A physics-augmented neural network framework for finite strain incompressible viscoelasticity

2025-11-04

AI Summary

This work addresses the challenge of modeling incompressible viscoelastic materials under finite strains. We propose a thermodynamically consistent physics-informed neural network (PINN) framework grounded in generalized standard material theory. The deformation gradient is multiplicatively decomposed, and the unimodularity of the inelastic part is strictly enforced to ensure objectivity, incompressibility, and material symmetry. A novel monotonic fully input-convex neural network parameterizes the free energy and dissipation potential; trainable gating layers coupled with ℓᵖ regularization automatically identify the intrinsic variable dimensionality, ensuring both structural adaptivity and physical consistency. Evolution equations are solved via implicit exponential time integration in an invariant-based representation. The model is calibrated jointly on synthetic and experimental data. It demonstrates superior fitting, interpolation, and extrapolation across broad loading paths and strain rates, and linearization recovers classical linear viscoelastic theory, validating its asymptotic consistency.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Computer Vision: Multi-modal Vision
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Web Mining and Content Analysis: Models for Web evolution

Abstract

We propose a physics-augmented neural network (PANN) framework for finite strain incompressible viscoelasticity within the generalized standard materials theory. The formulation is based on the multiplicative decomposition of the deformation gradient and enforces unimodularity of the inelastic deformation part throughout the evolution. Invariant-based representations of the free energy and the dual dissipation potential by monotonic and fully input-convex neural networks ensure thermodynamic consistency, objectivity, and material symmetry by construction. The evolution of the internal variables during training is handled by solving the evolution equations using an implicit exponential time integrator. In addition, a trainable gate layer combined with lp regularization automatically identifies the required number of internal variables during training. The PANN is calibrated with synthetic and experimental data, showing excellent agreement for a wide range of deformation rates and different load paths. We also show that the proposed model achieves excellent interpolation as well as plausible and accurate extrapolation behaviors. In addition, we demonstrate consistency of the PANN with linear viscoelasticity by linearization of the full model.

Problem

• Modeling finite strain incompressible viscoelastic materials with thermodynamic consistency
• Automatically determining required internal variables during neural network training
• Ensuring material objectivity and symmetry through invariant-based neural networks

Innovation

• Physics-augmented neural network for viscoelasticity modeling
• Implicit exponential time integrator for variable evolution
• Trainable gate layer with regularization for variable identification