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. 
 
 
 

Ultimate Strength:

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. 
 
 
   
 

Rupture:

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.
 
 
 
 
 
 
 
 

Elastic Region:

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. 

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.