Variational Formulation Of The Stress-Strain Problem In Capillary-Porous Materials With Fractal Structure
Volodymyr Shymanskyi, Yaroslav Sokolovskyy
20202020 IEEE 15th International Conference on Computer Sciences and Information Technologies (CSIT)15 citationsDOI
Abstract
Mathematical model of the linear elasticity problem for capillary-porous materials with fractal structure is constructed. The basic physical and geometric relationships of the stress-strain state of the considered material are obtained. Integro-differentiation apparatus of fractional order to account the fractal structure of the material in the ratios of linear elasticity was used. A variational formulation of the linear elasticity problem for capillary-porous materials with fractal structure is obtained. A method for getting an approximate solution for the considered problem is proposed. For partial cases the results obtained are analyzed.
Topics & Concepts
FractalElasticity (physics)Linear elasticityPorous mediumPorosityCapillary actionMaterials scienceFractal dimensionStress–strain curveMathematicsMathematical analysisStress (linguistics)Finite element methodComposite materialPhysicsThermodynamicsDeformation (meteorology)PhilosophyLinguisticsElasticity and Wave PropagationHeat Transfer and Mathematical ModelingAdvanced Theoretical and Applied Studies in Material Sciences and Geometry