Mustafa Reşit USAL, Ali Ünal ERDEM, Melek USAL

İzotropik matris malzemesi olan fiber takviyeli dielektrik viskoelastik ortamların elektro-termomekanik davranışı için matematiksel bir model

Bu çalışmada, matris malzemesi izotrop olan viskoelastik ve fiber-takviyeli dielektrik bir ortamın dış çevreden uygulanan elektro-mekanik yükler karşısındaki davranışı incelenmiştir. Matris malzemesi normalde izotrop bir ortam olup sırf fiber dağılımı nedeniyle yönlü bir ortam olma özelliği taşımaktadır. Bu bağlamda cisim davranış olarak kendisini elastik gerilme, dissipatif gerilme ve elektriksel polarizasyon tarzında ifade edecektir. Elektrostatik alanların etkisi yanında bünye teorisinin aksiyomları, özellikle objektivite ve maddesel simetri aksiyomları, ve malzemenin simetri grubuna ilişkin kavramlara dayanarak bünye fonksiyonelleri bulunurken gerek gerilme ve gerekse dissipatif gerilmenin argümanlarının somut olarak tayini için invaryantlar teorisine ait bulgular rutin bir yöntem olarak kullanılmıştır. Sonuç olarak; elastik gerilme, polarizasyon alanı ve dissipatif gerilmeye ait bünye denklemleri hem maddesel hem de uzaysal koordinatlarda elde edilmiş, simetrik ve asimetrik gerilmeler ise elastik gerilme, polarizasyon alanı ve dissipatif gerilme ifadelerini kullanarak yer değiştirme gradyanı ve türevi cinsinden bulunmuştur.

A mathematical model for the electro thermomechanical behavior of fiber-reinforced dielectric viscoelastic composites with isotropic matrix material

In this work a fiber-reinforced viscoelastic dielectric body with isotropic matrix material has been investigated with reference to its interaction with external electro-mechanical loading. Due to fiber distribution , overall structure attains a strong anisotropy, despite the fact that the matrix material is otherwise isotropic. In this context the body will respond by means of elastic stress, dissipative stres, and electric polarization. Besides fixing the effect of electrostatic forces , when working on the constitutive response functions; axioms of constitutive theory, in particular objectivity and material symmetry, have been used going through the isotropy group of the material when fixing invariant arguments of dissipative stress as well as elastic stress, all being based on the routine implementation of the theory of invariants. In the conclusion, constitutive response functions for the elastic stress, polarization, and dissipative stress have been obtained both in material coordinates and spatial coordinates, by the use of the expressions for the symmetric and asymmetric stress, polarization, and dissipative stress, with symmetric and asymmetric stress tensor having been obtained in terms of displacemet gradient and its material time derivatives.

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