From c1903186496fa66007f9e460891bece4ca88943b Mon Sep 17 00:00:00 2001 From: jtclemm Date: Tue, 11 Jun 2024 16:53:10 -0600 Subject: [PATCH] Small doc page clarifications --- doc/src/fix_deform.rst | 2 ++ doc/src/fix_wall_gran.rst | 11 +++++++++++ doc/src/pair_granular.rst | 27 ++++++++++++++------------- 3 files changed, 27 insertions(+), 13 deletions(-) diff --git a/doc/src/fix_deform.rst b/doc/src/fix_deform.rst index 9146b987c8..2c76463369 100644 --- a/doc/src/fix_deform.rst +++ b/doc/src/fix_deform.rst @@ -64,6 +64,8 @@ Syntax effectively an engineering shear strain rate *erate* value = R R = engineering shear strain rate (1/time units) + *erate/rescale* value = R (ONLY available in :doc:`fix deform/pressure ` command) + R = engineering shear strain rate (1/time units) *trate* value = R R = true shear strain rate (1/time units) *wiggle* values = A Tp diff --git a/doc/src/fix_wall_gran.rst b/doc/src/fix_wall_gran.rst index f6465d1159..0020de2b02 100644 --- a/doc/src/fix_wall_gran.rst +++ b/doc/src/fix_wall_gran.rst @@ -115,6 +115,17 @@ friction and twisting friction supported by the :doc:`pair_style granular `. +.. note:: + When *fstyle* *granular* is specified, the associated *fstyle_params* are taken as + those for a wall–particle interaction. For example, for the hertz/material normal + contact model with :math:`E = 960` and :math:`\nu= 0.2`, the effective Young’s + modulus for a wall–particle interaction is computed as :math:`E_{eff} = \frac{960} + {2(1-0.2^2)} = 500`. Any pair coefficients defined by :doc:`pair_style granular + ` are not taken into consideration. To model different + wall–particle interactions for particles of different material types, the user may + define multiple fix wall/gran commands operating on separate groups (e.g. based + on particle type) each with a different wall–particle effective Young's modulus. + Note that you can choose a different force styles and/or different values for the wall/particle coefficients than for particle/particle interactions. E.g. if you wish to model the wall as a different diff --git a/doc/src/pair_granular.rst b/doc/src/pair_granular.rst index bc469412d9..72f85bb599 100644 --- a/doc/src/pair_granular.rst +++ b/doc/src/pair_granular.rst @@ -111,7 +111,7 @@ For the *hertz* model, the normal component of force is given by: \mathbf{F}_{ne, Hertz} = k_n R_{eff}^{1/2}\delta_{ij}^{3/2} \mathbf{n} -Here, :math:`R_{eff} = \frac{R_i R_j}{R_i + R_j}` is the effective +Here, :math:`R_{eff} = R = \frac{R_i R_j}{R_i + R_j}` is the effective radius, denoted for simplicity as *R* from here on. For *hertz*, the units of the spring constant :math:`k_n` are *force*\ /\ *length*\ \^2, or equivalently *pressure*\ . @@ -120,13 +120,14 @@ For the *hertz/material* model, the force is given by: .. math:: - \mathbf{F}_{ne, Hertz/material} = \frac{4}{3} E_{eff} R_{eff}^{1/2}\delta_{ij}^{3/2} \mathbf{n} + \mathbf{F}_{ne, Hertz/material} = \frac{4}{3} E_{eff} R^{1/2}\delta_{ij}^{3/2} \mathbf{n} -Here, :math:`E_{eff} = E = \left(\frac{1-\nu_i^2}{E_i} + \frac{1-\nu_j^2}{E_j}\right)^{-1}` is the effective Young's -modulus, with :math:`\nu_i, \nu_j` the Poisson ratios of the particles of -types *i* and *j*\ . Note that if the elastic modulus and the shear -modulus of the two particles are the same, the *hertz/material* model -is equivalent to the *hertz* model with :math:`k_n = 4/3 E_{eff}` +Here, :math:`E_{eff} = E = \left(\frac{1-\nu_i^2}{E_i} + \frac{1-\nu_j^2}{E_j}\right)^{-1}` +is the effective Young's modulus, with :math:`\nu_i, \nu_j` the Poisson ratios +of the particles of types *i* and *j*. :math:`E_{eff}` is denoted as *E* from here on. +Note that if the elastic modulus and the shear modulus of the two particles are the +same, the *hertz/material* model is equivalent to the *hertz* model with +:math:`k_n = 4/3 E` The *dmt* model corresponds to the :ref:`(Derjaguin-Muller-Toporov) ` cohesive model, where the force @@ -417,11 +418,11 @@ discussion above. To match the Mindlin solution, one should set G_{eff} = \left(\frac{2-\nu_i}{G_i} + \frac{2-\nu_j}{G_j}\right)^{-1} -where :math:`G` is the shear modulus, related to Young's modulus :math:`E` -and Poisson's ratio :math:`\nu` by :math:`G = E/(2(1+\nu))`. This can also be -achieved by specifying *NULL* for :math:`k_t`, in which case a -normal contact model that specifies material parameters :math:`E` and -:math:`\nu` is required (e.g. *hertz/material*, *dmt* or *jkr*\ ). In this +where :math:`G_i` is the shear modulus of a particle of type :math:`i`, related to Young's +modulus :math:`E_i` and Poisson's ratio :math:`\nu_i` by :math:`G_i = E_i/(2(1+\nu_i))`. +This can also be achieved by specifying *NULL* for :math:`k_t`, in which case a +normal contact model that specifies material parameters :math:`E_i` and +:math:`\nu_i` is required (e.g. *hertz/material*, *dmt* or *jkr*\ ). In this case, mixing of the shear modulus for different particle types *i* and *j* is done according to the formula above. @@ -551,7 +552,7 @@ opposite torque on each particle, according to: .. math:: - \tau_{roll,i} = R_{eff} \mathbf{n} \times \mathbf{F}_{roll} + \tau_{roll,i} = R \mathbf{n} \times \mathbf{F}_{roll} .. math::