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Revisiting pyramid compression to quantify flexoelectricity: A three-dimensional simulation study

Amir Abdollahi's picture

Flexoelectricity is a universal property of all dielectrics by which they generate a voltage in response to an inhomogeneous deformation. One of the controversial issues in this field concerns the magnitude of flexoelectric coefficients measured experimentally, which greatly exceed theoretical estimates. Furthermore, there is a broad scatter amongst experimental measurements. The truncated pyramid compression method is one of the common setups to quantify flexoelectricity, the interpretation of which relies on simplified analytical equations to estimate strain gradients. However, the deformation fields in three-dimensional pyramid configurations are highly complex, particularly around its edges. In the present work, using three-dimensional self-consistent simulations of flexoelectricity, we show that the simplified analytical estimations of strain gradients in compressed pyramids significantly overestimate flexoelectric coefficients, thus providing a possible explanation to reconcile different estimates. In fact, the interpretation of pyramid compression experiments is highly nontrivial. We systematically characterize the magnitude of this overestimation, of over one order of magnitude, as a function of the truncated pyramid configuration. These results are important to properly characterize flexoelectricity, and provide design guidelines for effective electromechanical transducers exploiting flexoelectricity.







my question is what did you use as software to simulate your model, is it based on numerical software such as Ansys or you adopt your proper analytical equations?

and thank you

Amir Abdollahi's picture


We have used  a C++ library for the simulations of the model. This library has been developed in our group to simulate mathematical problems using Maximum Entropy Approximants. Please find below a link for more details:



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