In this paper, the application of non-local fractional continuum model for plane strain and plane stress elasticity is presented. The kinematics and stress concepts are discussed, and governing equations in terms of displacements for both plane problems are defined. The numerical implementation utilising generalised finite difference method is shown in detail. Three cases are solved to indicate the role of order of fractional continua and length scale: biaxial tension, pure shear and complex state. Classical (local) solution is obtained as a special case.

In this paper, the Riesz-Caputo fractional derivative of variable order with fixed memory is considered. The studied non-integer differential operator is approximated by means of modified basic rules of numerical integration. The three proposed methods are based on polynomial interpolation: piecewise constant, piecewise linear, and piecewise quadratic interpolation. The errors generated by the described methods and the experimental rate of convergence are reported. Finally, an application of the Riesz-Caputo fractional derivative of space-dependent order in continuum mechanics is depicted.

In interventional procedures, the balloon inflation is used to occlude the artery and thus reduce bleeding. There is no practically accepted measure of the procedure efficiency. A finite element method model with state‐of‐the‐art modelling techniques was built in order to predict the occlusion levels under the influence of different balloon inflation and its material stiffness. The geometries of a healthy human thoracic aorta and an occlusion balloon were idealized. The non‐linear constitutive material of Gasser‐Ogden‐Holzapfel model was employed for the thoracic aorta; the balloon was model as the hyperelastic model. The realistic physiological blood pressure and the balloon inflation pressures were applied to simulate the different occlusion levels. The final outcome shows an important influence of the material stiffness on the balloon deformation and thus the occlusion efficiency.

In this paper the numerical implementation of two-scale modelling of bone microstructure is presented. The study is a part of long-term project on bone remodelling which drives bone microstructure change based directly on trabeculae surface energy. The proposed approach is based on a first-order computational homogenization technique. The coincidence of macro-and micro-model kinematics is done with the use of uniform displacement and traction boundary conditions. The computational homogenization procedure is driven by a self-prepared manager which is coded in Python. The computation on real bone structure (a piece of female Wistar rat bone) is performed as well.

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