Publications Details

Dynamic Mode Decomposition of Solids

Yarrington, Cole Y.; Lechman, Jeremy B.

Dynamic mode decomposition (DMD) is a method that has gained notoriety in the field of turbulent fluid flows as a method for decomposing the flow field into modes that could be further deconstructed to understand their influence on the overall dynamics of the system. Forays into solids and non-linear systems were considered, but not applied. In this work, DMD was applied for the first time to the heat-diffusion and reactive heat diffusion equations on a random particle pack of uniform solid spheres. A verification of a linear heat-diffusion test problem was successful, showing equality between the normal modes and Koopman modes obtained from DMD. Further application to a non-linear reactive system revealed stability limits of the underlying modes which are dependent on microstructure and chemical kinetics. This work will enable the development of reactive material models based on further analysis using DMD to quantify the statistical dependencies of transient response on microstructural characteristics.