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144:. Flexoelectricity plays a critical role in explaining many interesting electromechanical behaviors in hard crystalline materials and core mechanoelectric transduction phenomena in soft biomaterials. Most excitingly, flexoelectricity is a size-dependent effect that becomes more significant in nanoscale systems, such as crack tips.
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In common useage flexoelectricity is the generation of polarization due to a strain gradient; inverse flexoectricity is when polarization, often due to an applied electric field, generates a strain gradient. Converse flexoelectricity is where a polarization gradient induces strain in a material.
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136:, but while piezoelectricity refers to polarization due to uniform strain, flexoelectricity refers specifically to polarization due to strain that changes from point to point in the material. This nonuniform strain breaks
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Hongguang Wang, Xijie Jiang, Yi Wang, Robert W. Stark, Peter A. van Aken, Jochen
Mannhart, Hans Boschker (2020). "Direct observation of huge flexoelectric polarization around crack tips".
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Thanh D. Nguyen, Sheng Mao, Yao-Wen Yeh, Prashant K. Purohit, Michael C. McAlpine (2013). "Nanoscale
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effect and the second term corresponds to the flexoelectric polarization induced by the strain gradient.
326:{\displaystyle P_{i}=e_{ijk}\epsilon _{jk}+\mu _{ijkl}{\frac {\partial \epsilon _{jk}}{\partial x_{l}}}}
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Pavlo Zubko, Gustau
Catalan, and Alexander K. Tagantsev (2013). "Flexoelectric Effect in Solids".
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