Mineralogy
"Hardness" is determined by comparison with other minerals. In the Mohs scale, a standard set of minerals are numbered in order of increasing hardness from 1 (talc) to 10 (diamond). A harder mineral will scratch a softer, so an unknown mineral can be placed in this scale by which minerals it scratches and which scratch it. A few minerals such as calcite and kyanite have a hardness that depends significantly on direction. Hardness can also be measured on an absolute scale using a sclerometer; compared to the absolute scale, the Mohs scale is nonlinear.
Specific strength
Tenacity is the customary measure of strength of a fiber or yarn. In the U.S. it is usually defined as the ultimate (breaking) force of the fiber (in gram-force units) divided by the denier.
Because denier is a measure of the linear density, the tenacity works out to be not a measure of force per unit area, but rather a quasi-dimensionless measure analogous to specific strength. 
A tenacity of formula_1 corresponds to: formula_2