ODE-DSN: A surrogate model for dynamic stiffness in microscopic RVE problems under nonuniform time-step strain inputs

Abstract In multiscale finite-element methods, solving macroscopic problems typically requires addressing computationally expensive microscopic representative volume element (RVE) problems. To reduce this computational burden, a data-driven approach using artificial neural networks has been employed to pretrain the strain–stress relationship of the microscopic RVE, bypassing the need for full microscale calculations. Existing research has also explored the use of recurrent neural networks to handle history-dependent materials. Building on this approach, this paper introduces a novel ordinary differential equation-dynamic stiffness network model to capture the dynamic stiffness of time-dependent materials and compute stress. The stiffness-based framework enhances the model’s physical consistency and interpretability, while the ordinary differential equation neural network effectively manages nonuniform time sampling in strain inputs. Examples demonstrate that the model accurately learns material behavior with limited data (around 560 random strain–stress sequences) and effectively handles nonuniform time steps. This method addresses the challenge of handling strain inputs with nonuniform time steps while offering potential advantages in computational efficiency and resource utilization.