\u03b1\u03c3\u03c4\u03b9\u03ba\u03cc\u03c4\u03b7\u03c4\u03b1, \u03c0\u03bb\u03b1\u03c3\u03c4\u03b9\u03ba\u03cc\u03c4\u03b7\u03c4\u03b1. \u03a3\u03c5\u03bc\u03bc\u03b5\u03c4\u03c1\u03af\u03b5\u03c2 (\u03b1\u03bd\u03b9\u03c3\u03bf\u03c4\u03c1\u03bf\u03c0\u03af\u03b1) \u03c4\u03c9\u03bd \u03c5\u03bb\u03b9\u03ba\u03ce\u03bd: \u03bf\u03c1\u03b8\u03bf\u03c4\u03c1\u03bf\u03c0\u03af\u03b1, \u03b5\u03b3\u03ba\u03ac\u03c1\u03c3\u03b9\u03b1 \u03b9\u03c3\u03bf\u03c4\u03c1\u03bf\u03c0\u03af\u03b1, \u03b9\u03c3\u03bf\u03c4\u03c1\u03bf\u03c0\u03af\u03b1. \u0391\u03bd\u03b1\u03bb\u03bb\u03bf\u03af\u03c9\u03c4\u03b5\u03c2 \u03c3\u03c5\u03bd\u03b1\u03c1\u03c4\u03ae\u03c3\u03b5\u03b9\u03c2. \u03a3\u03c5\u03bd\u03b8\u03ae\u03ba\u03b5\u03c2 \u03c3\u03c4\u03b1\u03c4\u03b9\u03ba\u03ae\u03c2 \u03b9\u03c3\u03bf\u03c1\u03c1\u03bf\u03c0\u03af\u03b1\u03c2 \u03b5\u03c4\u03b5\u03c1\u03bf\u03b3\u03b5\u03bd\u03ce\u03bd \u03c3\u03c9\u03bc\u03ac\u03c4\u03c9\u03bd: \u03b5\u03be\u03b9\u03c3\u03ce\u03c3\u03b5\u03b9\u03c2 \u03c0\u03b5\u03b4\u03af\u03bf\u03c5 \u03ba\u03b1\u03b9 \u03b1\u03c1\u03c7\u03ad\u03c2 \u03bb\u03bf\u03b3\u03b9\u03c3\u03bc\u03bf\u03cd \u03c4\u03c9\u03bd \u03bc\u03b5\u03c4\u03b1\u03b2\u03bf\u03bb\u03ce\u03bd (variational principles).\u00a0<\/div>
\u00a0<\/div>
\u039f\u03bc\u03bf\u03b3\u03b5\u03bd\u03bf\u03c0\u03bf\u03af\u03b7\u03c3\u03b7<\/b>.<\/span> \u0397 \u03ad\u03bd\u03bd\u03bf\u03b9\u03b1 \u03c4\u03bf\u03c5 \u03b1\u03bd\u03c4\u03b9\u03c0\u03c1\u03bf\u03c3\u03c9\u03c0\u03b5\u03c5\u03c4\u03b9\u03ba\u03bf\u03cd \u03c3\u03c4\u03bf\u03b9\u03c7\u03b5\u03af\u03bf\u03c5 \u03cc\u03b3\u03ba\u03bf\u03c5. \u03a0\u03b5\u03c1\u03b9\u03bf\u03b4\u03b9\u03ba\u03ad\u03c2 \u03ba\u03b1\u03b9 \u03c4\u03c5\u03c7\u03b1\u03af\u03b5\u03c2 \u03bc\u03b9\u03ba\u03c1\u03bf\u03b4\u03bf\u03bc\u03ad\u03c2. \u039f\u03bc\u03bf\u03b3\u03b5\u03bd\u03bf\u03c0\u03bf\u03b9\u03b7\u03bc\u03ad\u03bd\u03b7 (\u03ae \u03bc\u03b1\u03ba\u03c1\u03bf\u03c3\u03ba\u03bf\u03c0\u03b9\u03ba\u03ae) \u03c3\u03c5\u03bc\u03c0\u03b5\u03c1\u03b9\u03c6\u03bf\u03c1\u03ac \u03c4\u03c9\u03bd \u03c3\u03cd\u03bd\u03b8\u03b5\u03c4\u03c9\u03bd \u03c5\u03bb\u03b9\u03ba\u03ce\u03bd. \u03a4\u03b1 \u03ba\u03bb\u03b1\u03c3\u03b9\u03ba\u03ac \u03c6\u03c1\u03ac\u03b3\u03bc\u03b1\u03c4\u03b1 \u03c4\u03c9\u03bd Voigt \u03ba\u03b1\u03b9 Reuss. \u03a3\u03c4\u03b1\u03c4\u03b9\u03c3\u03c4\u03b9\u03ba\u03ae \u03c0\u03b5\u03b4\u03af\u03c9\u03bd.<\/div>
