Biyolojik Dokulara Vurgu ile Şişirilmiş Hiperelastik bir Tüpün Mekaniği

Abstract

İçi boş bir silindirin şişirilmesi, mühendisliğin çeşitli alanlarında karşılaşılan önemli bir problemdir. Endüstride, araba lastikleri ve itfaiye hortumları içten basınçlandırılırlar. Biyomekanikte, damarlar ve intervertebral diskler de şişirilmiş silindir problemi kullanılarak modellenebilir. Bahsedilen biyolojik dokuların yumuşak yapısı sıkıştırılamazlar ve yük altında büyük, doğrusal olmayan deformasyon sergilerler. Klasik doğrusal elastik teoriler böyle bir davranışı modellemede yetersiz kalır. Bunun yerine, yumuşak malzemelerin deformasyonu ve mekaniğini anlamak için sürekli ortamlar mekaniği temelli yüksek yer değiştirme formülasyonları gereklidir. Bu çalışmada, izotropik neo-Hookean malzemeden meydana gelen hiperelastik bir tüp düzlemsel gerinim ve genelleştirilmiş düzlemsel gerinim koşulları altında analiz edilmiştir. İlk olarak, her iki koşul için sürekli ortamlar mekaniği çerçevesinde bir analitik çözüm inşa edilmiştir. Sonrasında, aynı problem için sonlu elemanlar yöntemi işleme konulmuştur. Nümerik modelin doğrulaması ağ hassasiyet analizi kullanılarak sağlanmıştır. Analitik çözüm ile doğrulanmıştır. Buradan, öne sürülen analitik çözüm ile herhangi bir ticari sonlu elemanlar yazılımı ile elde edilmiş şişirilen neo-Hookean bir tüpün davranış hassasiyeti belirlenebilecektir. Analitik çözümle gelen ilginç bir yan sonuç, tüpün içerisindeki hidrostatik basıncın şişirme basıncından altı kat fazla çıkması olmuştur.

Keywords

• Hiperelastisite
• Sürekli Ortamlar Mekaniği
• Sonlu Elemanlar Yöntemi
• Anüler Silindir
• Biyolojik Doku

MECHANICS OF A HYPERELASTIC INFLATED TUBE WITH EMPHASIS ON BIOLOGICAL SOFT TISSUES

Abstract

Inflated hollow cylinder is an important problem encountered in a variety of fields in engineering. In industry, tires and fire hoses are pressurized from inside. In biomechanics, veins, arteries and intervertebral discs can also be modeled using the inflated cylinder problem. The soft ground substance of biological tissues in question are incompressible and portray large non-linear deformations under loading. Classical theories of linear elasticity are incapable of modeling such behavior. Instead, continuum mechanics based large displacement formulation and hyperelasticity are necessary to understand the deformation and mechanics of soft materials. In this study, inflation of a cylinder composed of an isotropic neo-Hookean type of material is analyzed in plane strain and generalized plane strain conditions. First, an analytical solution is established using a continuum mechanical framework. Second, the finite element method is employed to model the same problem. The numerical approach is verified by using a mesh sensitivity analysis and validated by using analytical solution. Therefore, the proposed analytical benchmark can quantify the accuracy of any commercial finite element software solution of neo-Hookean tube inflation. As a side result, it was also revealed that the hydrostatic pressure in the tube is more than six times the inflation pressure.

Keywords

• Hyperelasticity
• Continuum Mechanics
• Finite Element Method
• Annular Cylinder
• Biological Tissue

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