Determination of mechanical properties of geomaterials based on nano-indentation tests and fraction order models

The article focuses on efficient analysis and test methods to determine nano- and micromechanical properties of rocks and crystals. A modification of the classical elastic problems of contact mechanics implemented using the mathematical apparatus of fractional integro-differentiation is proposed. The authors build new models and algorithms aimed to advance the studies into properties and states of geomaterials based on the atomic-force microscopy techniques, and describe testing of the new approaches in calculation of the elastic modulus for hydrocarbons with nano-additives.