New finite strain elastoplastic equations for accurately and explicitly simulating pseudoelastic-to-plastic transition effects of shape memory alloys

doi:10.1007/s10483-020-2659-7

Applied Mathematics and Mechanics (English Edition) ›› 2020, Vol. 41 ›› Issue (10): 1583-1596.doi: https://doi.org/10.1007/s10483-020-2659-7

New finite strain elastoplastic equations for accurately and explicitly simulating pseudoelastic-to-plastic transition effects of shape memory alloys

Siyu WANG¹, Lin ZHAN¹, Huifeng XI¹, Heng XIAO^1,2

1. School of Mechanics and Construction Engineering, MOE Key Lab of Disaster Forecast and Control in Engineering, Jinan University, 601 West Huangpu Avenue, Guangzhou 510632, China;
2. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200072, China

收稿日期:2020-01-24 修回日期:2020-07-09 发布日期:2020-10-09
通讯作者: Heng XIAO E-mail:hxiao@jnu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (No. 11372172) and the Start-up Fund from Jinan University in Guangzhou of China

New finite strain elastoplastic equations for accurately and explicitly simulating pseudoelastic-to-plastic transition effects of shape memory alloys

Siyu WANG¹, Lin ZHAN¹, Huifeng XI¹, Heng XIAO^1,2

1. School of Mechanics and Construction Engineering, MOE Key Lab of Disaster Forecast and Control in Engineering, Jinan University, 601 West Huangpu Avenue, Guangzhou 510632, China;
2. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200072, China

Received:2020-01-24 Revised:2020-07-09 Published:2020-10-09
Contact: Heng XIAO E-mail:hxiao@jnu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (No. 11372172) and the Start-up Fund from Jinan University in Guangzhou of China

摘要/Abstract

摘要： A new finite strain elatoplastic J₂-flow model with coupling effects of both isotropic and anisotropic hardening is proposed with the co-rotational logarithmic rate. In terms of certain single-variable shape functions representing uniaxial loading and unloading curves, explicit multi-axial expressions for the three hardening quantities incorporated in the new model proposed are derived in unified forms for the purpose of automatically and accurately simulating complex pseudoelastic-to-plastic transition effects of shape memory alloys (SMAs) under multiple loading-unloading cycles. Numerical examples show that with only a single parameter of direct physical meaning for each cycle, accurate and explicit simulations may be achieved for extensive data from multiple cycle tests.

关键词: shape memory alloy (SMA), finite deformation, pseudo-elasticity, plasticity, cyclic loading, transition effect, elastoplastic equation, explicit and accurate approach

Abstract: A new finite strain elatoplastic J₂-flow model with coupling effects of both isotropic and anisotropic hardening is proposed with the co-rotational logarithmic rate. In terms of certain single-variable shape functions representing uniaxial loading and unloading curves, explicit multi-axial expressions for the three hardening quantities incorporated in the new model proposed are derived in unified forms for the purpose of automatically and accurately simulating complex pseudoelastic-to-plastic transition effects of shape memory alloys (SMAs) under multiple loading-unloading cycles. Numerical examples show that with only a single parameter of direct physical meaning for each cycle, accurate and explicit simulations may be achieved for extensive data from multiple cycle tests.

Key words: shape memory alloy (SMA), finite deformation, pseudo-elasticity, plasticity, cyclic loading, transition effect, elastoplastic equation, explicit and accurate approach

中图分类号:

74A99

Siyu WANG, Lin ZHAN, Huifeng XI, Heng XIAO. New finite strain elastoplastic equations for accurately and explicitly simulating pseudoelastic-to-plastic transition effects of shape memory alloys[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(10): 1583-1596.

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New finite strain elastoplastic equations for accurately and explicitly simulating pseudoelastic-to-plastic transition effects of shape memory alloys

New finite strain elastoplastic equations for accurately and explicitly simulating pseudoelastic-to-plastic transition effects of shape memory alloys

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