PI-GINOT: Data-free geometry-informed neural operator learning for finite-strain hyperelasticity on parametric DogBone specimens

Abstract

Parametric nonlinear solid-mechanics simulations are widely used in virtual testing, optimisation, and uncertainty analysis, but repeated finite-element simulations become costly when geometry changes. This paper presents PI-GINOT, a physics-informed neural operator that predicts finite-strain hyperelastic responses across a four-parameter family of DogBone specimens without using finite-element training data. Each specimen is described by a boundary point cloud, which is encoded into geometry features. A cross-attention decoder then predicts displacement at arbitrary points. Displacement boundary conditions are enforced exactly, while stresses are computed using automatic differentiation and a compressible Neo-Hookean plane-stress model. Training is guided by equilibrium, traction-free and symmetry conditions, deformation stability, and internal force consistency. Abaqus simulations are used only after training for validation. Across eight test geometries, PI-GINOT achieves displacement errors of 2.1%-7.1%, peak von Mises stress errors of 0.9%-13.3%, and section-force errors below 10.3%. Larger errors occur in individual stress components, especially for narrow specimens, mainly because of steep stress gradients near the gauge-to-fillet transition. These results show that PI-GINOT can provide useful geometry-dependent predictions for nonlinear solid mechanics without labelled simulation data, while also revealing where better local stress resolution is still needed.