PFC user¶
Module: solid
Category: materialprop
Type string: "PFC user"
Parameters¶
| Name | Description | Default | Units |
|---|---|---|---|
plastic_response |
[] |
Description¶
A user-specified flow curve may be provided using the plastic flow curve material type PFC user. The user enters a list of points representing \(\left(\varepsilon_{\beta},\Upsilon_{\beta}\right)\), where \(\varepsilon_{\beta}\) is the true strain corresponding to the apparent yield threshold \(\Upsilon_{\beta}\). Here, \(\varepsilon_{\beta}\) represents the total strain, not the plastic strain. The first point provided in this list, \(\left(\varepsilon_{0},\Upsilon_{0}\right)\), corresponds to the yield strain \(\varepsilon_{0}\) and yield stress \(\Upsilon_{0}\) for this material, such that the ratio \(\Upsilon_{0}/\varepsilon_{0}\) is used internally to calculate Young's modulus \(E\) for the selected material used in this plasticity analysis. It is the user's responsibility to ensure this consistency. The number of bond families, \(n_{f}\), is automatically set to the number of user-specified points on this flow curve. To maintain computational efficiency it is recommended to keep this number small, e.g., no greater than 30 points. Specifying only one point produces an elastic-perfectly plastic material response.
The response produced by the reactive plasticity material will agree nearly exactly with the user-specified points as long as the strain \(\varepsilon\) remains in the infinitesimal range. However, as the strain \(\varepsilon\) becomes finite, the reactive plasticity response may deviate non-negligibly from the user-specified flow curve, due to the nonlinearity of the hyperelastic relation describing the elastic response of the material. In practice, for isotropic elastic responses, using a natural neo-Hookean material (Section natural-Neo-Hookean) will produce the least amount of deviation when using large strains, since its uniaxial stress-strain response is nearly linear with \(\varepsilon\), \(\Phi\left(\varepsilon\right)=E\varepsilon\,e^{-\left(1-2\nu\right)\varepsilon}\), where \(E\) is Young's modulus and \(\nu\) is Poisson's ratio. As \(\nu\) approaches \(\frac{1}{2}\) this expression produces an exact linear response under uniaxial loading, \(\Phi\left(\varepsilon\right)=E\varepsilon\), even under finite deformation. When using \(\nu<\frac{1}{2}\), care must be taken not to exceed \(\varepsilon_{\text{max}}=\left(1-2\nu\right)^{-1}\), since the slope of \(\Phi\left(\varepsilon\right)\) becomes zero at that value and negative beyond it.