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- W2003604927 abstract "Mindlin's theory of elastic dielectrics with polarization gradient is used along with the values of material coefficients obtained by Askar et al. to solve two types of problems involving cylindrical and spherical cavities and a free linear crack in “plane-strain”. In the case of the two cavities the surface energy density of deformation and polarization is found to be changed by an amount directly proportional to a length parameter l1, of order of magnitude of the interatomic distance, and inversely proportional to the radius of curvature of the cavity. As for the crack a stress singularity of the order ε−½ as ε → 0 is obtained in the absence of any external forces. This singularity is of the same order as those given by classical elasticity and couple stress theories. However, the surface energy density of the crack surface is bounded. Для pacчeтa двyч типoв зaдaч кacaющичcя цилиндpичecкич и cфepичecкич тpeшин и cвoбoднoй линeйнoй щeли в плocкoм дeфopмиpoвaннoм cocтoянии, иcпoльзyeтcя тeopия Mиндлинa yпpyгич диэлeктpикoв и знaчeния кoэффициeнтoв мaтepиaлa, пoлyчeны Acкapoм, Ли и Kaкмaкoм, Для cлyчaя двyч тpeщин, плoтнocть пoвepчнocтнoй энepгии дeфopмaции и пoляpизaции oпpeдeляeтcя тaк, чтo oнa измeняeтcя пpocтo пpoпopциoнaльнo к пapaмeтpy длины l1 пppядкa вeличины мeждyaтoмнoгo paccмoяния и oбpaтнo пpoпopциoнaльнo к paдиycy кpивизны тpeщины, Taк, кaк для щeли пoлyчaeтcя cингyляpнocть пopядкa (ε−½ пpи (ϵ → 0 и пpи oтcyтcтвии вceч внeшнич cил. Этa cингyляpнocть oкaзывaeтcя тaкoгo жe caмoгo poдa, кaк cингyляpнocть, вытeкaющaя из тeopии yпpyгocти и тeopии мoмeнтныч нaпpяжeний. Ho oднaкo плoтнocть пoвepчнocтнoй энepгии oгpaничeнa нa пoвepчнocти щeли." @default.
- W2003604927 created "2016-06-24" @default.
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- W2003604927 date "1971-05-01" @default.
- W2003604927 modified "2023-10-16" @default.
- W2003604927 title "The effect of surface curvature and discontinuity on the surface energy density and other induced fields in elastic dielectrics with polarization gradient" @default.
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- W2003604927 doi "https://doi.org/10.1016/0020-7683(71)90103-x" @default.
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