git-svn-id: svn://svn.icms.temple.edu/lammps-ro/trunk@4127 f3b2605a-c512-4ea7-a41b-209d697bcdaa

doc/Manual.html

@@ -149,6 +149,8 @@ listed above.
   4.16 <A HREF = "Section_howto.html#4_16">Thermostatting, barostatting, and compute temperature</A> 
 <BR>
   4.17 <A HREF = "Section_howto.html#4_17">Walls</A> 
+<BR>
+  4.18 <A HREF = "Section_howto.html#4_18">Elastic constants</A> 
 <BR></UL>
 <LI><A HREF = "Section_example.html">Example problems</A> 
 
@@ -253,6 +255,8 @@ listed above.
 
 
 
+
+
 
 
 

doc/Manual.txt

@@ -106,7 +106,8 @@ listed above.
   4.14 "Extended spherical and aspherical particles"_4_14 :b
   4.15 "Output from LAMMPS (thermo, dumps, computes, fixes, variables)"_4_15 :b
   4.16 "Thermostatting, barostatting, and compute temperature"_4_16 :b
-  4.17 "Walls"_4_17 :ule,b
+  4.17 "Walls"_4_17 :b
+  4.18 "Elastic constants"_4_18 :ule,b
 "Example problems"_Section_example.html :l
 "Performance & scalability"_Section_perf.html :l
 "Additional tools"_Section_tools.html :l
@@ -159,6 +160,7 @@ listed above.
 :link(4_15,Section_howto.html#4_15)
 :link(4_16,Section_howto.html#4_16)
 :link(4_17,Section_howto.html#4_17)
+:link(4_18,Section_howto.html#4_18)
 
 :link(9_1,Section_errors.html#9_1)
 :link(9_2,Section_errors.html#9_2)

doc/Section_example.html

@@ -30,7 +30,7 @@ Site</A>.
 </P>
 <P>These are the sample problems in the examples sub-directories:
 </P>
-<DIV ALIGN=center><TABLE  WIDTH="0%"  BORDER=1 >
+<DIV ALIGN=center><TABLE  BORDER=1 >
 <TR><TD >colloid</TD><TD >  big colloid particles in a small particle solvent, 2d system</TD></TR>
 <TR><TD >crack</TD><TD >	  crack propagation in a 2d solid</TD></TR>
 <TR><TD >dipole</TD><TD >   point dipolar particles, 2d system</TD></TR>

doc/Section_howto.html

@@ -1025,7 +1025,7 @@ discussed below, it can be referenced via the following bracket
 notation, where ID in this case is the ID of a compute.  The leading
 "c_" would be replaced by "f_" for a fix, or "v_" for a variable:
 </P>
-<DIV ALIGN=center><TABLE  WIDTH="0%"  BORDER=1 >
+<DIV ALIGN=center><TABLE  BORDER=1 >
 <TR><TD >c_ID </TD><TD > entire scalar, vector, or array</TD></TR>
 <TR><TD >c_ID[I] </TD><TD > one element of vector, one column of array</TD></TR>
 <TR><TD >c_ID[I][J] </TD><TD > one element of array 
@@ -1198,7 +1198,7 @@ data and scalar/vector/array data.
 input, that could be an element of a vector or array.  Likewise a
 vector input could be a column of an array.
 </P>
-<DIV ALIGN=center><TABLE  WIDTH="0%"  BORDER=1 >
+<DIV ALIGN=center><TABLE  BORDER=1 >
 <TR><TD >Command</TD><TD > Input</TD><TD > Output</TD><TD ></TD></TR>
 <TR><TD ><A HREF = "thermo_style.html">thermo_style custom</A></TD><TD > global scalars</TD><TD > screen, log file</TD><TD ></TD></TR>
 <TR><TD ><A HREF = "dump.html">dump custom</A></TD><TD > per-atom vectors</TD><TD > dump file</TD><TD ></TD></TR>
@@ -1448,36 +1448,36 @@ frictional walls, as well as triangulated surfaces.
 <A NAME = "4_18"></A><H4>4.18 Elastic constants 
 </H4>
 <P>Elastic constants characterize the stiffness of a material. The formal
-definition is provided by the linear relation that holds between
+definition is provided by the linear relation that holds between the
-the stress and strain tensors in the limit of infinitesimal deformation.
+stress and strain tensors in the limit of infinitesimal deformation.
-In tensor notation, this is expressed as s_ij = C_ijkl * e_kl, where 
+In tensor notation, this is expressed as s_ij = C_ijkl * e_kl, where
 the repeated indices imply summation. s_ij are the elements of the
-symmetric stress tensor. e_kl are the elements of the symmetric
+symmetric stress tensor. e_kl are the elements of the symmetric strain
-strain tensor. C_ijkl are the elements of the fourth rank tensor
+tensor. C_ijkl are the elements of the fourth rank tensor of elastic
-of elastic constants. In three dimensions, this tensor has 3^4=81
+constants. In three dimensions, this tensor has 3^4=81 elements. Using
-elements. Using Voigt notation, the tensor can be written
+Voigt notation, the tensor can be written as a 6x6 matrix, where C_ij
-as a 6x6 matrix, where C_ij is now the derivative of s_i
+is now the derivative of s_i w.r.t. e_j. Because s_i is itself a
-w.r.t. e_j. Because s_i is itself a derivative w.r.t. e_i, it follows
+derivative w.r.t. e_i, it follows that C_ij is also symmetric, with at
-that C_ij is also symmetric, with at most 6*5/2 = 21 distinct elements.
+most 6*5/2 = 21 distinct elements.
 </P>
 <P>At zero temperature, it is easy to estimate these derivatives by
-deforming the cell in one of the six directions using 
+deforming the cell in one of the six directions using the command
-the command <A HREF = "displace_box.html">displace_box</A> 
+<A HREF = "displace_box.html">displace_box</A> and measuring the change in the
-and measuring the change in the stress tensor. A general-purpose
+stress tensor. A general-purpose script that does this is given in the
-script that does this is given in the examples/elastic directory
+examples/elastic directory described in <A HREF = "Section_example.html">this
-described in <A HREF = "Section_example.html">this section</A>.
+section</A>.
 </P>
-<P>Calculating elastic constants at finite temperature is more challenging,
+<P>Calculating elastic constants at finite temperature is more
-because it is necessary to run a simulation that perfoms time averages
+challenging, because it is necessary to run a simulation that perfoms
-of differential properties. One way to do this is to measure the change in 
+time averages of differential properties. One way to do this is to
-average stress tensor in an NVT simulations when the cell volume undergoes a
+measure the change in average stress tensor in an NVT simulations when
-finite deformation. In order to balance
+the cell volume undergoes a finite deformation. In order to balance
-the systematic and statistical errors in this method, the magnitude of the
+the systematic and statistical errors in this method, the magnitude of
-deformation must be chosen judiciously, and care must be taken to fully
+the deformation must be chosen judiciously, and care must be taken to
-equilibrate the deformed cell before sampling the stress tensor. Another
+fully equilibrate the deformed cell before sampling the stress
-approach is to sample the triclinic cell fluctuations that occur in an 
+tensor. Another approach is to sample the triclinic cell fluctuations
-NPT simulation. This method can also be slow to converge and requires
+that occur in an NPT simulation. This method can also be slow to
-careful post-processing <A HREF = "#Shinoda">(Shinoda)</A>
+converge and requires careful post-processing <A HREF = "#Shinoda">(Shinoda)</A>
 </P>
 <HR>
 

