Reproduce “Physics-informed neural networks for modeling rate- and temperature-dependent plasticity” on OpenResearch

About this paper

Rajat Arora, Pratik Kakkar, Biswadip Dey, Amit Chakraborty

A Physics-Informed Neural Network (PINN) framework is developed to model strain-rate and temperature-dependent elastic-viscoplastic deformation in solids, demonstrating accurate predictions for stress, plastic strain, and displacement fields within trained data ranges. The work introduces a modified mean squared error for numerically stiff equations and a physics-based loss weighting strategy to enhance training stability.

Key insights

• Using a mixed-variable PINN output formulation (displacement, stress, plastic strain, material strength) is critical for achieving accurate and convergent solutions in solid mechanics, outperforming models that derive stress from displacement gradients.
• The proposed MMSE loss criterion effectively mitigates 'exploding gradients' caused by highly nonlinear power-law constitutive equations, enabling stable training of PINNs for viscoplasticity.
• A simple, non-adaptive, physics-based weighting strategy for loss function components can effectively balance contributions from various physical laws and boundary conditions, leading to robust PINN training without additional computational overhead.

Summary by alphaXiv.