\u00a0<\/div>
\u039f\u03c1\u03b9\u03c3\u03bc\u03ad\u03bd\u03b5\u03c2 \u03b1\u03ba\u03c1\u03b9\u03b2\u03b5\u03af\u03c2 \u03bb\u03cd\u03c3\u03b5\u03b9\u03c2<\/b>.<\/span> \u03a3\u03cd\u03bd\u03b8\u03b5\u03c4\u03b1 \u03c5\u03bb\u03b9\u03ba\u03ac \u03bc\u03b5 \u03b1\u03c0\u03bb\u03ad\u03c2 \u03ae \u03b9\u03b5\u03c1\u03b1\u03c1\u03c7\u03b9\u03ba\u03ad\u03c2 \u03c3\u03c4\u03c1\u03c9\u03bc\u03b1\u03c4\u03ce\u03b4\u03b5\u03b9\u03c2 \u03bc\u03b9\u03ba\u03c1\u03bf\u03b4\u03bf\u03bc\u03ad\u03c2 (laminates). \u03a4\u03b1 \u03c3\u03cd\u03bd\u03bf\u03bb\u03b1 \u03c4\u03c9\u03bd \u03cc\u03bc\u03bf\u03b9\u03c9\u03bd, \u03c3\u03cd\u03bd\u03b8\u03b5\u03c4\u03c9\u03bd, \u03c3\u03c6\u03b1\u03b9\u03c1\u03b9\u03ba\u03ce\u03bd \u03ae \u03ba\u03c5\u03bb\u03b9\u03bd\u03b4\u03c1\u03b9\u03ba\u03ce\u03bd \u03c3\u03c4\u03bf\u03b9\u03c7\u03b5\u03af\u03c9\u03bd (assemblages of composite spheres or cylinders) \u03c4\u03bf\u03c5 Hashin.<\/div>
\u00a0<\/div>
\u03a3\u03cd\u03bd\u03b8\u03b5\u03c4\u03b1 \u03c5\u03bb\u03b9\u03ba\u03ac \u03bc\u03b5 \u03b3<\/b>\u03c1\u03b1\u03bc\u03bc\u03b9\u03ba\u03ac \u03b5\u03bb\u03b1\u03c3\u03c4\u03b9\u03ba\u03ad\u03c2 \u03c6\u03ac\u03c3\u03b5\u03b9\u03c2<\/b>.<\/span> \u0397 \u03bf\u03bb\u03bf\u03ba\u03bb\u03b7\u03c1\u03c9\u03c4\u03b9\u03ba\u03ae \u03bc\u03bf\u03c1\u03c6\u03ae \u03c4\u03bf\u03c5 \u03c0\u03c1\u03bf\u03b2\u03bb\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2 \u03bf\u03bc\u03bf\u03b3\u03b5\u03bd\u03bf\u03c0\u03bf\u03af\u03b7\u03c3\u03b7\u03c2. \u03a4\u03bf \u03c0\u03c1\u03cc\u03b2\u03bb\u03b7\u03bc\u03b1 Eshelby. \u03a3\u03cd\u03bd\u03b8\u03b5\u03c4\u03b1 \u03c5\u03bb\u03b9\u03ba\u03ac \u03bc\u03b5 \u03b1\u03c1\u03b1\u03b9\u03ad\u03c2 \u03c3\u03c5\u03b3\u03ba\u03b5\u03bd\u03c4\u03c1\u03ce\u03c3\u03b5\u03b9\u03c2 \u03c3\u03c9\u03bc\u03b1\u03c4\u03b9\u03b4\u03af\u03c9\u03bd. \u039f\u03b9 \u03b1\u03c1\u03c7\u03ad\u03c2 \u03bb\u03bf\u03b3\u03b9\u03c3\u03bc\u03bf\u03cd \u03c4\u03c9\u03bd \u03bc\u03b5\u03c4\u03b1\u03b2\u03bf\u03bb\u03ce\u03bd Hashin-Shtrikman. \u03a5\u03bb\u03b9\u03ba\u03ac \u03bc\u03b5 \u03c4\u03c5\u03c7\u03b1\u03af\u03b5\u03c2 \u03bc\u03b9\u03ba\u03c1\u03bf\u03b4\u03bf\u03bc\u03ad\u03c2. \u0399\u03c3\u03cc\u03c4\u03c1\u03bf\u03c0\u03b5\u03c2 \u03bc\u03b9\u03ba\u03c1\u03bf\u03b4\u03bf\u03bc\u03ad\u03c2: \u03c4\u03b1 \u03c6\u03c1\u03ac\u03b3\u03bc\u03b1\u03c4\u03b1 Hashin-Shtrikman. \u0395\u03bb\u03bb\u03b5\u03b9\u03c8\u03bf\u03b5\u03b9\u03b4\u03b5\u03af\u03c2 \u03bc\u03b9\u03ba\u03c1\u03bf\u03b4\u03bf\u03bc\u03ad\u03c2: \u03c4\u03b1 \u03c6\u03c1\u03ac\u03b3\u03bc\u03b1\u03c4\u03b1 Willis. \u03a3\u03c9\u03bc\u03b1\u03c4\u03b9\u03b4\u03b9\u03b1\u03ba\u03ad\u03c2 (particulate) \u03bc\u03b9\u03ba\u03c1\u03bf\u03b4\u03bf\u03bc\u03ad\u03c2: \u03b5\u03ba\u03c4\u03b9\u03bc\u03ae\u03c3\u03b5\u03b9\u03c2 Ponte Castaneda \u03ba\u03b1\u03b9 Willis. \u039a\u03bf\u03ba\u03ba\u03ce\u03b4\u03b5\u03b9\u03c2 (granular) \u03bc\u03b9\u03ba\u03c1\u03bf\u03b4\u03bf\u03bc\u03ad\u03c2: \u03b7 \u03b1\u03c5\u03c4\u03bf\u03c3\u03c5\u03bd\u03b5\u03c0\u03ae\u03c2 (self-consistent) \u03b5\u03ba\u03c4\u03af\u03bc\u03b7\u03c3\u03b7.\u00a0<\/div>
\u00a0<\/div>
\u0395\u03c6\u03b1\u03c1\u03bc\u03bf\u03b3\u03ad\u03c2<\/b>.<\/span> \u0397 \u03b5\u03c0\u03af\u03b4\u03c1\u03b1\u03c3\u03b7\u03c2 \u03c4\u03b7\u03c2 \u03bc\u03b9\u03ba\u03c1\u03bf\u03b4\u03bf\u03bc\u03ae\u03c2 \u03ba\u03b1\u03b9 \u03c4\u03c9\u03bd \u03b9\u03b4\u03b9\u03bf\u03c4\u03ae\u03c4\u03c9\u03bd \u03c4\u03c9\u03bd \u03c6\u03ac\u03c3\u03b5\u03c9\u03bd \u03c3\u03c4\u03b7 \u03bc\u03b1\u03ba\u03c1\u03bf\u03c3\u03ba\u03bf\u03c0\u03b9\u03ba\u03ae \u03b1\u03c0\u03cc\u03ba\u03c1\u03b9\u03c3\u03b7 \u03c3\u03cd\u03bd\u03b8\u03b5\u03c4\u03c9\u03bd \u03c5\u03bb\u03b9\u03ba\u03ce\u03bd \u03bc\u03b5 \u03c3\u03c9\u03bc\u03b1\u03c4\u03b9\u03b4\u03b9\u03b1\u03ba\u03ad\u03c2 (particulate), \u03c3\u03c4\u03c1\u03c9\u03bc\u03b1\u03c4\u03ce\u03b4\u03b5\u03b9\u03c2 (lamellar), \u03b9\u03bd\u03ce\u03b4\u03b5\u03b9\u03c2 (fibrous) \u03ba\u03b1\u03b9 \u03ba\u03bf\u03ba\u03ba\u03ce\u03b4\u03b5\u03b9\u03c2 (granular) \u03bc\u03b9\u03ba\u03c1\u03bf\u03b4\u03bf\u03bc\u03ad\u03c2.<\/div><\/div><\/div>\n\t\t\t\t\t<\/div>
\n\t\t\t\t\t
<\/i>\u0392\u03b9\u03b2\u03bb\u03b9\u03bf\u03b3\u03c1\u03b1\u03c6\u03af\u03b1<\/span><\/div>

\u03a0\u03c1\u03bf\u03c4\u03b5\u03b9\u03bd\u03cc\u03bc\u03b5\u03bd\u03b7 \u0392\u03b9\u03b2\u03bb\u03b9\u03bf\u03b3\u03c1\u03b1\u03c6\u03af\u03b1:<\/strong><\/span><\/p>

  • Ponte Castaneda, P., Heterogeneous Materials, Lecture Notes, 2005.<\/li>
