Reduced order modeling of structural problems with damage and plasticity

Abstract

Model order reduction (MOR) techniques are used across the engineering sciences to reduce the computational complexity of high‐fidelity simulations. MOR methods reduce the computation time by representing the problem using a lower number of degrees of freedom (DOF). The use of reduced order models (ROM) in the analysis of structural problems with damage and plasticity has the potential to significantly reduce computational time and increase efficiency. Of course, the approximation of a problem in a lower dimensional space introduces an approximation error that needs to be kept small enough so that the results of the ROM maintain their validity. One well‐known reduced order modeling approach is the proper orthogonal decomposition (POD). POD is used to extract the dominant modes of the structure, which are then used to solve a problem in the smaller dimensional subspace. To overcome the limitations of the POD regarding nonlinear problems, the discrete empirical interpolation method (DEIM) is employed. An exemplary uncertainty quantification application is used to investigate the methodology. The investigation shows that the POD‐based DEIM can significantly reduce the computational effort of highly nonlinear structural simulations incorporating damage while maintaining a high approximation accuracy.