A note on the use of Dynamic Mode Decomposition in mechanics. (March 2022) - Simha, C. Hari Manoj; Biglarbegian, Mohammad
Abstract: We advocate for the use of Dynamic Mode Decomposition (DMD) in mechanics. Snapshots of the temperature or displacement fields are obtained; and the DMD algorithm, which, remarkably, requires a few lines of code, is applied to matrices obtained by time shifting the snapshots. Only the higher-order modes are retained to obtain a lower-rank matrix and used for analysis. We show that DMD can be used to: predict temperature fields during transient heat conduction, estimate natural frequency of a linear elastic structure; identify the onset of plasticity in an elastic–plastic plate with a hole; and obtain a reduced-order model that describes the large deformation of a non-linear elastic structure. Highlights: Dynamic mode decomposition is applied to mechanics. Data-driven method constructs low dimensional model. Low-rank matrix is used to estimate natural frequency of structure. DMD is used to model elastic–plastic material. DMD is used to model large-scale deformation of Mooney–Rivlin material.