@Article{icces.2023.010584,
AUTHOR = {Leilei Chen, Haozhi Li, Lu Meng, Pan Chen, Pei Li},
TITLE = {Direct FE<sup>2</sup> Method For Concurrent Multilevel Modeling of Piezoelectric  Structures},
JOURNAL = {The International Conference on Computational \& Experimental Engineering and Sciences},
VOLUME = {26},
YEAR = {2023},
NUMBER = {4},
PAGES = {1--2},
URL = {http://www.techscience.com/icces/v26n4/54085},
ISSN = {1933-2815},
ABSTRACT = {In this paper, a Direct FE<sup>2</sup> method is proposed to simulate the electromechanical coupling problem of 
inhomogeneous materials. The theoretical foundation for the proposed method, downscaling and upscaling 
principles, is the same as that of the FE<sup>2</sup> method. The two-level simulation in the Direct FE<sup>2</sup> method may be 
addressed in an integrative framework where macroscopic and microscopic degrees of freedom (DOFs) are 
related by multipoint constraints (MPCs) [1]. This critical characteristic permits simple implementation in 
commercial FE software, eliminating the necessity for recurrent data transfer between two scales [2-4]. The 
capabilities of Direct FE<sup>2</sup> are validated using four numerical examples, including two benchmark examples, 
a piezoelectric arc honeycomb example and a piezoelectric composite structure example.},
DOI = {10.32604/icces.2023.010584}
}