modulus of elasticity

Or known as elastic modulus, is the unit of measurement of an object's or substance's resistance to being deformed elastically when a stress is applied to it.

The elastic modulus of an object is defined as the slope of its stress-strain curve in the elastic deformation region and has the form: \[\delta=\frac{\text{stress}}{\text{strain}}\].

This means that a stiffer material will have a higher elastic modulus and vice versa, as based on the formula a higher elastic modulus indicates a greater ability to withstand deformation under applied stress. Since strain is a dimensionless quantity, the units of \[\delta\] will be the same as the units of stress. See elastic and plastic deformation for stress-strain curve.

Types of elastic modulus:

• Young's modulus, given as \[E\]
  Describes tensile elasticity along a line when opposing forces are applied. It is the ratio of tensile stress to tensile strain.
  
• Shear modulus, given as \[G\]
  Describes shear when an object is acted upon by opposing forces. It is calculated as shear stress over shear strain.
  
• Bulk modulus, given as \[K\]
  Similar to Young's modulus, except in three dimensions. It is a measure of volumetric elasticity, calculated as volumetric stress divided by volumetric strain.