Ogden–Roxburgh model

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The Ogden–Roxburgh model[1] is an approach published in 1999 which extends hyperelastic material models to allow for the Mullins effect.[2] It is used in several commercial finite element codes, and is named after R.W. Ogden and D. G. Roxburgh. The fundamental idea of the approach can already be found in a paper by De Souza Neto et al. from 1994.[3] The basis of pseudo-elastic material models is a hyperelastic second Piola–Kirchhoff stress S0, which is derived from a suitable strain energy density function W(C):

S=2WC.

The key idea of pseudo-elastic material models is that the stress during the first loading process is equal to the basic stress S0. Upon unloading and reloading S0 is multiplied by a positive softening function η. The function η thereby depends on the strain energy W(C) of the current load and its maximum Wmax(t):=max{W(τ),τt} in the history of the material:

S=η(W,Wmax)S0,where η{=1,W=Wmax,<1,W<Wmax.

It was shown that this idea can also be used to extend arbitrary inelastic material models for softening effects.[4]

References

  1. Ogden, R. W; Roxburgh, D. G. (1999). "A pseudo–elastic model for the Mullins effect in filled rubber". Proceedings of the Royal Society of London A. 455 (1988): 2861–2877. Bibcode:1999RSPSA.455.2861W. doi:10.1098/rspa.1999.0431.
  2. Mullins, L. (1969). "Softening of Rubber by Deformation". Rubber Chemistry and Technology. 42 (1): 339–362. doi:10.5254/1.3539210. Retrieved 16 September 2023.
  3. De Souza Neto, E. A.; Perić, D.; Owen, D. R. J. (1994). "A phenomenological three-dimensional rate-independent continuum damage model for highly filled polymers : Formulation and computational aspects". Journal of the Mechanics and Physics of Solids. 42 (10): 1533–1550. doi:10.1016/0022-5096(94)90086-8.
  4. Naumann, C.; Ihlemann, J. (2015). "On the thermodynamics of pseudo-elastic material models which reproduce the Mullins effect". International Journal of Solids and Structures. 69–70: 360–369. doi:10.1016/j.ijsolstr.2015.05.014.