Tweaks to doc page

This commit is contained in:
Dan S. Bolintineanu
2019-04-01 22:13:49 -06:00
parent 2cc35ee777
commit d3ea115436

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@ -346,16 +346,17 @@ option by an additional factor of {a}, the radius of the contact region. The tan
Here, {a} is the radius of the contact region, given by \(a = \delta R\) for all normal contact models,
except for {jkr}, where it is given implicitly by \(\delta = a^2/R - 2\sqrt\{\pi \gamma a/E\}\),
see discussion above. To match the Mindlin solution, one should set \(k_t = 8G\), where
\(G\) is the shear modulus, related to Young's modulus \(E\) by \(G = E/(2(1+\nu))\), where \(\nu\)
is Poisson's ratio. This can also be achieved by specifying {NULL} for \(k_t\), in which case
a normal contact model that specifies material parameters \(E\) and \(\nu\) is required (e.g. {hertz/material},
{dmt} or {jkr}). In this case, mixing of shear moduli for different particle types {i} and {j} is done according
to:
see discussion above. To match the Mindlin solution, one should set \(k_t = 8G^*\), where
\(G^*\) is the effective shear modulus, which relates to material properties according to:
\begin\{equation\}
1/G = 2(2-\nu_i)(1+\nu_i)/E_i + 2(2-\nu_j)(1+\nu_j)/E_j
1/G^* = 2(2-\nu_i)(1+\nu_i)/E_i + 2(2-\nu_j)(1+\nu_j)/E_j
\end\{equation\}
This can also be achieved by specifying {NULL} for \(k_t\), in which case
a normal contact model that specifies material parameters \(E\) and \(\nu\) is required (e.g. {hertz/material},
{dmt} or {jkr}).
The {mindlin_rescale} option uses the same form as {mindlin}, but the magnitude of the tangential
displacement is re-scaled as the contact unloads, i.e. if \(a < a_\{t_\{n-1\}\}\):
\begin\{equation\}