AI-Assisted Extension of a Nonlinear FEA Program to Material Plasticity: Benchmark-Driven Validation Against Commercial FEA

Abstract

This paper extends a previously published AI-assisted nonlinear finite element analysis library for large-displacement beam structures to material plasticity, under the same human-AI collaborative workflow used for the geometrically-nonlinear original. Two constitutive paths are implemented: a Ramberg-Osgood deformation model and a J2 incremental plasticity model with isotropic hardening, fibre section integration, and a Newton radial-return algorithm required for tabular hardening curves. The implementation is validated against Abaqus B31 beam elements and, decisively, against an independent S4R shell reference model that carries no beam-section idealisation. The converged fibre-integration section tracks the shell reference to within 4-8% across the full load range, a level consistent with ordinary beam-versus-shell theory. A circumferential point-count study of the Abaqus PIPE section (8, 16, 64 points) shows monotonic convergence toward the same fibre answer, while the default PIPE section diverges increasingly from the shell reference as plasticity deepens, reaching about 65% in tip rotation near the fully-plastic moment. Across a multi-support displacement-controlled bend matrix and a moving-support passage test at moderate plasticity, the library agrees with Abaqus to single-digit percentages, and the incremental model reproduces the freezing of plastic strain under elastic unloading confirmed independently in the commercial code. The paper contributes a verified open plasticity extension, a shell-validated characterisation of the commercial PIPE section\'s plastic-range behaviour, practical guidance on material-definition and validation-metric pitfalls, and an extended taxonomy of errors specific to AI-assisted development of numerical software.

Introduction

This paper extends a previously developed AI-assisted nonlinear finite element analysis (FEA) framework by incorporating material nonlinearity into the analysis of large-displacement 2D beam structures. While the earlier work addressed only geometric nonlinearity using linear elastic materials, the present study introduces both the Ramberg–Osgood deformation plasticity model and a J2 incremental plasticity model with isotropic hardening, enabling realistic simulation of loading, unloading, reloading, and residual plastic deformation.

The motivation comes from S-Lay offshore pipeline installation, where pipeline sections undergo repeated bending and unloading as they pass over stinger rollers. Because deformation plasticity cannot capture permanent plastic strains after unloading, an incremental plasticity formulation is necessary for accurate prediction of accumulated strain.

Main Contributions

The paper makes four major contributions:

• Development and verification of an open-source J2 incremental plasticity extension with fibre-based section integration and Newton-based radial return mapping for tabular hardening.
• Validation of beam plasticity behaviour against Abaqus shell models, demonstrating that the proposed fibre-integration approach more accurately represents plastic bending than the default Abaqus PIPE beam section.
• Identification of two important verification challenges: hidden material-definition errors and misleading comparisons based on identical loads instead of identical curvatures.
• Extension of the error taxonomy for AI-assisted engineering software development, identifying new error classes specific to plasticity algorithms.

Background

The paper distinguishes between two plasticity approaches:

• Ramberg–Osgood deformation plasticity, suitable only for monotonic loading because it assumes stress depends solely on total strain and predicts no residual deformation.
• J2 incremental plasticity, which separates elastic and plastic strains, incorporates yield criteria and flow rules, and accurately models unloading, reloading, and permanent deformation.

Material nonlinearity in beam elements is represented through cross-sectional numerical integration, comparing:

• Fibre integration, which discretizes the actual pipe wall thickness.
• Thin-wall integration, used by the Abaqus PIPE section.

A shell model using Abaqus S4R elements serves as an independent physics-based reference because it directly resolves wall stresses without beam approximations.

Methodology

The geometric formulation from the previous work is retained, while material behaviour is extended by:

• Implementing Ramberg–Osgood fibre integration for monotonic analysis.
• Developing a Newton-based radial return algorithm for J2 plasticity with tabulated hardening curves.
• Storing plastic strain history at every fibre to preserve path-dependent behaviour.

Two interchangeable beam section models are implemented:

• A highly accurate 200-strip fibre model.
• A simplified polar thin-wall model reproducing the Abaqus PIPE section.

Human–AI Collaborative Development

The study follows a structured human–AI collaboration:

• The AI implemented algorithms, generated Abaqus input files, predicted numerical results, and proposed explanations for discrepancies.
• The human researcher executed all commercial FEA simulations, verified material definitions against original source models, interpreted results, and approved each development stage.

