Material Nonlinearity: Hardening Laws

Description

Hardening models describe the change of yield surface due to plastic strain accumulation.

• Isotropic

  The yield stress is a function of the equivalent plastic strain and the yield surface expands while its centre remains fixed.

  Isotropic hardening is available for beam, plate and brick elements.

  

• Kinematic

  The centre of the yield surface is a function of the plastic strain and moves in stress space while the size and shape of the yield surface remains unchanged.

  Kinematic hardening is available for beam elements only.

  

• Takeda

  This is a special case of a mixed hardening model, which combines isotropic and kinematic hardening models. The model was developed specifically for reinforced concrete members under repeated dynamic loading/unloading.

  Takeda hardening model is available for beam elements only.

  A valid Takeda model curve is trilinear and passes through the origin (0, 0). There are two gradient changes in the curve:

  1. The cracking point [Pcr (cracking load), Dcr (cracking deflection)]
  2. The yield point [Py (yield load), Dy (yield deflection)]

  An example curve is shown below:

  

Literature

Takeda, T., Sozen, M.A. & Nielsen, N.N. 1970, "Reinforced Concrete Response to Simulated Earthquakes", Journal of the Structural Division, Proceedings of the American Society of Civil Engineers, vol.96, no. ST12, December.

See Also

• Materials: Nonlinearity