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