BELTRAMI’s or HAIGH’s THEORY

MAXIMUM STRAIN ENERGY THEORY (BELTRAMI’s or HAIGH’s THEORY)

            The failure or yielding occurs when the strain energy per unit volume in a strained material reaches the limiting strain energy (or strain energy at the yield point) per unit volume as determined from simple tension test.

            This theory is also known as Beltrami’s or Haigh’s theory.

           According to this theory, the maximum energy which a body can store without deforming plastically is constant for that material irrespective of the manner of loading.

(1/2E) [σ₁² + σ₂² + σ₃² - 2ν (σ₁ σ₂ + σ₂ σ₃ + σ₃ σ₁)] = σ_e²/2E

     [σ₁² + σ₂² + σ₃² - 2ν (σ₁ σ₂ + σ₂ σ₃ + σ₃ σ₁)] = σ_e²

           This theory breaks down for a case when, σ₁ = σ₂ = σ₃ = - σ

           And in that case failure is predicted when

σ = σ_e/√3(1-2v)

          But in fact with this type of loading, when there is uniform pressure all round, no failure occurs. This theory holds feasible for ductile materials.