Simplification of the Isotropic Generalized Stop-Type Prandtl-Ishlinskii Vector Hysteresis Operator Using Analytical Return-Point Mapping
For researchers and engineers using hysteresis models in finite element simulations, this simplification reduces computational cost without sacrificing accuracy.
The authors simplified the generalized Prandtl-Ishlinskii stop-type hysteresis operator by replacing nonlinear mapping with identity, enabling a closed-form solution for isotropic cases. This reduced computation time significantly while maintaining accuracy comparable to the original model.
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.