tthe contact velocity should use normal vector instead of distance vector - slidergrid - grid of elastic sliders on a frictional surface
HTML git clone git://src.adamsgaard.dk/slidergrid
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---
DIR commit 7226d7854eb5fe81d9ea7c55f6bf134a462991c9
DIR parent 40de282160ee90a414a91f45c48f1a8bfd2bd6bc
HTML Author: Anders Damsgaard Christensen <adc@geo.au.dk>
Date: Wed, 20 Apr 2016 11:24:44 -0700
tthe contact velocity should use normal vector instead of distance vector
Diffstat:
M doc/doc.pdf | 0
M doc/doc.tex | 39 +++++++++++++++++++++++++------
M slidergrid/slider.c | 6 +++---
3 files changed, 35 insertions(+), 10 deletions(-)
---
DIR diff --git a/doc/doc.pdf b/doc/doc.pdf
Binary files differ.
DIR diff --git a/doc/doc.tex b/doc/doc.tex
t@@ -13,7 +13,7 @@
%\usepackage{float}
%\usepackage{subfig}
%\usepackage{rotating}
-%\usepackage{amsmath}
+\usepackage{amsmath}
\usepackage[T1]{fontenc} % Font encoding
\usepackage{charter} % Serif body font
t@@ -50,15 +50,40 @@ of Oceanography\\University of California, San Diego}\\[3mm] Last revision:
\section{Methods}
The Lagrangian points are connected with visco-elastic beams which are resistive
to relative translational or rotational movement between a pair of bonded
-points. The bond deformation in each degree of freedom is determined by an
-incremental method, derived from \citet{Potyondy2004}, and used to determine the
-resistive forces. The interaction can be decomposed into bond tension and
-compression, bond shearing, bond twisting, and bond bending. These components
-are independent and can be determined individually. The generated forces are
-added to the force and torque balance on each point.
+points. At the beginning of each time step the accumulated strain on each
+inter-point bond is determined by considering the relative motion of the bonded
+points. The bond deformation is decomposed per kinematic degree of freedom,
+andis determined by an incremental method derived from \citet{Potyondy2004}.
+The strain can be decomposed into bond tension and compression, bond shearing,
+bond twisting, and bond bending. The accumulated strains are used to determine
+the magnitude of the forces and torques resistive to the deformation.
+
+The deformation and reactive forces are determined relative to the orientation
+of the bond. Common geometrical vectors include the inter-distance vector
+$\boldsymbol{d}$ between points $\boldsymbol{p}_i$ and $\boldsymbol{p}_j$:
+\begin{equation}
+ \boldsymbol{d}_{i,j} = \boldsymbol{p}_i - \boldsymbol{p}_j
+\end{equation}
+which in normalized form constitutes the bond-parallel normal vector:
+\begin{equation}
+ \boldsymbol{n}_{i,j} = \frac{\boldsymbol{d}_{i,j}}{||\boldsymbol{d}_{i,j}||}
+\end{equation}
+
+The points are moving by translational and rotational velocities. The combined
+relative velocity between the points is found as \citep{Hinrichsen2004,
+ Luding2008}:
+\begin{equation}
+ \boldsymbol{v}_{i,j} = \boldsymbol{v}_i - \boldsymbol{v}_j +
+ \frac{||d_{i,j}||}{2} d_{i,j} \times \omega_i +
+ \frac{||d_{i,j}||}{2} d_{i,j} \times \omega_j
+\end{equation}
+
+
+
\subsection{Bond tension and compression}
+
\subsection{Bond shear}
\subsection{Bond twist}
DIR diff --git a/slidergrid/slider.c b/slidergrid/slider.c
t@@ -218,9 +218,9 @@ void bond_shear_deformation(slider* s1, const slider s2,
const Float3 vel = add_float3(vel_linear,
add_float3(
multiply_scalar_float3(dist_norm/2.,
- cross_float3(dist, s1->angvel)),
+ cross_float3(n, s1->angvel)),
multiply_scalar_float3(dist_norm/2.,
- cross_float3(dist, s2.angvel))));
+ cross_float3(n, s2.angvel))));
// Tangential component of the relative contact interface velocity
// Hinrichsen and Wolf 2004, eq. 13.9
t@@ -509,7 +509,7 @@ void bond_twist_kelvin_voigt(slider* s1, const slider s2,
const Float m_n = -1.0*(m_n_elastic + m_n_viscous);
// determine torque on slider from shear on this bond
- /*const Float3 torque = multiply_scalar_float3( -1.0,
+ const Float3 torque = multiply_scalar_float3( -1.0,
cross_float3(
multiply_float3_scalar(
s1->neighbor_distance[idx_neighbor], 0.5),