(6425b80b) · Commits · 郑智淋 / lammps

doc/Eqs/stress_tensor.jpg

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doc/Eqs/stress_tensor.tex

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		@@ -5,14 +5,14 @@
		\begin{eqnarray*}
		S_{ab} & = & - \left[ m v_a v_b +
		\frac{1}{2} \sum_{n = 1}^{N_p} (r_{1_a} F_{1_b} + r_{2_a} F_{2_b}) +
		\frac{1}{2} \sum_{n = 1}^{N_b} (r_{1_a} F_{1_b} + r_{2_a} F_{2_b}) +
		\frac{1}{3} \sum_{n = 1}^{N_a} (r_{1_a} F_{1_b} + r_{2_a} F_{2_b} +
		r_{3_a} F_{3_b}) + \right. \\
		&& \left. \frac{1}{4} \sum_{n = 1}^{N_d} (r_{1_a} F_{1_b} + r_{2_a} F_{2_b} +
		\frac{1}{2} \sum_{n = 1}^{N_b} (r_{1_a} F_{1_b} + r_{2_a} F_{2_b}) + \right. \\
		&& \left. \frac{1}{3} \sum_{n = 1}^{N_a} (r_{1_a} F_{1_b} + r_{2_a} F_{2_b} +
		r_{3_a} F_{3_b}) +
		\frac{1}{4} \sum_{n = 1}^{N_d} (r_{1_a} F_{1_b} + r_{2_a} F_{2_b} +
		r_{3_a} F_{3_b} + r_{4_a} F_{4_b}) + \right. \\
		&& \left. \frac{1}{4} \sum_{n = 1}^{N_i} (r_{1_a} F_{1_b} + r_{2_a} F_{2_b} +
		r_{3_a} F_{3_b} + r_{4_a} F_{4_b}) +
		\frac{1}{4} \sum_{n = 1}^{N_i} (r_{1_a} F_{1_b} + r_{2_a} F_{2_b} +
		r_{3_a} F_{3_b} + r_{4_a} F_{4_b})
		\right]
		\sum_{n = 1}^{N_f} r_{i_a} F_{i_b} \right]
		\end{eqnarray*}

		\end{document}

doc/compute_stress_atom.html

+16 −12

Original line number	Diff line number	Diff line
		@@ -18,7 +18,7 @@
		<UL><LI>ID, group-ID are documented in <A HREF = "compute.html">compute</A> command
		<LI>stress/atom = style name of this compute command
		<LI>zero or more keywords may be appended
		<LI>keyword = <I>ke</I> or <I>pair</I> or <I>bond</I> or <I>angle</I> or <I>dihedral</I> or <I>improper</I>
		<LI>keyword = <I>ke</I> or <I>pair</I> or <I>bond</I> or <I>angle</I> or <I>dihedral</I> or <I>improper</I> or <I>fix</I>
		</UL>
		<P><B>Examples:</B>
		</P>
		@@ -51,14 +51,20 @@ second term is a pairwise energy contribution where <I>n</I> loops over the
		atoms in the pairwise interaction, and <I>F1</I> and <I>F2</I> are the forces on
		the 2 atoms resulting from the pairwise interaction. The third term
		is a bond contribution of similar form for the <I>Nb</I> bonds which atom
		<I>I</I> is part of. The remaining terms are for the <I>Na</I> angle, <I>Nd</I>
		<I>I</I> is part of. There are similar terms for the <I>Na</I> angle, <I>Nd</I>
		dihedral, and <I>Ni</I> improper interactions atom <I>I</I> is part of.
		Finally, there is a term for the <I>Nf</I> <A HREF = "fix.html">fixes</A> that apply
		internal constraint forces to atom <I>I</I>. Currently, only the <A HREF = "fix_shake.html">fix
		shake</A> and <A HREF = "fix_rigid.html">fix rigid</A> commands
		contribute to this term.
		</P>
		<P>As the coefficients in the formula imply, a virial contribution
		produced by a small set of atoms (e.g. 4 atoms in a dihedral or 3
		atoms in a Tersoff 3-body interaction) is assigned in equal portions
		to each atom in the set. E.g. 1/4 of the dihedral virial to each of
		the 4 atoms.
		the 4 atoms, or 1/3 of the fix virial due to SHAKE constraints applied
		to atoms in a a water molecule via the <A HREF = "fix_shake.html">fix shake</A>
		command.
		</P>
		<P>If no extra keywords are listed, all of the terms in this formula are
		included in the per-atom stress tensor. If any extra keywords are
		@@ -81,22 +87,20 @@ the system and the sum is divided by 3V, where V is the volume of the
		system, the result should be -P, where P is the total pressure of the
		system.
		</P>
		<P>These lines in an input script should yield that result (assuming
		there is no fix or long-range contribution to the stress). I.e. the
		<P>These lines in an input script should yield that result. I.e. the
		last 2 columns of thermo output will be the same:
		</P>
		<PRE>compute peratom all stress/atom
		compute p all sum peratom<B>1</B> peratom<B>2</B> peratom<B>3</B>
		compute p all sum c_peratom<B>1</B> c_peratom<B>2</B> c_peratom<B>3</B>
		variable press equal -(c_p<B>1</B>+c_p<B>2</B>+c_p<B>3</B>)/(3*vol)
		thermo_style custom step temp etotal press v_press
		</PRE>
		<P>IMPORTANT NOTE: The per-atom stress does NOT include contributions due
		to fixes (e.g. <A HREF = "fix_shake.html">SHAKE</A>) or long-range Coulombic
		interactions (via the <A HREF = "kspace_style.html">kspace_style</A> command). The
		former needs to be added to LAMMPS. We're not sure if the latter is
		possible to compute. There are also a few pair styles for manybody
		potentials that are not yet instrumented to yield per-atom stress.
		See the Restrictions below.
		to long-range Coulombic interactions (via the
		<A HREF = "kspace_style.html">kspace_style</A> command). We're not sure this is
		even possible to compute. There are also a few pair styles for
		manybody potentials that are not yet instrumented to yield per-atom
		stress. See the Restrictions below.
		</P>
		<P><B>Output info:</B>
		</P>

