PFC math¶
Module: solid
Category: materialprop
Type string: "PFC math"
Parameters¶
| Name | Description | Default | Units |
|---|---|---|---|
nf |
nf | 1 | [] |
e0 |
e0 | 0 | [] |
emax |
emax | 1 | [] |
plastic_response |
plastic flow curve | [] |
Description¶
Alternatively, a mathematical expression may be supplied to describe \(\Upsilon\left(\varepsilon\right)\), using the plastic flow curve material type PFC math.
It is the user's responsibility to ensure that the supplied mathematical function produces \(\Upsilon_{0}/\varepsilon_{0}\) equal to Young's modulus for the elastic material model being used. The actual response produced by the reactive plasticity material will agree nearly exactly with the mathematical expression for \(\Upsilon\left(\varepsilon\right)\) 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 (see 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.