Engineers design solutions to human needs based on their expert knowledge of the properties of the materials and systems they work with.

These properties are often modeled mathematically. An engineer needs to predict the behavior of the final design, whether it be the strength of a bridge or building frame, the traffic capacity of a highway, or the functioning of an artificial heart or kidney.

These properties are commonly determined by stressing the material to failure.

For structural materials, common properties that are measured are:

Compressive Strength

In mechanics, compressive strength (or compression strength) is the capacity of a material or structure to withstand loads tending to reduce size (as opposed to tensile strength which withstands loads tending to elongate). 

Some materials fracture at their compressive strength limit; others deform irreversibly, so a given amount of deformation may be considered as the limit for compressive load. Compressive strength is a key value for design of structures.

Tensile Strength

Ultimate tensile strength  is the maximum stress that a material can withstand while being stretched or pulled before breaking. In brittle materials the ultimate tensile strength is close to the yield point, whereas in ductile materials the ultimate tensile strength can be higher.

Elasticity

    the ability of an object or material to resume its normal shape after being stretched 

     or compressed; stretchiness.

Plastic Behavior

 The ability of a solid to permanently change shape when subjected to stress. This is also known as plastic deformation. For example, a piece of metal that is bent or pounded into a new shape is displaying plasticity

Extension:

Paper Cup Walk

Paper Cup Engineering ( from ZOOM)

Measure crushing strength of 1 paper cup( in bricks)

How many paper cups will support a student?

When properly designed and loaded, a column (or grouping of columns) is able to support a lot of weight because it transfers it directly to the ground. A column can fail in two basic ways. A load placed off center subjects the column to bending, or buckling. To prevent this, it is important to center a load squarely over the middle third of the top of the column. The second kind of failure occurs when the maximum strength of a column's material is exceeded by the weight of the load. When this happens, the column crushes, or collapses.

Even hollow, thin-walled columns made of weaker material can be made strong under the weight of a heavy load. A paper cup with its bottom removed, for example, is no match for the weight of a person standing on it. It crushes easily because the paper is weak in compression. Filled with sand, however, the paper cup can withstand the same weight -- and then some. Why is this so? Paper is fairly strong by itself in tension. It resists the sand's outward thrust, preventing it from spreading out. Thus contained, the sand in turn prevents the paper from collapsing by resisting the downward force of the weight and making the column stronger in compression. Engineers can sometimes use an inexpensive filler material that is strong in compression -- like sand or loose rocks -- to reinforce a hollow, thin-walled column, allowing them to build safely and cost-effectively.

-http://www.teachersdomain.org/resource/phy03.sci.phys.mfw.zcolumnsii/