# Resource and Tutorial: thermostatics derivative simplification tables

When studying thermodynamics, do you feel lost in an alphabet soup of too many derivatives? Do you take a “random walk” through various identities hoping to stumble upon the right answer? If so, then this document will help! It describes a systematic way to express any thermostatics derivative in terms of fundamental thermodynamic state variables (pressure, temperature, entropy, and specific volume) and basic material properties such as specific heat, bulk modulus, thermal expansion coefficient, Gruneisen’s parameter, etc.

# Tutorial: How to do input/output in FORTRAN

One of these days, you might encounter FORTRAN source code (very common in legacy material models even in modern C++ codes). You might have to “tweak” the FORTRAN even if you aren’t an expert. This program illustrates how to read and write numbers and strings in FORTRAN, which should familiarize you with the syntax. See next entry for further assistance in deciphering Fortran.

# Tutorial: Define Your Strain!

This single-page document emphasizes the need for experimentalists and theorists alike to ALWAYS define their strain measure. For every percent increase in strain, the most popular measures of strain will disagree by as much as 1.5%. This might not sound like much, but try running a simple shear Von Mises strain cycle using log strain and engineering strain. You will find that the engineering strain calculation produces anomalous PRESSURES because volumetric strain does NOT equal the trace of strain EXCEPT for logarithmic strain.

# Tutorial: Mohr's Circle

A self-study refresher with interesting tidbits such as Pole Point and how to do Mohr’s circle for nonsymmetric matrices — very useful for quickly doing a polar decomposition! (Last posted 2003, but considerable work has been performed recently to incorporate Mohr’s circle as part of the opensource VTK for visualization in finite element simulations).

# Tutorial: Rotation

A REALLY BIG (long download time) tutorial on how to describe rotation. Topics include coordinate transformations, tensor transformations, converting an axis and angle of rotation into a rotation tensor, Euler angles, quaternions, and generating a uniformly random rotation tensor. This document also discusses the common numerical problem of “mixing” rotations in such a way that the mixed rotation is physically reasonable. The pages in the document that deal with random rotations contain some complicated figures, so don’t worry if your pdf reader pauses for a while on those pages. As a matter of fact, watching the pdf viewer render the figures is like an informative movie because it draws the random dots in the same order as I computed them. By watching the rendering, you can see the nonuniform clustering quite clearly.] (Last posted here 020509, but a formal publication is anticipated)