What is meant by yield of isotropic plastic material? How is yield of Isotropic plastic material different from the term normal yield which is referred as transition from elastic behaviour to plastic. I am bit confused of term Yield of Isotropic plastic material.

Edit: yes I am talking about Isotropic material and requesting for answers based on what graph of yield criteria explains

Please help, thanks!

  • $\begingroup$ I think you are taking about plasticity of isotropic material. If we see yield criteria for isotropic material then for an isotropic material the yield criteria will be a function of the invariants of the stress deviator. So it's bit different from normal yield I guess. $\endgroup$
    – Rajakr
    Commented Nov 3, 2020 at 16:42
  • $\begingroup$ If you mean polymers, their yield is time sensitive . So strain rate matters and when you measure it matters . I expect ASTM will have written standard procedures . $\endgroup$ Commented Apr 7, 2021 at 0:55

2 Answers 2


I think the confusion is on the term "isotropic", which means uniform behavior in all directions, as opposed to "anisotropic", which is defined as the material’s tendency to react differently to stresses applied in different directions. Most polymers are isotropic but can be made of anisotropic, so the author felt the need to distinguish the one discussed in the article.

Thus, the yield of the isotropic plastic material equals the normal/typical yield of the sampling plastic.


In terms of yield surfaces, the 2D yield surface of an isotropic material will be mirrored over the line sigma_1 = sigma_2. In 3D, an isotropic yield surface will have rotational symmetry about the line sigma_1 = sigma_2 = sigma_3 (the hydrostatic axis). These symmetry constraints imply that the yield surface will intersect each principal stress axis at the same value. Additionally, if the material is isotropically hardened, the yield surface will expand outward concentrically to the original yield surface.

In contrast, a the yield surface for an anisotropic yield surface does not have these symmetry requirements, and can intersect the different principal stress axes at different values. For a 2D yield surface, the degree of anisotropy, R, is given by R = sigma_2 / sigma_1, where R=1 corresponds to an isotropic material.


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