Material performance index

A combination of material properties to maximize or minimize after eliminating free geometric variables from an engineering objective and constraints. Changing a geometric constraint can change the index: strength-limited rectangular cantilevers give ${\sigma }_f/\rho$ with fixed height, but $\sqrt{{\sigma }_f}/\rho$ with fixed width.

Specific strength is strength divided by density, with the strength convention stated explicitly. For a uniform tie carrying tensile force $F$, allowable stress ${\sigma }_f$ requires area $A\ge F/{\sigma }_f$. Its mass $m=\rho AL$ is therefore at least $FL/({\sigma }_f/\rho )$. Maximizing ${\sigma }_f/\rho$ minimizes mass under this simple strength-limited model. A material with higher strength can still be worse if its density increases more. Mechanical fatigue, buckling, joining and temperature limits can impose additional constraints not captured by this single ratio.