DC Deshpande-Fleck¶

Module: solid

Category: materialprop

Type string: "DC Deshpande-Fleck"

Parameters¶

Name	Description	Default	Units
`beta`	beta	0	[]

Description¶

The material type for the Deshpande-Fleck criterion is DC Deshpande-Fleck. It is based on the yield criterion for plasticity introduced in ¹. For this criterion, we let

\[ \Xi\left(\mathbf{F}\right)=\sqrt{\frac{\sigma_{e}^{2}+\left(3\beta\sigma_{m}\right)^{2}}{1+\beta^{2}}} \]

where \(\sigma_{e}\) is the von Mises stress, \(\sigma_{m}=\frac{1}{3}\tr\boldsymbol{\sigma}_{0}\) is the hydrostatic stress, \(\beta\) is a material parameter that controls the contribution of the hydrostatic stress to this criterion (\(\beta=0\) recovers the von Mises yield criterion). This criterion was introducted to model yielding of polymer foams, for which Deshpande and Fleck recommended using \(\beta=1/3\). On Wikipedi, this criterion is described as a modification of the Drucker-Prager criterion, but note that Deshpande and Fleck describe this material model as "phenomenological", i.e., intended to fit experimental data well, though they do suggest that \(3\beta\) represents the ratio of hydrostatic strength to shear strength.

Example:

<criterion type="DC Deshpande-Fleck">
  <beta>0.3333</beta>
</criterion>

Deshpande, VS and Fleck, NA, "Multi-axial yield behaviour of polymer foams", Acta materialia 49, 10 (2001), pp. 1859--1866. ↩