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Hill yield criteria : ウィキペディア英語版
Hill yield criterion
Rodney Hill has developed several yield criteria for anisotropic plastic deformations. The earliest version was a straightforward extension of the von Mises yield criterion and had a quadratic form. This model was later generalized by allowing for an exponent ''m''. Variations of these criteria are in wide use for metals, polymers, and certain composites.
== Quadratic Hill yield criterion ==
The quadratic Hill yield criterion〔R. Hill. (1948). ''A theory of the yielding and plastic flow of anisotropic metals.'' Proc. Roy. Soc. London, 193:281–297〕 has the form
:
F(\sigma_-\sigma_)^2 + G(\sigma_-\sigma_)^2 + H(\sigma_-\sigma_)^2 + 2L\sigma_^2 + 2M\sigma_^2 + 2N\sigma_^2 = 1 ~.

Here ''F, G, H, L, M, N'' are constants that have to be determined experimentally and \sigma_ are the stresses. The quadratic Hill yield criterion depends only on the deviatoric stresses and is pressure independent. It predicts the same yield stress in tension and in compression.

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