ON DEVELOPING OF A THERMOELASTIC CONTINUUM DAMAGE MODEL FOR DIELECTRIC COMPOSITE MATERIALS

Year 2017, Volume: 9 Issue: 3, 33 - 54, 30.12.2017

Melek Usal

Abstract

This paper deals with developing a continuum damage mechanics model belonging to constitutive equations
which represent linear electro-thermo-elastic behavior of a composite material, where the material was
reinforced with arbitrarily distributed single fiber family and which have micro-cracks. The composite medium
is assumed to be dielectric, incompressible, homogeneous, and dependent on temperature gradient. The matrix
material made of elastic material involving an artificial anisotropy because of fibers reinforcing by arbitrary
distributions and the existence of micro-cracks, has been assumed as an isotropic medium. It is accepted that the
fiber family is inextensible. Using the basic laws, of continuum damage mechanics and continuum
electrodynamics and the equations belonging to kinematic of fiber, the constitutive functionals have been
obtained. It has been detected as a result of the thermodynamic constraints that stress potential function depends
on two symmetric tensors and two vectors, and the heat flux vector function depends on two symmetric tensors
and three vectors. To determine arguments of the constitutive functionals, findings relating to the theory of
invariants have been used as a method because of that isotropy constraint is imposed on the matrix material.
Finally, the constitutive equations of symmetric stress, polarization field, asymmetric stress, heat flux vector and
strain-energy density release rate have been written in material coordinates. 

Keywords

Electro-thermoelastic behavior, Continuum damage mechanics, Constitutive equations, Composite materials, Invariants

DİELEKTRİK KOMPOZİT MALZEMELER İÇİN BİR TERMOELASTİK SÜREKLİ ORTAM HASAR MODELİNİN GELİŞTİRİLMESİ ÜZERİNE

Abstract

Bu makale, keyfi dağılımlı tek fiber ailesi ile takviyeli ve mikro çatlaklara sahip bir kompozit malzemenin lineer
elektro-termo elastik davranışını temsil eden kurucu denklemlere ait bir sürekli ortam hasar mekaniği modeli
geliştirmeyi ele almaktadır. Kompozit ortamın dielektrik, sıkıştırılamaz, homojen olduğu ve sıcaklık gradyanına
bağlı olduğu varsayılmaktadır. Keyfi dağılımlı fiber takviyesi ve mikro çatlakların varlığı nedeniyle yapay bir
anizotropi içeren elastik malzemeden yapılmış matris malzemesi izotropik bir ortam olarak kabul edilmiştir.
Fiber ailesinin uzatılmaz olduğu kabul edilmektedir. Sürekli ortam hasar mekaniğinin ve sürekli ortam
elektrodinamiğinin temel kanunları ve süreklilik fiber kinematiğine ait denklemleri kullanılarak bünye
fonksiyonelleri elde edilmiştir. Termodinamik kısıtlamaların sonucu olarak, gerilme potansiyeli fonksiyonunun
iki simetrik tensör ve iki vektöre bağlı olduğu ve ısı akısı vektör fonksiyonunun ise iki simetrik tensör ve üç
vektöre bağlı olduğu belirlenmiştir. Bünye fonksiyonellerinin argümanlarını belirlemek için, invaryantlar
teorisine ilişkin bulgular, matris malzemesine uygulanan izotropi kısıtlaması nedeniyle bir yöntem olarak
kullanılmıştır. Sonunda, simetrik gerilmenin, polarizasyon alanının, asimetrik gerilmenin, ısı akısı vektörünün ve
gerinme-enerjisi yoğunluğunun değişim hızının bünye denklemleri maddesel koordinat sisteminde yazılmıştır. 

Keywords

: Elektro-termoelastik davranış, Sürekli Ortam Hasar Mekaniği, Bünye denklemleri, Kompozit malzemeler, İnvaryantlar

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