Finite Element Calculation of the Linear Elasticity Problem for Biomaterials with Fractal Structure

Aims: The aim of this study was to develop the mathematical models linear elasticity theory biomaterials by taking into account their fractal structure. This further aimed construct a variational formulation problem, obtain main relationships finite element method calculate rheological characteristics biomaterial with structure, and application software for calculating components stress-strain state while considering obtained results were analyzed. Background: development adequate structure is an urgent scientific task. Finding its solution will make it possible analyze behavior exposed external loads existing effects memory, spatial non-locality, self-organization, deterministic chaos in material. Objective: objective deformation process under load. Methods: equations construction load used. Mathematical apparatus integro-differentiation fractional order take A problem formulated. piecewise basis finding approximate Results: relations which takes biomaterial, obtained. constructed. finite-element calculation using piecewise-linear are found. Conclusion: Using makes Also, approach determine residual stresses play important role appearance during repeated loads.