PSI - Issue 80

Xinpeng Tian et al. / Procedia Structural Integrity 80 (2026) 451–461 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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demonstrate that the material length scale parameter can modulate the flexoelectric response by adjusting the crack opening displacement and stress distribution.

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(c) (d) Fig. 6. Comparisons of physical fields near the penny-shaped crack for various length scale parameters l along the predefined path ( x 1 = x 3 = 0, 0 < x 2 < R ) 5. Conclusions The CMFEM is developed for 3D crack analyses in solids with the direct flexoelectricity to deal with higher order derivatives in governing equations of the gradient theory. In the CMFEM C 0 continuous approximations are applied independently to displacements and strains. The constraint between the independent mechanical strains and displacement is satisfied by a collocation method at considered collocation points on each finite element. The J integral expression for 3D crack problems with the direct flexoelectric effect is also derived to characterize the fracture property of flexoelectric solids, where some additional surface integrals are occurring in the 3D J-integral expression in comparison with 2D case. Numerical results indicate that as the tensile loading increases, the stress concentration effect near the crack tip becomes more prominent, resulting in a corresponding enhancement of the electric field intensity induced by the flexoelectric effect. Besides, with the increase of the length scale parameter, both the crack surface displacement and flexoelectric fields decrease accordingly.

Acknowledgements The authors acknowledge the support by the Slovak Research Agency through the grant VEGA-2/0084/24. This work is also supported by the National Natural Science Foundation of China (Grant Nos. 12202155 and 12172142).