Sonlu Elemanlar Yöntemi ve Hassasiyet Analizi ile İki Fazlı Yumuşak Dokuların Malzeme Özelliklerinin Tayini

İki fazlı yumuşak dokuların malzeme özellikleri bu dokuların işlevlerini yerine getirmeleri açısından önemlidir. Bu makalede, iki fazlı dokuların elastik sabitlerinin ve hidrolik geçirgenliğinin, deneysel veriler, sonlu elemanlar yöntemi ve optimizasyon ile nasıl belirlenebileceği gösterilmiştir. Dokuların bünye denklemlerini içeren iki fazlı teori ile birlikte optimizasyon algoritmasının matematiksel formülasyonu tarif edilmiştir. Bu algoritmada anahtar rol oynayan ve malzeme özelliklerini güncellemek için yapılan hassasiyet analizi ayrıntılarıyla açıklanmıştır. Optimizasyon algoritması, yanal kısıtlı ve yanal kısıtsız sıkıştırma deneyi konfigürasyonları üstünde örneklendirilmiştir. Algoritmanın, lineer elastik katı fazlı bir dokuda Young modülü ve hidrolik geçirgenliğin, deneysel veri sayısı ve niteliğine de bağlı olarak görece az sayıda malzeme özelliği güncellemesiyle gerçek değerlerine yakınsamalarını sağladığı gözlemlenmiştir.

Anahtar Kelimeler:

İki fazlı doku, Eklem kıkırdağı, Sonlu elemanlar, Malzeme özellikleri, Optimizasyon

Determination of Material Properties of Biphasic Tissues Using Finite Element Method and Sensitivity Analysis

The material properties of biphasic tissues are important for these tissues to fulfill their function. In this paper, it is presented how the elastic constants and hydraulic permeability of biphasic tissues can be determined using experimental data, finite element method and optimization. The biphasic theory, containing the constitutive law of the tissues, together with the mathematical formulation of the optimization algorithm is described. Sensitivity analysis, which plays a key role in this algorithm and is utilized to update the material properties, is explained in detail. The optimization algorithm is exemplified with confined compression and unconfined compression experimental configurations. It has been observed that the algorithm, depending also on the number and quality of the experimental data, can make the Young’s modulus and hydraulic permeability values converge to their actual values with a relatively small number of material updates in case of a linear elastic solid phase.

Keywords:

Biphasic tissue, Articular cartilage, Finite element, Material properties, Optimization,

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