Modulus of elasticty, brittleness, strength, stiffness, elastic limit, are standard terms of the theory of elasticity. They are, however, more often than not misinterpreted when used in "technical" debates about bicycles. Many times they are abused as a "scientific evidence" of some natural feel like: "steel is softer then aluminium". Softness, by the way, is not a standard quantity in the theory of elasticity. It can be interpreted as a reciprocal quantity to stiffness. The measure of stiffnes of a material is its modulus of elasticity, or Young modulus, E, which is defined as a ratio of stress vs. strain. In that sense the common bicycle myth that steel is softer than aluminium is a total nonsense. It is not true that steel has relatively low modulus of elasticity, i.e. is a "soft material". In fact its modulus of elasticity (Young modulus) is the highest of all commonly used engineering materials: it is 210 GPa, which is 3 times greater than aluminium (with 69 GPa), 1.75 times greater than titanium (120 Gpa) and at least 1.4 greater than carbon fiber (150 GPa). You can find these figures in a table on Wikipedia page: http://en.wikipedia.org/wiki/Young%27s_modulus. Steel is the stiffest material to make a frame of, unless you are considering a tungsten or a diamond one.

It is perfectly OK with me if someone feels a steel frame to be softer than aluminium. But please don't try to prove this by misinterpretation of some half-understood theory.

P.S. I am not a "steel-hater". Steel is the best engineering material for most applications because of its strength, stiffness, ductility, fatigue strength, weldability and price - but certainly not because of it's softness.