Modeling the flexoelectric effect around the tip of nano-cracks using a collocation MFEM

Tian, Xinpeng; Popović, Slobodan; Zhou, Haiyang; Deng, Qian; Sládek, J.; Sládek, V.

doi:10.1016/j.engfracmech.2023.109452

Cited by 13 publications

(4 citation statements)

References 34 publications

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“…Thus, both fundamental field variables and their associated derivatives in x 3 -direction are equal to zero. Then, the 3D constitutive relations given by equations ( 4)-( 7) can be reduced to the 2D constitutive relations [24,32,39] given by…”

Section: Flexoelectricity Theorymentioning

confidence: 99%

“…The compatibility between such approximations is satisfied at certain collocation points on each finite element. On the basis of the static collocation MFEM proposed by authors previously [7,32], the dynamic collocation MFEM is proposed for the analysis of the interaction between the mechanical wave and flexoelectric effect in flexoelectric media. In particular, during the mechanical wave propagation in the flexoelectric medium, it involves an extremely complex dynamic electromechanical coupling where huge number of DOFs would be introduced.…”

Section: Collocation Mfem For the Dynamics Of Flexoelectric Solidsmentioning

confidence: 99%

“…where K e uu , K e uϕ , K e ϕ u , and K e ϕ ϕ are components of the element stiffness matrix, which are the same as that in the static collocation MFEM [32]. F e u , F e r , F e ϕ , and F e w are components of the element loading vector, and vary with time.…”

Section: Discretization and Collocation Of The Feesmentioning

confidence: 99%

“…Our previously proposed collocation MFEM [7,32] only focus on static problems. In this work, to study the propagation of mechanical waves, we develop the dynamic version of it.…”

Section: Introductionmentioning

confidence: 99%

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Modeling mechanical waves propagation in flexoelectric solids

Zhou,

Tian,

Deng

et al. 2024

Smart Mater. Struct.

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In this paper, the propagation of mechanical waves in flexoelectric solids with the consideration of both the direct and converse flexoelectric effects is studied via a collocation mixed finite element method (MFEM). The dynamic effects associated with mechanical waves propagation are accounted by introducing the kinetic energy in the Hamilton's principle. In the proposed collocation MFEM, a quadratic polynomial is independently assumed for each component of the mechanical strain and electric field. The independently assumed mechanical strain and electric field are collocated with their counterparts computed from the displacement and electric potential at 9 Gaussian quadrature points. Thus, except for the fundamental field variables, no additional degrees of freedom (DOFs) are introduced. By performing the numerical experiments using the collocation MFEM, it is found that due to the direct flexoelectric effect, the propagation of mechanical waves can result in electric polarization in materials. Besides, the converse flexoelectric effect can induce mechanical waves when there are non-uniform transient electric field applied to the material. Numerical results indicate that by increasing the loading speed of the time varying mechanical displacement load, the direct flexoelectric effect associated with the mechanical strain gradient could be significantly enhanced.

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Section: Flexoelectricity Theorymentioning

confidence: 99%

Section: Collocation Mfem For the Dynamics Of Flexoelectric Solidsmentioning

confidence: 99%

Section: Discretization and Collocation Of The Feesmentioning

confidence: 99%

“…Our previously proposed collocation MFEM [7,32] only focus on static problems. In this work, to study the propagation of mechanical waves, we develop the dynamic version of it.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations