Hierarchical cellular materials are ubiquitous in nature and lead many extraordinary mechanical properties, such as ultralight, ultrastiff, and high toughness. In this study, we introduce three families of 3D hierarchical lattice metamaterials, i.e., cubic, octahedron, and hybrid families, made out of ferroelectric materials. Multiscale asymptotic homogenization (MAH) is introduced for predicting the effective thermo-electro-mechanical properties of hierarchical ferroelectric metamaterials. The effect of hierarchy order, lattice topology (including aspect ratio) and relative density on piezoelectric and pyroelectric figures of merit, which assess the multifunctional performance of ferroelectric metamaterials when used as sensors and energy harvesters, is explored. Although 1 st -order lattice ferroelectric metamaterials remarkably improve the piezoelectric and pyroelectric figures of merit compared to fully-solid ferroelectric materials, increasing hierarchy order can further improve these figures of merit. Hybrid hierarchical lattice ferroelectric metamaterials show improved piezoelectric and pyroelectric properties that are not achievable by their fractal-like counterparts. For example, compared to the 1 st -order BCC ferroelectric metamaterials with an FOM33 of more than 50 times higher than bulk ferroelectric materials, FOM33 of the 2 nd -order octet-truss/BCC hierarchical metamaterials can be improved by 50.7%; this improvement is 43.8% and 43.2% for 2 nd -order BCC and 2 nd -order octet-truss self-similar hierarchical metamaterials, respectively. Finally, scaling relationships for predicting the thermo-electro-mechanical properties of lattice hierarchical ferroelectric metamaterials, covering the whole range of relative densities, are proposed. The study highlights the potential applications of bioinspired hierarchical structures, with integrated mechanical, piezoelectric, and pyroelectric properties, as hydrophone, pressure and temperature sensors, and energy harvesters.

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Figure 1: (a) Aggregation of the force and form diagrams of a truss cellular unit-cell and (b) aggregation of the force and form diagrams of a shell-based cellular (shellular) unit-cell (similar to the Schwarz P unit-cell) generated in 3DGS.

It has been widely known that for complicated beam-like structures with various types of attachments and/or discontinuities analytical techniques are not always applicable. In this paper, a very efficient numerical method based on the Tau method is proposed to tackle the mentioned problem. A general form of the linear vibrational eigen-equation, based on the Euler–Bernoulli bending theory, together with its boundary conditions and continuity equations is considered. The problem is then formulated using a segmented form of the operational Tau method which is called the segmented operational Tau method. To investigate the reliability and accuracy of the proposed method some vibrational problems are solved and compared with the analytical solutions providing the exact frequencies and mode shapes. For a complicated case of a non-uniform beam with various types of attachments, since there was no analytical solution, results are validated with the finite element method. This paper has provided a platform for solving free vibrational problems of many complicated constrained systems through a very simple, highly accurate technique.

The multi-physics of piezoelectric materials under different environmental conditions has been an active research subject for a few decades. Particularly, the thermoelastic behaviour of smart materials and structures is of great importance to their reliability in different applications. Traditionally, the Fourier heat conduction theory was introduced in dealing with the thermoelastic reactions of smart materials and structures. This may lead to reasonable analyses and useful guidelines in design of smart structures, especially when no severe thermal gradient is involved. However, when a severe thermal gradient is indeed involved in the service environment of a smart structure, the analysing results based on the Fourier heat conduction theory is unrealistic and usually rendered useless. Non-Fourier heat conduction theories have been introduced in the thermoelastic analysis of smart materials and structures in recent years and resulted in reasonable results. In this paper, we review the recent results of a thermopiezoelectric problem of a one-dimensional (1-D), finite length, functionally graded medium excited by a moving heat source using both the Fourier and Non-Fourier heat conduction theories. Numerical examples are displayed to illustrate the effects of non-homogeneity index, length and thermal relaxation time on the results.