PFC paper¶
Module: solid
Category: materialprop
Type string: "PFC paper"
Parameters¶
| Name | Description | Default | Units |
|---|---|---|---|
Y0 |
Y0 | 0 | [] |
Ymax |
Ymax | 0 | [] |
w0 |
w0 | 1 | [] |
we |
we | 0 | [] |
nf |
nf | 1 | [] |
r |
r | 0.9 | [] |
Description¶
This custom method for specifying the flow curve was provided in the paper that introduced reactive plasticity 1, therefore it is called PFC paper.
This method assumes that \(\Upsilon_{\beta}\) values are evenly distributed between the initial yield threshold \(\Upsilon_{\text{0}}\) (e.g., the yield stress) and a final yield threshold \(\Upsilon_{\text{max}}\), parameters which may be identified from a stress strain curve (Figure a-b). Beyond \(\Upsilon_{\text{max}}\), the material either behaves as if it is perfectly plastic (a scenario which may be valid around the ultimate strength, for example), or it transitions to a linear hardening regime.
The family mass fractions \(w_{\beta}\) govern the influence of each family on the overall material response. The simplest model for \(w_{\beta}\) involves specifying the mass fraction of the first yielding family \(w_{0}\), which controls the slope of the initial post-yield response (Figure a), and then evenly weighting the rest of the bond families. In cases where the material transitions to a linear hardening regime, we can recover this behavior by adding one more bond family, \(\beta=n_{f}\), that never yields, thus remaining elastic. The associated mass fraction \(w_{\beta}\) for \(\beta=n_{f}\) is called the elastic mass fraction and denoted \(w_{e}\); a non-zero value for this parameter may be specified whenever we wish to include linear hardening behavior (Figure b). The effect of the mass fraction parameters \(w_{0}\) and \(w_{e}\) is explored parametrically in Figure c and Figure d, respectively. In general, most ductile materials have \(w_{0}\) very close to unity, which provides hardening behavior over a finite strain range. As \(w_{0}\to1\) the stress-strain behavior approaches perfect plasticity. In contrast, when \(w_{e}=0\), the material response becomes perfectly plastic once the final yield threshold \(\Upsilon_{\text{max}}\) has been exceeded.
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Zimmerman, Brandon K., Jiang, David, Weiss, Jeffrey A., Timmins, Lucas H., and Ateshian, Gerard A., "On the use of constrained reactive mixtures of solids to model finite deformation isothermal elastoplasticity and elastoplastic…", Journal of the Mechanics and Physics of Solids (2021), pp. 104534. ↩