Physics-Informed Deep Learning for Computational Elastodynamics without Labeled Data

Numerical methods such as finite element have been flourishing in the past decades for modeling solid mechanics problems via solving governing partial differential equations (PDEs). A salient aspect that distinguishes these numerical is how they approximate physical fields of interest. Physics-informed deep learning (PIDL) a novel approach developed recent years PDE solutions and shows promise to solve computational without using any labeled data (e.g., measurement unavailable). The philosophy behind it quantity interest solution variables) by neural network (DNN) embed law regularize network. To this end, training equivalent minimization well-designed loss function contains residuals PDEs well initial/boundary conditions (I/BCs). In paper, we present physics-informed (PINN) with mixed-variable output model elastodynamics resort data, which I/BCs are forcibly imposed. particular, both displacement stress components taken DNN output, inspired hybrid finite-element analysis, largely improves accuracy trainability Since conventional PINN framework augments all residual soft manner Lagrange multipliers, weakly imposed may not be satisfied especially when complex present. overcome issue, composite scheme DNNs established based on multiple single can forcible manner. proposed demonstrated several elasticity examples different I/BCs, including static dynamic wave propagation truncated domains. Results show context applications.