# Computational approaches for dynamically loaded low-ductility metals

A generic Charpy simulation showing fracture at locations not observed in the lab

Eulerian simulations of un-notched Charpy impact specimens, provide unsatisfactory results in that experimentally observed bend angle, absorbed energy, and fracture mode are not reproduced. The Utah CSM group is independently confirming poor simulation fidelity using conventional constitutive models. From there, we aim to identify the cause, and investigate solutions using capabilities in the Kayenta material framework.

UofU Contributors/collaborators:
Krishna Kamojjala (PhD student, Mech. Engr., UofU)
Scot Swan (MS student, Mech. Engr., UofU)

# Verification Research: The method of manufactured solutions (MMS)

MMS stands for “Method of Manufactured Solutions,” which is a rather sleazy sounding name for what is actually a respected and rigorous method of verifying that a finite element (or other) code is correctly solving the governing equations.

A simple introduction to MMS may be found on page 11 of The ASME guide for verification and validation in solid mechanics. The basic idea is to analytically determine forcing functions that would lead to a specific, presumably nontrivial, solution (of your choice) for the dependent variable of a differential equation.  Then you would verify a numerical solver for that differential equation by running it using your analytically determined forcing function.  The difference between the code’s prediction and your selected manufactured solution provides a quantitative measure of error.

# 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)