  • Willis, J.R., Mechanics of Composite Materials, Lecture Notes, 2002.<\/li>
  • Milton, G. W., Theory of Composites, Cambridge University Press, 2002.<\/li>
  • \u00a0Christensen, R. M., Mechanics of Composite Materials, New York: Wiley-Interscience, 1979.<\/li>
  • Torquato, S., Random Heterogeneous Materials: Microstructure and Macroscopic Properties,
    Springer, 2002.<\/li><\/ul>

    \u00a0\u03a3\u03c5\u03bd\u03b1\u03c6\u03ae \u03b5\u03c0\u03b9\u03c3\u03c4\u03b7\u03bc\u03bf\u03bd\u03b9\u03ba\u03ac \u03c0\u03b5\u03c1\u03b9\u03bf\u03b4\u03b9\u03ba\u03ac:<\/strong><\/span><\/p>

    • Journal of the Mechanics and Physics of Solids<\/li>
    • International Journal of Solids and Structures<\/li>
    • Advances in Applied Mechanics<\/li><\/ul><\/div>\n\t\t\t\t\t<\/div>
      \n\t\t\t\t\t
      <\/i>\u0393\u03bb\u03ce\u03c3\u03c3\u03b1 \u0394\u03b9\u03b4\u03b1\u03c3\u03ba\u03b1\u03bb\u03af\u03b1\u03c2<\/span><\/div>

      \u0395\u03bb\u03bb\u03b7\u03bd\u03b9\u03ba\u03ae<\/p><\/div>\n\t\t\t\t\t<\/div>

      \n\t\t\t\t\t
      <\/i>\u039c\u03ad\u03b8\u03bf\u03b4\u03bf\u03c2 \u0394\u03b9\u03b4\u03b1\u03c3\u03ba\u03b1\u03bb\u03af\u03b1\u03c2<\/span><\/div>

      \u0394\u03b9\u03b1\u03bb\u03ad\u03be\u03b5\u03b9\u03c2<\/p><\/div>\n\t\t\t\t\t<\/div>

      \n\t\t\t\t\t
      <\/i>\u0391\u03be\u03b9\u03bf\u03bb\u03cc\u03b3\u03b7\u03c3\u03b7<\/span><\/div>

      \u00a0<\/p>
      \u0393\u03c1\u03b1\u03c0\u03c4\u03ae \u03a4\u03b5\u03bb\u03b9\u03ba\u03ae \u0395\u03be\u03ad\u03c4\u03b1\u03c3\u03b7:<\/strong><\/td>50%<\/td><\/tr>
      \u0393\u03c1\u03b1\u03c0\u03c4\u03ad\u03c2 \u03b5\u03c1\u03b3\u03b1\u03c3\u03af\u03b5\u03c2<\/strong><\/td>30%<\/td><\/tr>
      \u03a0\u03c1\u03bf\u03c6\u03bf\u03c1\u03b9\u03ba\u03ae \u03c0\u03b1\u03c1\u03bf\u03c5\u03c3\u03af\u03b1\u03c3\u03b7 \u03bf\u03bc\u03b1\u03b4\u03b9\u03ba\u03ae\u03c2 \u03b5\u03c1\u03b3\u03b1\u03c3\u03af\u03b1\u03c2<\/strong><\/td>20%<\/td><\/tr><\/tbody><\/table><\/div>\n\t\t\t\t\t<\/div>
      \n\t\t\t\t\t
      <\/i>\u03a6\u03cc\u03c1\u03c4\u03bf\u03c2 \u0395\u03c1\u03b3\u03b1\u03c3\u03af\u03b1\u03c2 (\u03c3\u03b5 \u03ce\u03c1\u03b5\u03c2)<\/span><\/div>
      \u0394\u03c1\u03b1\u03c3\u03c4\u03b7\u03c1\u03b9\u03cc\u03c4\u03b7\u03c4\u03b1<\/strong><\/td>\u03a6\u03cc\u03c1\u03c4\u03bf\u03c2 \u0395\u03c1\u03b3\u03b1\u03c3\u03af\u03b1\u03c2 \u0395\u03be\u03b1\u03bc\u03ae\u03bd\u03bf\u03c5<\/strong><\/td><\/tr>
