Potential Free FEM Workflow

CAD (probably not free)

NetGen convert .stl into file type readable by GMSH

GMSH

FEniCS scripted through python or Matlab

Python is really easy to install on Unix systems.  Please note that in the example instead of x, and y for the dirchelet boundary condition, x[0] and x[1] were used instead inorder to get program to work.

Post Processing: GMSH (again)

The real question is whether I will be able to script the whole process via python.  I think so (and whether it can do time dependent contact mechanics problems).

Updates incoming 🙂

Update 8/02/2016

I have found getfem++ to be rather buggy. That is the sample problems have errors on my machine. It is a shame, because getfem++ looked so dang nice. If I come back to it I will update again here.

Potential Free FEM Workflow

Slip Systems

When talking about slip systems, the it is important to speak the language. There is a common way for defining crystallographic lines and planes within the unit cell.

Lines/Directions

Lines or directions are defined by two points.  The first point is the origin on the unit cell. Then the other end of the vector is projected onto the three axes measured by the unit cell dimensions.  The three indices are then reduced to the smallest possible integer values.  Finally the values are given in brackets [uwv]  Overbars are used to represent negative numbers so instead of [-100] we would write [100].  Unfortunately in wordpress in overline is a little bit annoying to use so I will sometimes use the less compact form with the negative in front.

Hexagonal crystals (like sapphire) use a four-axis (Miller-Bravis) coordinate system. The first three axes  are all on the x-y plane with 120 degree separation between them.  The fourth axis is the z-axis.

Planes

Although planes are typically defined by the direction normal. Crystallographers define them by their Miller indices (hkl).  Let a plane intersect not pass through the origin.  Then let the plane pass through the x, y and z axes at the points a, b, c.  If the plane passes doesn’t pass through an axis, assign the value of ∞.  Then the reciprocal of these numbers (when moved to a lowest common integer) are the Miller indices.  For example (001) is the xy plane

 

Slip

Slip is the usual method of plastic deformation in metals by blocks fof the crystal sliding past one another along definite crystallographic planes.  There exists a slip plane, and a slip direction.  The plane is the plane which gets moved and the slip line is the direction.  Generally slip occurs in the plane of greatest atomic density and the direction is the closest packed direction with the plane. This is because slip keeps a single crystal as a single crystal.

 

Dislocations

A dislocation is a type of defect in the crystal structure.  Specifically it is a line defect. It is what is responsible for slip.  Typically, it is an extra half plane of atoms in the crystal lattice.  This half plane can then move easily move perpendicularly through the crystal.

 

(In Future Include and describe some figures).

 

 

 

 

Sources:

Callister, William D. Materials Science and Engineering.

Slip Systems

Diplomacy Notes

I have started playing diplomacy online.  Here I am printing some of my commonly used opening messages so that I can reuse them in future games.

 

From a recent game as Austria:

Dear Turkey,

Conventional wisdom states that Austria and Turkey should each recruit allies and attack the other. However, I think that is a terrible idea. Why? Because, we both have bigger fish to fry in the beginning. Italy threatens your ability to dominate the Mediterranean and Russia will always be eyeing your territory in order to establish a good defensive position in the south with the inability to be flanked (the stalemate line runs right through Turkey. For Austria, it is nearly impossible to actually attack Turkey. No, it is impossible for Austria to attack Turkey’s homeland. Not only that but Germany, Russia and Italy are all eyeing Austria’s lands. I would therefore like to propose an alliance. An Austrian Turkish alliance. We will split up the Balkans 2-2 your choice on whether you want Rumania or Greece I will take the other and we can both agree to attack the enemy of your choosing (Russia or Italy) depending on whether you are interested in pursuing a naval strategy or northern strategy. This will allow Turkey early expansion opportunity and Austria some time to make her homeland safe.

Please consider my proposal,
Your friend, Austria

Dear Russia,

Perhaps nobody shares the security concern of the dual monarchy and the tsar. Not only do we both have 4 hostile neighbours, but we are both part of the dreaded central triangle (Germany, Russia, Austria). My experience says that a Russo-Austrian alliance is more beneficial, long term than a German-Austrian. We can collaborate more (on the Germans and the Turks), and more importantly an Austrian alliance seals off one of the more important defences in Russia.

Your Friend,
The Hapsburgs

Austria-Italian Relations

As you are aware, the center must hold. Austria and Italy are more or less forced to ally on the first turn. Italy needs help expanding (either into France) or into Turkey. Expanding into Turkey with Austria is the most popular option with good reasons. Your homeland is safe due to the alliance with Austria, and you get to attack Turkey through their most vulnerable location, Smyrna and Syria. I would suggest a Lepantao:
Naples to ION,
ROM to APU or NAP
VEN to PIE (note that the typical DMZ of PIE does far more for France than it does for Italy (and depending on your relationship with Germany and England, it gives you opportunity for growth.

Let me know your thoughts,

Austria

Dear Germany,

Austria and Germany both have the most complicated security relations on the board. For good reason they rarely attack each other in the beginning. The last game I played saw a Germany attack Austria and they were both eliminated by 1904. I would like to propose a mutual security pact. Right now you are probably more interested in the west, and I am more interested in the south, however I believe that it is in both of our interests to gang up on Russia if they come after either of us. If Russia is attacking the German or the Austrian, then we should work together to rid the world of such behaviour.

Dear England,

Your are perhaps Austria’s only natural ally in this game, by that I mean, you are close enough that we can help one another, but far enough away that neither of us covets the other’s territory. I have two issues I want to discuss. The first is Scandinavia. I believe that you should make it a priority to go after Scandinavia. The four supply centers can be held by only three units. I believe that it would be in your and my best interest if you were able to hold the nordic countries. More importantly, it would deny Russia and Germany those supply centers which they would only use to attack us.

The second discussion I want to have is on Italy. I believe next to a Turkish attack, the French opening is one of Italy’s bolder moves. Spain, Marseilles and Tunis make a good base of operations for Italy, so you might find a willing ally. On your end, that would leave you as the dominate naval power in the north and sitting in very good position. If I were you I would feel him out on this issue.

Your Friend, Austria

Diplomacy Notes