A note on the use of Dynamic Mode Decomposition in mechanics

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. •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.