A pre-registration approach required the AI to make quantitative predictions before every benchmark simulation, ensuring that results could objectively confirm or reject hypotheses.

Verification and Findings

During verification, the fibre-based model initially disagreed with the Abaqus PIPE beam element, predicting smaller tip rotations under plastic loading. Further investigation—including shell model comparisons—revealed that:

• The fibre integration model closely matches the shell reference, accurately representing plastic bending.
• The default Abaqus PIPE section systematically underestimates plastic deformation because of insufficient cross-sectional integration.
• A previously unnoticed material property transcription error caused misleading intermediate results and was discovered only through manual inspection of the original Abaqus model, illustrating the necessity of independent human verification.

Benchmark Analysis

The framework is evaluated using a 10 m cantilever pipe subjected to progressively increasing end moments from 1300 to 1450 kNm, covering the elastic-plastic transition. Additional loading–unloading cycles verify that the J2 incremental plasticity model successfully predicts residual plastic deformation, unlike deformation plasticity.

Conclusion

1) The open beam FEA library of [1] now carries verified material plasticity: a Ramberg-Osgood path for monotonic screening and a J2 incremental path, with Newton radial return, fibre section integration, and committed plastic state, for path-dependent analysis. Plastic strain freezes exactly on unloading, confirmed against the commercial code. 2) Against an independent shell reference, the converged fibre-integration section tracks physical reality to within 4-8% across the full load range, while the default Abaqus B31/PIPE section under-integrates the plastic bending response, diverging by up to about 65% in rotation near the fully-plastic moment. A point-count study (8, 16, 64) confirms this as a quadrature-convergence effect. 3) Across a multi-support bend matrix and a moving-support passage test at moderate plasticity, both section models agree with Abaqus in low single digits, and the compatibility section reproduces the default Abaqus PIPE response within about 1%. 4) Two definition and metric pitfalls, silent material-table mismatches and matched-load rather than matched-curvature comparison, are documented as the dominant hazards of the campaign, alongside an extended four-class error taxonomy for AI-assisted numerical software development. 5) Domain-expert-guided AI collaboration, with mandatory benchmark verification, pre-registered predictions, and, critically, an independent physics reference, produced a verified plasticity extension and corrected a natural misreading of the commercial code, not by trusting either implementation but by anchoring both to shell-level physics.

References

[1] Sivaraman S M 2026 AI-assisted development of a nonlinear finite element analysis program: a case study using a large language model Int. J. Res. Appl. Sci. Eng. Technol. 14 253-264, DOI 10.22214/ijraset.2026.83397 [2] Sivaraman S M 2015 A VBA based computer program for nonlinear FEA of large displacement 2D beam structures Int. J. Res. Appl. Sci. Technol. 3 1-21 [3] Ramberg W and Osgood W R 1943 Description of stress-strain curves by three parameters NACA Technical Note 902 [4] DNV 2021 DNV-ST-F101 Submarine pipeline systems (Hovik: DNV) [5] Simo J C and Hughes T J R 1998 Computational Inelasticity (New York: Springer) [6] Crisfield M A 1991 Non-linear Finite Element Analysis of Solids and Structures vol 1 (Chichester: Wiley) [7] Bathe K J 1996 Finite Element Procedures (Englewood Cliffs: Prentice Hall) [8] De Souza R M 2000 Force-based finite element for large displacement inelastic analysis of frames PhD thesis University of California Berkeley [9] Holsgrove S C and Lyons L P R 1989 Benchmark Tests for Two-Dimensional Thin Beams and Axisymmetric Shells NAFEMS Report N4 [10] Bai Y and Bai Q 2014 Subsea Pipeline Design, Analysis and Installation (Amsterdam: Gulf Professional Publishing) [11] Dassault Systemes 2024 Abaqus Analysis User\'s Guide: Beam cross-section library (Providence: Dassault Systemes Simulia) [12] Hou X et al 2024 Large language models for software engineering: a systematic literature review ACM Trans. Softw. Eng. Methodol. (in press) arXiv:2308.10620

Copyright

Copyright © 2026 Sreeknath Manakkattil Sivaraman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.