New finite strain elastoplastic equations for accurately and explicitly simulating pseudoelastic-to-plastic transition e
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APPLIED MATHEMATICS AND MECHANICS (ENGLISH EDITION) 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 XIAO1,2,†
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 Jan. 24, 2020 / Revised Jul. 9, 2020) 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 Chinese Library Classification O33 2010 Mathematics Subject Classification
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74A99
Introduction
Shape memory alloys (SMAs) with wide applications in various fields, such as actuators, biomedical devices, and energy absorbers, display two kinds of recovery effects under loading cycles and thermal cycles, namely, the pseudo-elastic effect and the shape memory effect. In the past decades, much attention has been directed to effectively simulating such remarkable effects from various standpoints based on either a micromechanism-based standpoint or a ∗ Citation: WANG, S. Y., ZHAN, L., XI, H. F., and XIAO, H. New finite strain elastoplastic equations for accurately and explicitly simulating pseudoelastic-to-plastic transition effects of SMAs. Applied Mathematics and Mechanics (English Edition) (2020) https://doi.org/10.1007/s10483-020-2659-7 † Corresponding author, E-mail: [email protected] Project supported by the National Natural Science Foundation of China (No. 11372172) and the Start-up Fund from Jinan University in Guangzhou of China ©Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2020
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Siyu WANG, Lin ZHAN, Huifeng XI, and Heng XIAO
phenomenological standpoint. Certain representative results may be found in Refs. [1]–[8]. A survey is given by Patoor et al.[9] and Lagoudas et al.[10] . For an SMA sample, it is know
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