THEORIES OF FAILURE /YIELDING
Theories of failure


Ultimate Aim DESIGN

Failure material failure


Uncertainties
Material
Loading ,Geometry
Ignorance
Mathematical limitations etc.

Simplified Criteria Theories of yielding


Principal stress
Principal strain
are extremum




1. Maximum-Principal Stress Theory











More useful for Brittle material ,is also called Rankine criteria for failure.



2. Maximum-Principal Strain Theory






In case of compressive state of stress





3. Maximum Shear Stress Theory





is called Tresca theory useful for ductile material--- cup and cone in simple tension 450

Tresca theory fails in hydro static state of stresses




4. Total strain energy theory --( Beltrami & Haigh)






5. Shear or Distortion Strain Energy Theory