Optimal design of micro/nano structures for metamaterials

No.: APVV 18-0004
Duration: 01. 07. 2019 – 30. 06. 2023
Teamleader: J. Sladek
Team members: V. Sladek, O. Hrytsyna, M. Repka, L. Sator, M. Vrabec

Advanced metamaterials for health monitoring of structures are analyzed in the project for optimal design. The piezoelectric response is observed in metamaterials if large strains are occurred in structures. Large strains are observed mainly in nano-sized structures. The classical continuum mechanics cannot be applied for such structures, since it is indifferent to the material microstructure. The intrinsic limitations of classical elasticity are overcome in advanced continuum models. The nano-sized structures with flexoelectric properties can be analyzed successfully. For this purpose, the key task is to determine the higher-order elastic and flexoelectric coefficients in flexoelectric gradient theory. Due to missing experimental methods to obtain these coefficients, a numerical experiments are employed. Unknown flexoelectric coefficient is obtained by fitting the results by gradient theory with microsctructural analysis. Microstructure is not modelled in the gradient theory. The variational principle is applied to derive the governing equations with bearing in mind the constitutive equations leading to both the direct and converse flexoelectricity phenomena. The finite element method (FEM) and meshless formulations are developed to solve problems of flexoelectricity. The mixed FEM is developed in the project, where the C0 continuous interpolation is applied independently for displacement and displacement gradients. Similarly the electric potential and electric intensity vector are approximated by C0 elements. The kinematic constraints between strains and displacements are satisfied by collocation at some cleverly chosen internal points in elements. The attention is paid also to treatment of surface stress effect important in nano-sized structures. The former elegant mathematical theory incorporating surface stresses in elasticity given by Gurtin and Murdoch is extended here to piezoelectricity.