Accelerating the time-domain microscopic response prediction of linear viscoelastic materials with neural-network-assisted dimensionality reduction and frequency-time domain interconversion

초록

Viscoelastic materials such as polymers and composites exhibit time-and frequency-dependent mechanical responses influenced by microstructural heterogeneity. Accurate prediction is essential, but finite element squared (FE2) analysis is costly because repeated representative volume element (RVE) finite element analysis (FEA) under periodic boundary conditions (PBC) is required at the microscale. This study develops a frequency-domain microscopic response prediction and time-domain reconstruction framework for accelerating constitutive response evaluation within time-domain FE2. We combine frequency-domain RVE analysis, proper orthogonal decomposition (POD), and deep neural networks (DNN), followed by an inverse fast Fourier transform (IFFT) to reconstruct time-domain responses. POD reduces the dimensionality of the microscopic stress field; the DNN predicts the reduced POD coefficients over a wide frequency range; IFFT recovers relaxation moduli. This frequency-time conversion strategy captures both storage and loss modulus of viscoelasticity while eliminating direct hereditary integral evaluations. Numerical analysis using ellipsoidal, sphero-cylindrical, and diverse microstructure RVE models shows relative root mean square errors (RRMSE) below 0.05% for both frequency-and time-domain responses. Compared with direct simulations, runtime is reduced from 19-245 h to 7-17 h and memory from 64.3-324.4 GB to 6.48-64.8 GB, depending on the model. These results show that the method enhances efficiency without compromising accuracy.

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