Parsimonious Universal Function Approximator for Elastic and Elasto-Plastic Cavity Expansion Problems

TL;DR

This paper introduces a new physics-informed neural network (PINN) approach with a parsimonious loss function to accurately solve elastic and elasto-plastic cavity expansion problems in geotechnics, demonstrating high accuracy across diverse material behaviors.

Contribution

The study proposes a novel parsimonious loss function for PINNs, enabling effective and accurate solutions for complex elastic and plastic PDEs in cavity expansion problems.

Findings

High accuracy in elastic and plastic regimes

Effective across isotropic and anisotropic materials

Provides insights for future complex geotechnical problems

Abstract

Cavity expansion is a canonical problem in geotechnics, which can be described by partial differential equations (PDEs) and ordinary differential equations (ODEs). This study explores the potential of using a new solver, a physics-informed neural network (PINN), to calculate the stress field in an expanded cavity in the elastic and elasto-plastic regimes. Whilst PINNs have emerged as an effective universal function approximator for deriving the solutions of a wide range of governing PDEs/ODEs, their ability to solve elasto-plastic problems remains uncertain. A novel parsimonious loss function is first proposed to balance the simplicity and accuracy of PINN. The proposed method is applied to diverse material behaviours in the cavity expansion problem including isotropic, anisotropic elastic media, and elastic-perfectly plastic media with Tresca and Mohr-Coulomb yield criteria. The results indicate that the use of a parsimonious prior information-based loss function is highly beneficial to deriving the approximate solutions of complex PDEs with high accuracy. The present method allows for accurate derivation of solutions for both elastic and plastic mechanical responses of an expanded cavity. It also provides insights into how PINNs can be further advanced to solve more complex problems in geotechnical practice.