doc/compute_stress_atom.txt

+16 −12

Original line number	Diff line number	Diff line
		@@ -15,7 +15,7 @@ compute ID group-ID stress/atom keyword ... :pre
		ID, group-ID are documented in "compute"_compute.html command
		stress/atom = style name of this compute command
		zero or more keywords may be appended
		keyword = {ke} or {pair} or {bond} or {angle} or {dihedral} or {improper} :ul
		keyword = {ke} or {pair} or {bond} or {angle} or {dihedral} or {improper} or {fix} :ul

		[Examples:]

		@@ -47,14 +47,20 @@ second term is a pairwise energy contribution where {n} loops over the
		atoms in the pairwise interaction, and {F1} and {F2} are the forces on
		the 2 atoms resulting from the pairwise interaction. The third term
		is a bond contribution of similar form for the {Nb} bonds which atom
		{I} is part of. The remaining terms are for the {Na} angle, {Nd}
		{I} is part of. There are similar terms for the {Na} angle, {Nd}
		dihedral, and {Ni} improper interactions atom {I} is part of.
		Finally, there is a term for the {Nf} "fixes"_fix.html that apply
		internal constraint forces to atom {I}. Currently, only the "fix
		shake"_fix_shake.html and "fix rigid"_fix_rigid.html commands
		contribute to this term.

		As the coefficients in the formula imply, a virial contribution
		produced by a small set of atoms (e.g. 4 atoms in a dihedral or 3
		atoms in a Tersoff 3-body interaction) is assigned in equal portions
		to each atom in the set. E.g. 1/4 of the dihedral virial to each of
		the 4 atoms.
		the 4 atoms, or 1/3 of the fix virial due to SHAKE constraints applied
		to atoms in a a water molecule via the "fix shake"_fix_shake.html
		command.

		If no extra keywords are listed, all of the terms in this formula are
		included in the per-atom stress tensor. If any extra keywords are
		@@ -77,22 +83,20 @@ the system and the sum is divided by 3V, where V is the volume of the
		system, the result should be -P, where P is the total pressure of the
		system.

		These lines in an input script should yield that result (assuming
		there is no fix or long-range contribution to the stress). I.e. the
		These lines in an input script should yield that result. I.e. the
		last 2 columns of thermo output will be the same:

		compute peratom all stress/atom
		compute p all sum peratom[1] peratom[2] peratom[3]
		compute p all sum c_peratom[1] c_peratom[2] c_peratom[3]
		variable press equal -(c_p[1]+c_p[2]+c_p[3])/(3*vol)
		thermo_style custom step temp etotal press v_press :pre

		IMPORTANT NOTE: The per-atom stress does NOT include contributions due
		to fixes (e.g. "SHAKE"_fix_shake.html) or long-range Coulombic
		interactions (via the "kspace_style"_kspace_style.html command). The
		former needs to be added to LAMMPS. We're not sure if the latter is
		possible to compute. There are also a few pair styles for manybody
		potentials that are not yet instrumented to yield per-atom stress.
		See the Restrictions below.
		to long-range Coulombic interactions (via the
		"kspace_style"_kspace_style.html command). We're not sure this is
		even possible to compute. There are also a few pair styles for
		manybody potentials that are not yet instrumented to yield per-atom
		stress. See the Restrictions below.

		[Output info:]

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