      \u0394\u03b9\u03b1\u03bb\u03ad\u03be\u03b5\u03b9\u03c2<\/td>70<\/td><\/tr>
      \u0395\u03c1\u03b3\u03b1\u03c3\u03af\u03b5\u03c2<\/td>35<\/td><\/tr>
      \u0391\u03c5\u03c4\u03bf\u03c4\u03b5\u03bb\u03ae\u03c2 \u039c\u03b5\u03bb\u03ad\u03c4\u03b7<\/td>45<\/td><\/tr>
      \u03a3\u03cd\u03bd\u03bf\u03bb\u03bf \u03bc\u03b1\u03b8\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2 (25 \u03ce\u03c1\u03b5\u03c2 \u03c6\u03cc\u03c1\u03c4\u03bf\u03c5 \u03b5\u03c1\u03b3\u03b1\u03c3\u03af\u03b1\u03c2 \u03b1\u03bd\u03ac \u03c0\u03b9\u03c3\u03c4\u03c9\u03c4\u03b9\u03ba\u03ae \u03bc\u03bf\u03bd\u03ac\u03b4\u03b1)<\/strong><\/td>150<\/strong><\/td><\/tr><\/tbody><\/table>

      \u00a0<\/p><\/div>\n\t\t\t\t\t<\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"

      \u039c\u03a51100 \u03a3\u03a5\u039d\u0398\u0395\u03a4\u0391 \u03a5\u039b\u0399\u039a\u0391 (\u0395\u039a2) \u039c\u03a51100 \u03a3\u03a5\u039d\u0398\u0395\u03a4\u0391 \u03a5\u039b\u0399\u039a\u0391 (\u0395\u039a2) \u03a0\u03bb\u03b7\u03c1\u03bf\u03c6\u03bf\u03c1\u03af\u03b5\u03c2 \u039c\u03b1\u03b8\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2 \u03a0\u03b5\u03c1\u03af\u03b3\u03c1\u03b1\u03bc\u03bc\u03b1 \u039c\u03b1\u03b8\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2 \u039a\u03b1\u03c4\u03b7\u03b3\u03bf\u03c1\u03af\u03b1 \u039c\u03b1\u03b8\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2\u03a4\u03cd\u03c0\u03bf\u03c2 \u039c\u03b1\u03b8\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2\u039a\u03c9\u03b4\u03b9\u03ba\u03cc\u03c2 \u0393\u03c1\u03b1\u03bc\u03bc\u03b1\u03c4\u03b5\u03af\u03b1\u03c2\u0395\u03be\u03ac\u03bc\u03b7\u03bd\u03bf\u0394\u03b9\u03ac\u03c1\u03ba\u03b5\u03b9\u03b1ECTS Units\u03a4\u03bf\u03bc\u03ad\u03b1\u03c2\u039a\u03b1\u03c4\u03b5\u03cd\u03b8\u03c5\u03bd\u03c3\u03b7\u0394\u03b9\u03b4\u03ac\u03c3\u03ba\u03c9\u03bd \u03a0\u03c1\u03bf\u03c0\u03c4\u03c5\u03c7\u03b9\u03b1\u03ba\u03cc\u0395\u039a2\u039c\u03a511008\u03bf (\u0395\u03b1\u03c1\u03b9\u03bd\u03cc)5 \u03ce\u03c1\u03b5\u03c2\/\u03b5\u03b2\u03b4\u03bf\u03bc\u03ac\u03b4\u03b16\u039c\u03b7\u03c7\u03b1\u03bd\u03b9\u03ba\u03ae\u03c2, \u03a5\u03bb\u03b9\u03ba\u03ce\u03bd & \u039a\u03b1\u03c4\u03b5\u03c1\u03b3\u03b1\u03c3\u03b9\u03ce\u03bd\u039c\u03b7\u03c7\u03b1\u03bd\u03b9\u03ba\u03ae, \u03a5\u03bb\u03b9\u03ba\u03ac & \u039a\u03b1\u03c4\u03b5\u03c1\u03b3\u03b1\u03c3\u03af\u03b5\u03c2\u00a0\u0391\u03b3\u03cc\u03c1\u03b1\u03c2 \u039c\u03b9\u03c7\u03ac\u03bb\u03b7\u03c2 \u039a\u03b1\u03c4\u03b7\u03b3\u03bf\u03c1\u03af\u03b1 \u039c\u03b1\u03b8\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2: \u03a0\u03c1\u03bf\u03c0\u03c4\u03c5\u03c7\u03b9\u03b1\u03ba\u03cc\u03a4\u03cd\u03c0\u03bf\u03c2<\/p>\n","protected":false},"author":1,"featured_media":9407,"parent":8475,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-10721","page","type-page","status-publish","has-post-thumbnail","hentry"],"acf":[],"yoast_head":"\n\u039c\u03a51100 \u03a3\u03a5\u039d\u0398\u0395\u03a4\u0391 \u03a5\u039b\u0399\u039a\u0391 (\u0395\u039a2) - \u03a4\u03bc\u03ae\u03bc\u03b1 \u039c\u03b7\u03c7\u03b1\u03bd\u03bf\u03bb\u03cc\u03b3\u03c9\u03bd \u039c\u03b7\u03c7\u03b1\u03bd\u03b9\u03ba\u03ce\u03bd<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mie.uth.gr\/?page_id=10721\" \/>\n<meta property=\"og:locale\" content=\"el_GR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u039c\u03a51100 \u03a3\u03a5\u039d\u0398\u0395\u03a4\u0391 \u03a5\u039b\u0399\u039a\u0391 (\u0395\u039a2) - \u03a4\u03bc\u03ae\u03bc\u03b1 \u039c\u03b7\u03c7\u03b1\u03bd\u03bf\u03bb\u03cc\u03b3\u03c9\u03bd \u039c\u03b7\u03c7\u03b1\u03bd\u03b9\u03ba\u03ce\u03bd\" \/>\n<meta property=\"og:description\" content=\"\u039c\u03a51100 \u03a3\u03a5\u039d\u0398\u0395\u03a4\u0391 \u03a5\u039b\u0399\u039a\u0391 (\u0395\u039a2) \u039c\u03a51100 \u03a3\u03a5\u039d\u0398\u0395\u03a4\u0391 \u03a5\u039b\u0399\u039a\u0391 (\u0395\u039a2) \u03a0\u03bb\u03b7\u03c1\u03bf\u03c6\u03bf\u03c1\u03af\u03b5\u03c2 \u039c\u03b1\u03b8\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2 \u03a0\u03b5\u03c1\u03af\u03b3\u03c1\u03b1\u03bc\u03bc\u03b1 \u039c\u03b1\u03b8\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2 \u039a\u03b1\u03c4\u03b7\u03b3\u03bf\u03c1\u03af\u03b1 \u039c\u03b1\u03b8\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2\u03a4\u03cd\u03c0\u03bf\u03c2 \u039c\u03b1\u03b8\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2\u039a\u03c9\u03b4\u03b9\u03ba\u03cc\u03c2 \u0393\u03c1\u03b1\u03bc\u03bc\u03b1\u03c4\u03b5\u03af\u03b1\u03c2\u0395\u03be\u03ac\u03bc\u03b7\u03bd\u03bf\u0394\u03b9\u03ac\u03c1\u03ba\u03b5\u03b9\u03b1ECTS Units\u03a4\u03bf\u03bc\u03ad\u03b1\u03c2\u039a\u03b1\u03c4\u03b5\u03cd\u03b8\u03c5\u03bd\u03c3\u03b7\u0394\u03b9\u03b4\u03ac\u03c3\u03ba\u03c9\u03bd \u03a0\u03c1\u03bf\u03c0\u03c4\u03c5\u03c7\u03b9\u03b1\u03ba\u03cc\u0395\u039a2\u039c\u03a511008\u03bf (\u0395\u03b1\u03c1\u03b9\u03bd\u03cc)5 \u03ce\u03c1\u03b5\u03c2\/\u03b5\u03b2\u03b4\u03bf\u03bc\u03ac\u03b4\u03b16\u039c\u03b7\u03c7\u03b1\u03bd\u03b9\u03ba\u03ae\u03c2, \u03a5\u03bb\u03b9\u03ba\u03ce\u03bd & \u039a\u03b1\u03c4\u03b5\u03c1\u03b3\u03b1\u03c3\u03b9\u03ce\u03bd\u039c\u03b7\u03c7\u03b1\u03bd\u03b9\u03ba\u03ae, \u03a5\u03bb\u03b9\u03ba\u03ac & \u039a\u03b1\u03c4\u03b5\u03c1\u03b3\u03b1\u03c3\u03af\u03b5\u03c2\u00a0\u0391\u03b3\u03cc\u03c1\u03b1\u03c2 \u039c\u03b9\u03c7\u03ac\u03bb\u03b7\u03c2 \u039a\u03b1\u03c4\u03b7\u03b3\u03bf\u03c1\u03af\u03b1 \u039c\u03b1\u03b8\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2: \u03a0\u03c1\u03bf\u03c0\u03c4\u03c5\u03c7\u03b9\u03b1\u03ba\u03cc\u03a4\u03cd\u03c0\u03bf\u03c2\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mie.uth.gr\/?page_id=10721\" \/>\n<meta property=\"og:site_name\" content=\"\u03a4\u03bc\u03ae\u03bc\u03b1 \u039c\u03b7\u03c7\u03b1\u03bd\u03bf\u03bb\u03cc\u03b3\u03c9\u03bd \u039c\u03b7\u03c7\u03b1\u03bd\u03b9\u03ba\u03ce\u03bd\" \/>\n<meta property=\"article:modified_time\" content=\"2025-09-26T06:21:48+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mie.uth.gr\/wp-content\/uploads\/2021\/02\/SquarePlaceholder150.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"150\" \/>\n\t<meta property=\"og:image:height\" content=\"150\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u0395\u03ba\u03c4\u03b9\u03bc\u03ce\u03bc\u03b5\u03bd\u03bf\u03c2 \u03c7\u03c1\u03cc\u03bd\u03bf\u03c2 \u03b1\u03bd\u03ac\u03b3\u03bd\u03c9\u03c3\u03b7\u03c2\" \/>\n\t<meta name=\"twitter:data1\" content=\"3 \u03bb\u03b5\u03c0\u03c4\u03ac\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/mie.uth.gr\\\/?page_id=10721\",\"url\":\"https:\\\/\\\/mie.uth.gr\\\/?page_id=10721\",\"name\":\"\u039c\u03a51100 \u03a3\u03a5\u039d\u0398\u0395\u03a4\u0391 \u03a5\u039b\u0399\u039a\u0391 (\u0395\u039a2) - 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