doc/Section_howto.txt

@@ -1437,36 +1437,36 @@ frictional walls, as well as triangulated surfaces.
 4.18 Elastic constants :link(4_18),h4
 
 Elastic constants characterize the stiffness of a material. The formal
-definition is provided by the linear relation that holds between
+definition is provided by the linear relation that holds between the
-the stress and strain tensors in the limit of infinitesimal deformation.
+stress and strain tensors in the limit of infinitesimal deformation.
-In tensor notation, this is expressed as s_ij = C_ijkl * e_kl, where 
+In tensor notation, this is expressed as s_ij = C_ijkl * e_kl, where
 the repeated indices imply summation. s_ij are the elements of the
-symmetric stress tensor. e_kl are the elements of the symmetric
+symmetric stress tensor. e_kl are the elements of the symmetric strain
-strain tensor. C_ijkl are the elements of the fourth rank tensor
+tensor. C_ijkl are the elements of the fourth rank tensor of elastic
-of elastic constants. In three dimensions, this tensor has 3^4=81
+constants. In three dimensions, this tensor has 3^4=81 elements. Using
-elements. Using Voigt notation, the tensor can be written
+Voigt notation, the tensor can be written as a 6x6 matrix, where C_ij
-as a 6x6 matrix, where C_ij is now the derivative of s_i
+is now the derivative of s_i w.r.t. e_j. Because s_i is itself a
-w.r.t. e_j. Because s_i is itself a derivative w.r.t. e_i, it follows
+derivative w.r.t. e_i, it follows that C_ij is also symmetric, with at
-that C_ij is also symmetric, with at most 6*5/2 = 21 distinct elements.
+most 6*5/2 = 21 distinct elements.
 
 At zero temperature, it is easy to estimate these derivatives by
-deforming the cell in one of the six directions using 
+deforming the cell in one of the six directions using the command
-the command "displace_box"_displace_box.html 
+"displace_box"_displace_box.html and measuring the change in the
-and measuring the change in the stress tensor. A general-purpose
+stress tensor. A general-purpose script that does this is given in the
-script that does this is given in the examples/elastic directory
+examples/elastic directory described in "this
-described in "this section"_Section_example.html.
+section"_Section_example.html.
 
-Calculating elastic constants at finite temperature is more challenging,
+Calculating elastic constants at finite temperature is more
-because it is necessary to run a simulation that perfoms time averages
+challenging, because it is necessary to run a simulation that perfoms
-of differential properties. One way to do this is to measure the change in 
+time averages of differential properties. One way to do this is to
-average stress tensor in an NVT simulations when the cell volume undergoes a
+measure the change in average stress tensor in an NVT simulations when
-finite deformation. In order to balance
+the cell volume undergoes a finite deformation. In order to balance
-the systematic and statistical errors in this method, the magnitude of the
+the systematic and statistical errors in this method, the magnitude of
-deformation must be chosen judiciously, and care must be taken to fully
+the deformation must be chosen judiciously, and care must be taken to
-equilibrate the deformed cell before sampling the stress tensor. Another
+fully equilibrate the deformed cell before sampling the stress
-approach is to sample the triclinic cell fluctuations that occur in an 
+tensor. Another approach is to sample the triclinic cell fluctuations
-NPT simulation. This method can also be slow to converge and requires
+that occur in an NPT simulation. This method can also be slow to
-careful post-processing "(Shinoda)"_#Shinoda
+converge and requires careful post-processing "(Shinoda)"_#Shinoda
 
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 :line