In this paper, the efficiency and accuracy of reduced-order models derived by using the discrete empirical interpolation method were verified for the analysis of nonlinear hyperelastic Also, the matrix version of discrete empirical interpolation method was applied to the analysis of nonlinear hyperelastic materials.
Nonlinear analysis was performed using the Newton-Raphson method within finite element framework. Offline/online strategies were used to construct an efficient reduced-order model. In the offline stage, analysis of the full order model was performed, and data was generated by solving the full order model and by the snapshot method. Then, a proper orthogonal decomposition was applied to the snapshot matrix to extract a proper orthogonal mode. And, the interpolation point was selected by applying the discrete empirical interpolation method algorithm from the proper orthogonal mode, and sample elements were selected. In the online step, only the interpolation points selected in the offline step and the sample elements are calculated, and the full order model is approximated using the Galerkin projection.
Two examples were chosen to verify the accuracy and efficiency of a nonlinear hyperelastic material parametric reduced-order model using discrete empirical interpolation. The parametric reduced-order model of the rubber specimen for tensile testing showed 80.73% reduction in computational time compared to the full order model. As a result of performing 100 samplings on the parametric reduced-order model, the accuracy was verified with the average error of 0.015%. In addition, the parametric reduced-order model of the elastic rubber mount showed that the computational time was reduced by 99.61% compared to the full order model. As a result of performing 50 samplings on the parametric reduced-order model, the accuracy was verified with the average error of 0.0025%. As a result of the reduced-order model constructed by applying a matrix version of discrete empirical interpolation method to nonlinear hyperelastic material, the accuracy was verified with the error of 0.12%.