Modulus of toughness is the ability of a material to absorb energy in plastic deformation. It is defined as the amount of strain energy density (strain on a unit volume of material) that a given material can absorb before it fractures. Modulus of toughness is measured in units of PSI or Pascals. It can be determined in a test by calculating the total area under the stress-strain curve up until the fracture point of the specimen. A material's modulus of toughness will vary depending on the material's ductility; two materials with the same yield strength can vary greatly in their modulus of toughness if one of the materials is more ductile than the other. The ductile material will stretch further and have a greater area under its stress-strain curve.
When civil engineers are designing new structures, it is critical that they have access to modulus of toughness data when choosing materials. When designing a structure that may be susceptible to accidental overload, it is safer to select a more ductile material with a higher modulus of toughness, even if other, cheaper materials have the same yield strength.