Evaluation of Hyperelastic Material Properties of Sheep Anterior Cruciate Ligament by In-Vitro and 3D Finite Element Analysis

Öz

Modeling of ligament tissues in computer simulations in biomechanics is important for achieving the simulation anatomically. These are often described as hyperelastic materials in these types of studies. However, in order to be defined as a hyperelastic material, a mathematical material model created with data obtained from tests such as tension, compression, and creep is needed. There are many phenomenological models that can be used as material models. In this study, ligament tissue simulation was created according to Neo-Hookean, Ogden 2nd Order and Yeoh 2nd Order hyperelastic material models. In-vitro uniaxial tensile testing of sheep anterior cruciate ligament was performed for data on the stressstrain curve to be used by the models. According to the data obtained from the tensile test, the material constants required for the material models were calculated. As a result of the analysis, it was determined that Ogden 2nd Order and Yeoh 2nd Order models were close results and Neo-Hookean model gave results with different stress values. The fit of the stress-strain curves obtained from three models and in-vitro test was evaluated according to the Root Mean Square Error(RMSE) values. RMSE values of Neo-Hookean, Ogden 2nd Order and Yeoh 2nd Order hyperelastic material models were obtained as 4.9597, 1.9704 and 2.3644, respectively. As a result, the Ogden 2nd Order hyperelastic material model with a high number of material constants produced results closer to in-vitro test results compared to both normal and von-mises stress values and RMSE values. Among the three models analyzed for simulations of ligament tissue, it was determined that the use of this material model was more appropriate.

Anahtar Kelimeler

• Biomechanics
• Sheep Anterior Cruciate Ligament
• Hyperelasticity
• Finite Element Method

Koyun Ön Çapraz Bağının Hiperelastik Malzeme Özelliklerinin In-Vitro ve 3 Boyutlu Sonlu Elemanlar Analizi ile Değerlendirilmesi

Öz

Biyomekanik alanındaki bilgisayar simülasyonlarında bağ dokularının modellenmesi simülasyonun anatomiye uygun olarak başarılması için önemlidir. Bağ dokuları, bu tip çalışmalarda çoğunlukla hiperelastik malzeme olarak tanımlanırlar. Ancak hiperelastik malzeme olarak tanımlanması için çekme, basma, sürünme vb. gibi testlerden elde edilmiş verilerle oluşturulan bir matematiksel malzeme modeline ihtiyaç vardır. Malzeme modeli olarak kullanılabilecek birçok fenomenolojik model bulunmaktadır. Bu çalışmada, bağ dokusunun simülasyonu, Neo-Hookean, Ogden 2. Derece ve Yeoh 2. Derece hiperelastik malzeme modellerine göre oluşturulmuştur. Modellerin kullanacağı gerilme-birim şekil değiştirme eğrisi verileri için koyun ön çapraz bağının in-vitro olarak tek eksenli çekme deneyi yapılmıştır. Deneyden elde edilen verilere göre malzeme modelleri için gerekli olan malzeme sabitleri hesaplanmıştır. Yapılan analizler sonucunda bağ dokusunda, Ogden 2. Derece ve Yeoh 2. Derece modellerinin birbirine yakın, Neo-Hookean modelinin ise farklı gerilme değerlerine sahip sonuçlar verdiği belirlenmiştir. Üç modelden ve in-vitro testten elde edilen gerilme-birim şekil değiştirme eğrilerinin uyumu Kök Ortalama Kare Hatası(RMSE) değerlerine göre değerlendirilmiştir. Neo-Hookean, Ogden 2. Derece ve Yeoh 2. Derece hiperelastik malzeme modellerinin RMSE değerleri sırasıyla 4.9597, 1.9704 ve 2.3644 olarak elde edilmiştir. Sonuç olarak, malzeme sabiti sayısı fazla olan Ogden 2. Derece hiperelastik malzeme modeli hem normal ve vonmises gerilme değerlerine hem de RMSE değerlerine göre in-vitro test sonuçlarına daha yakın sonuçlar üretmiştir. Bağ dokusunu simülasyonları için analiz edilen üç model arasında bu malzeme modelinin kullanımının daha uygun olduğu belirlenmiştir.

Anahtar Kelimeler

• Biyomekanik
• Koyun Ön Çapraz Bağı
• Hiperelastisite
• Sonlu Elemanlar Yöntemi

Kaynakça

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