On size effect of elastic modules in thin fibres

• Main Authors: Nahirnyi, T., Tchervinka, K
• Format: Article
• Language: English
• Published: Центр математичного моделювання Інституту прикладних проблем механіки і математики ім. Я.С. Підстригача НАН України 2010
• Series: Фізико-математичне моделювання та інформаційні технології
• Online Access: http://dspace.nbuv.gov.ua/handle/123456789/22467

In the paper the dependence of elasticity modules in thin fibres on the fibre radius is investigated. The relations of local gradient approach in thermomechanics are taken as a starting point. The approach is based on including of a chemical potential gradient in the space of state parameters along with the stress and strain tensors. The chemical potential disturbance is identified with disturbance of the bonding energy. It is shown that the dependence of elasticity modules on the fibre radius is essential in the fibres of radius less than ten times of the size of nearsurface nonhomogeneity region. Using asymptotic expansions of modified Bessel functions the Young’s modulus, Poisson’s ratio, Lam?’s parameters, and bulk modulus at large fibre radius are studied. The agreement of the obtained results with known in the literature theoretical and experimental data is shown.