Deformation Behavior Modeling of SMAs Under Cyclic Loading Based on Rational Interpolation

WANG Xiaoming; XIAO Heng

doi:10.21656/1000-0887.430279

Volume 44 Issue 6

Jun. 2023

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WANG Xiaoming, XIAO Heng. Deformation Behavior Modeling of SMAs Under Cyclic Loading Based on Rational Interpolation[J]. Applied Mathematics and Mechanics, 2023, 44(6): 694-707. doi: 10.21656/1000-0887.430279

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Deformation Behavior Modeling of SMAs Under Cyclic Loading Based on Rational Interpolation

doi: 10.21656/1000-0887.430279

WANG Xiaoming^{1
,
,},
XIAO Heng^2
,

1.
Institute of Applied Mechanics, Ningbo Polytechnic, Ningbo, Zhejiang 315000, P.R.China
2.
School of Mechanics and Construction Engineering, Jinan University, Guangzhou 510632, P.R.China

Received Date: 2022-09-05
Rev Recd Date: 2022-10-27
Publish Date: 2023-06-01

Abstract

Abstract

A finite elastoplasticity model was proposed to simulate deformation behaviors of SMAs under cyclic loading. First, the explicit formulations of shape functions were given with the rational interpolation method to exactly match any given experimental data. Second, a finite elastoplasticity J2 flow model based on the logarithmic objective rate was built to couple the moving of the yielding center and the expanding of the yielding surface. Third, 3 explicit hardening functions under the single loading cycle were deduced in the uniaxial case, to construct the smooth, unified and multiaxial hardening function through introduction of the local factor and the multiaxial extended invariant. Finally, the model results were compared with the classical test data to prove the effectiveness of the new model. The research results show that, the new model can produce intense Bauschinger effects and simulate the complex deformation of SMAs through improvement of the evolution equation of the back stress. The new smooth unified hardening function can automatically degenerate under the single loading cycle to give results exactly matching the test data. The effective plastic work evolution law deduced with the constitutional equation, and the parameter equations dependent on the effective plastic work contained in the shape functions through rational interpolation, enable the proposed model to predict deformations well.
- J2 flow model,
- SMAs,
- logarithmic objective rate,
- yielding,
- hardening function,
- shape function

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References(53)

References

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