The largest value of the stress for which the material will return to its original length after the stress is removed is called the elastic limit. If the material is stressed beyond this limit, then it behaves inelastically and will have permanent deformation . 
 
 
 

Young's Modulus also known as the Elasticity Modulus of a material is the ratio of the stress versus the strain within the Elastic region. This is usually found from the slope of the stress vs. strain curve. 

Elasticity Modulus = Stress / Strain

This is a more generalized version of the Hook's law, similar to the spring constant. 
 
 
 

The stress/strain point at which material behavior changes from elastic to plastic is known as the Yield Point. In practice this is difficult to determine, the Offset Yield Point is used in tabulations of material properties. At the Offset Yield Point the sample has deformed plastically to an extent that will leave the material with a permanent strain of 0.002 (0.2%) when it is at zero stress. The stress, at which this occurs, is the Offset Yield Stress. 
 
 
 
 

The ultimate strength is defined as the maximum stress that a material can withstand before it ruptures. It is determined by dividing the maximum load by the original cross-sectional area of the test specimen. 
 
 
 
 
 
 
 
 
 
 
 

A material stressed beyond its plastic region reaches a stage, with very large displacements, where the material ultimately breaks. This point is called the Rupture Point of the material.
 
 
 
 
 
 
 
 
 
 

In the elastic region, there is a straight line relationship between stress and strain. Within this loading range, if the force is removed, the structure will return to its original dimensions. The slope of this linear portion describes a structure's elastic or Young's Modulus, and is calculated as stress/strain. 

When a material is stressed beyond its Elastic Limit it will reach the yield of the strength material and will no longer shrink back to it's original length when the stress is removed. It will have permanent deformation. This region is called the plastic region.
 
 
 
 
 
 
 
 

Resilience is the capacity of a material to absorb energy when it is deformed elastically and then, upon unloading to have this energy recovered.

It is represented by the area under the curve in the elastic region. 
 
 
 
 
 
 
 

Toughness is the ability of a material to absorb energy during the plastic deformation.

It is represented by the area under the curve from the unstrained state to the rupture point.