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Optimization of Johnson-Cook Constitutive Model for Lead-free Solder Using Genetic Algorithm and Finite Element Simulations

D.S.Liu1, C.L.Hsu1,2

Advanced Institute of Manufacturing for High-tech Innovations and Department of Mechanical Engineering, National Chung Cheng University, Chia-yi County, Taiwan, R.O.C.
Corresponding author. Tel.: +886-5-2720411 (Ext: 23347); fax: +886-5-2720589; Email:

Computers, Materials & Continua 2014, 40(3), 165-178.


To ensure the reliability of microelectronics packages, the high strain rate deformation behavior of the solder joints must be properly understood. Accordingly, the present study proposes a hybrid experimental / numerical method for determining the optimal constants of the Johnson-Cook (J-C) constitutive model for 96.5Sn-3Ag-0.5Cu (SAC305) solder alloy. In the proposed approach, FEM simulations based on the J-C model are performed to describe the load-time response of an SAC305 ball solder joint under an impact velocity of 0.5 m/s. The optimal values of the constitutive model are then determined using an iterative Genetic Algorithm approach based on a comparison of the simulated load-time response and the experimental load-time response. The optimality of the optimized constants is demonstrated by comparing the experimental and simulation results for the load-time curves under impact speeds of 0.3 ∼ 1.0 m/s. It is shown that a good agreement exists between the two sets of results for all values of the impact speed. In other words, the results confirm the validity of the proposed hybrid approach as a means of evaluating the high strain-rate response of lead-free solder.


Cite This Article

. D.S.Liu and . C.L.Hsu, "Optimization of johnson-cook constitutive model for lead-free solder using genetic algorithm and finite element simulations," Computers, Materials & Continua, vol. 40, no.3, pp. 165–178, 2014.

cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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