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

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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