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Finite element analysis was performed to investigate the indentation response of elasto-plastic solids for conical indenters of half included angles of 60°and 70.3°. The interdependence indentation parameters resulting from a single indentation load-depth curve is considered. Regarding dimensional analysis, several dimensionless relationships are constructed as functions of the reduced elastic modulus-loading curvature ratio E * /C and the strain hardening exponent n. Further, the duality between corresponding parameters with dual indenters is explored. Finally, a new method based on dual indenters is proposed to extract the strain hardening exponent and the reduced elastic modulus of an indented material. The accuracy of this method is verified and discussed with experimental data from the literature and representative materials.

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Effects of vacancies and Stone-Wales defects on the mechanical properties of silicene are investigated through molecular dynamic finite element method with Tersoff potential. Young's modulus, Poisson's ratio and uniaxial tensile stress-strain curves are considered in the armchair and zigzag directions. It is found that pristine and lowly defective silicene sheets exhibit almost the same elastic nature up to fracture points. However, a single defect weakens significantly the silicene sheet, resulting in a considerable reduction in the fracture strength. One 2-atom vacancy in the sheet's center reduces 18-20 % in fracture stress and 33-35 % in fracture strain. The weakening effects of Stone-Wales defects vary with the tensile direction and the orientation of these defects.