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A confliction in using 2nd Piola and Cauchy stress in built-in equations of modeling elastoplasticity in Comsol
Posted Aug 25, 2020, 3:18 a.m. EDT Structural & Acoustics, General, Structural Mechanics Version 5.5 2 Replies
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Dear all,
I have been working on modeling of elastoplastic reponse of a metal during last months in Comsol 5.5. Since I ran into a confliction in equation view of related nodes, I was wondering wether I am wrong or its a bug. Based on weak expression in elastic node and structural mechanics module user's guide, by selecting include geometry nonlinearity button in step node, 2nd Piola stresses are replaced in the formulations instead of Cauchy stresses. On the other hand, by adding a plasticity sub-node in linear elastic material node of solid mechanics module, assuming that plastic strains are small and the formulation is based on decomposition of strains, it is seen that stress-based variables in equation view of plasticity node are defined based on ** Cauchy stresses** (solid.sl11, solid.sl12, solid.sl13, ..). Another proof for usage of Cauchy stresses in plasticity is comparing solid.sl11-equivalent plastic strain and solid.Sl11-equivalent plastic strain diagrams (in uniaxial modeling) with given stress-equivalent plastic strain response of an uniaxial tensile test . Knowing that in elastoplastic formulations, exmployed stress types (1st Piola, 2nd Piola, or Cauchy) must be the same, why elastic node is employing 2nd Piola stresses while the plastic one is using Cauchy stresses?
Thanks for your responses
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Hi,
The stresses in the Linear Elastic Material node are computed using the elastic strains, that is after removing the plastic strains from the total strains. These (2nd P-K stresses) are thus independent of whatever stress measure is used in the Plasticity node, long as the Plasticity node delivers the correct plastic strains.
For large strain plasticity, the stress-strain curve is assumed to be true (Cauchy) stress vs. true strain. For small strain plasticity, all stress measures are equal.
-------------------Henrik Sönnerlind
COMSOL
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Hi,
The stresses in the Linear Elastic Material node are computed using the elastic strains, that is after removing the plastic strains from the total strains. These (2nd P-K stresses) are thus independent of whatever stress measure is used in the Plasticity node, long as the Plasticity node delivers the correct plastic strains.
For large strain plasticity, the stress-strain curve is assumed to be true (Cauchy) stress vs. true strain. For small strain plasticity, all stress measures are equal.
Thanks for your reply, I believe that from perspective view of continuum mechanics, since mechanical behavior of the material is simulated by one constituve equation (as a function of stress and elastic,plastic,external, or thermal strains), "theses (2nd P-K stresses)" should not be "independent of whatever stress measure is used in the Plasticity node". This will be more obvious when we add an external strain tensor (for adding considerably high amounts of strains) besides elastic and plastic ones. In this case, for external strain tensor and elastic one 2nd P-K stress is used while Cauchy stress is used for plasticity calculations!
Best Regards,