Below are shown comparisons of the exact and numerical solution for the vortex ring problem on a square domain.
Breaking from conventional monolithic, layered, or woven designs for protective structures (bumpers, armor, etc.), micromanufacturing technology is now maturing to the point where precisely engineered microstructures may soon be possible. In anticipation of such advances, novel microstructures are being here designed to optimize the ability of protective structures to thwart impact loadings. Preliminary work shows that a variety of specially designed microstructures can distribute structural damage away from an impact site rather than allowing damage to be concentrated at the impact zone. The merits of these design concept are investigated numerically and experimentally in the scope of safety net design.
S. Leelavanichkul (Research fellow, Mechanical Engineering, UofU)
A. Cherkaev (Prof. of Mathematics, UofU)
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.
The publication, “Caveats concerning conjugate stress and strain measures (click to download)” contains an analytical solution for the stress in a fiber reinforced composite in the limit as the matrix material goes to zero stiffness. Because the solution is exact for arbitrarily large deformations, it is a great test case for verification of anisotropic elasticity codes, and it nicely illustrates several subtle concepts in large-deformation continuum mechanics.
Also see related viewgraphs entitled “The distinction between large distortion and large deformation.”