Simplification of the Isotropic Generalized Stop-Type Prandtl-Ishlinskii Vector Hysteresis Operator Using Analytical Return-Point Mapping

2026-07-08

AI Summary

This work proposes a simplified thermodynamically consistent generalized Prandtl–Ishlinskii (GPI) hysteresis operator to address the high computational cost of traditional GPI models, which require local iterative updates for each hysteresis unit. By replacing the nonlinear mapping with an identity mapping, the new formulation directly weights the outputs of individual hysteresis units while preserving the non-hysteretic response characterized by ramp-stop basis functions. Computational efficiency is significantly enhanced through the incorporation of an analytical solution for local plastic correction and an explicit return-point mapping under isotropic conditions, thereby eliminating the need for per-unit Newton iterations. Numerical experiments demonstrate that the proposed model achieves accuracy comparable to the original GPI model while substantially reducing computational time.

Abstract

While the thermodynamically formulated generalized Prandtl-Ishlinskii stop-type operator effectively captures hysteresis nonlinearities, it requires a local iterative procedure to update each hysteron, resulting in considerable computational effort. In this work, we propose a simplified thermodynamic formulation of the generalized Prandtl-Ishlinskii stop operator. The nonlinear mapping on the stop operator is replaced by an identity, such that the hysteresis operators are directly weighted through their outputs, while the nonlinear anhysteretic response, represented by ramp dead-zone basis functions, is fully preserved. For isotropic cases, this simplification enables a closed-form solution for the local plastic correction, eliminating per-hysteron iterative Newton updates. The resulting constitutive mapping is integrated into a finite element solver, and numerical results show a significant reduction in computation time with accuracy comparable to the generalized model.

Problem

• hysteresis
• Prandtl-Ishlinskii operator
• computational efficiency
• isotropic
• iterative procedure

Innovation

• Prandtl-Ishlinskii operator
• hysteresis modeling
• analytical return-point mapping
• computational efficiency
• isotropic hysteresis