TY - JOUR
T1 - A 3D collocation MFEM for the analysis of flexoelectric solids
AU - Hu, Yuchen
AU - Zhou, Haiyang
AU - Tian, Xinpeng
AU - Deng, Qian
AU - Sladek, Jan
AU - Sladek, Vladimir
AU - Shen, Shengping
N1 - Publisher Copyright:
© 2025 Elsevier Masson SAS
PY - 2025/5/1
Y1 - 2025/5/1
N2 - In this paper, a three-dimensional (3D) collocation mixed finite element method (CMFEM) is proposed for the analysis of flexoelectric solids. In this 3D CMFEM, the independent approximations by quadratic interpolation polynomials are applied for the pair of elastic displacements and strains as well as for the pair of electric potential and electric field, with the compatibility of approximations for each pair being satisfied at the selected Gauss points inside each finite element. Thus, C0 continuous approximations of strains and electric fields can be obtained based on standard finite elements without introducing any additional nodal degrees of freedom (DOFs) except the primary field variables. The accuracy of the present method is validated through comparing the numerical results with the analytical solutions for a cantilever beam and a truncated pyramid. Using the developed CMFEM, we also model the flexoelectric effect in the 3D Mode III crack and find that the flexoelectric field along the crack front line is nonuniform, which is different from previous 2D study and shows the importance of the proposed 3D CMFEM. Besides, numerical results indicate that with the increase of the thicknesses, the out-of-plane displacement and flexoelectric response would decrease.
AB - In this paper, a three-dimensional (3D) collocation mixed finite element method (CMFEM) is proposed for the analysis of flexoelectric solids. In this 3D CMFEM, the independent approximations by quadratic interpolation polynomials are applied for the pair of elastic displacements and strains as well as for the pair of electric potential and electric field, with the compatibility of approximations for each pair being satisfied at the selected Gauss points inside each finite element. Thus, C0 continuous approximations of strains and electric fields can be obtained based on standard finite elements without introducing any additional nodal degrees of freedom (DOFs) except the primary field variables. The accuracy of the present method is validated through comparing the numerical results with the analytical solutions for a cantilever beam and a truncated pyramid. Using the developed CMFEM, we also model the flexoelectric effect in the 3D Mode III crack and find that the flexoelectric field along the crack front line is nonuniform, which is different from previous 2D study and shows the importance of the proposed 3D CMFEM. Besides, numerical results indicate that with the increase of the thicknesses, the out-of-plane displacement and flexoelectric response would decrease.
KW - 3D CMFEM
KW - 3D Mode III crack
KW - Quadratic interpolation polynomials
KW - The flexoelectric effect
UR - https://www.scopus.com/pages/publications/85214014800
U2 - 10.1016/j.euromechsol.2024.105547
DO - 10.1016/j.euromechsol.2024.105547
M3 - 文章
AN - SCOPUS:85214014800
SN - 0997-7538
VL - 111
JO - European Journal of Mechanics, A/Solids
JF - European Journal of Mechanics, A/Solids
M1 - 105547
ER -