A micromechanical approach for the Cosserat modeling of composites

2017

Smart Mater. Struct.

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The use of multifunctional composite materials adopting piezo-electric periodic cellular lattice structures with auxetic elastic behavior is a recent and promising solution in the design of piezoelectric sensors. In the present work, periodic anti-tetrachiral auxetic lattice structures, characterized by different geometries, are taken into account and the mechanical and piezoelectrical response are investigated. The equivalent piezoelectric properties are obtained adopting a rst order computational homogenization approach, generalized to the case of electro-mechanical coupling, and various polarization directions are adopted. Two examples of in-plane and out-of-plane strain sensors are proposed as design concepts. Moreover, a piezo-elasto-dynamic dispersion analysis adopting the Floquet-Bloch decomposition is performed. The acoustic behavior of the periodic piezoelectric material with auxetic topology is studied and possible band gaps are detected.

Section: In-plane Auxetic Strain Sensormentioning

confidence: 95%

Auxetic behavior and acoustic properties of microstructured piezoelectric strain sensors

Bellis

2017

Smart Mater. Struct.

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“…at the numerator, the group velocities becomes which are equivalent to the energy velocity components (46), (47).…”

Section: Appendixd Group Velocitymentioning

confidence: 99%

Acoustic wave polarization and energy flow in periodic beam lattice materials

International Journal of Solids and Structures

Lepidi

2018

The free propagation of acoustic plane waves through cellular periodic materials is generally accompanied by a flow of mechanical energy across the adjacent cells. The paper focuses on the energy transport related to dispersive waves propagating through nondissipative microstructured materials. The generic microstructure of the periodic cell is described by a beam lattice model, suitably reduced to the minimal space of dynamic degrees-of-freedom. The linear eigenproblem governing the wave propagation is stated and the complete eigensolution is considered to study both the real-valued dispersion functions and the complex-valued waveforms of the propagating elastic waves. First, a complete family of nondimensional quantities (polarization factors) is proposed to quantify the linear polarization or quasi-polarization, according to a proper energetic criterion. Second, a vector variable related to the periodic cell is introduced to assess the directional flux of mechanical energy, in analogy to the Umov-Poynting vector related to the material point in solid mechanics. The physical-mathematical relation between the energy flux and the velocity of the energy transport is recognized. The formal equivalence between the energy and the group velocity is pointed out, according to the mechanical assumptions. Finally, all the theoretical developments are successfully applied to the prototypical beam lattice material characterized by a periodic tetrachiral microstructure. As case study, the tetrachiral material offers interesting examples of perfect and nearly-perfect linear polarization. Furthermore, the nonlinear dependence of the energy fluxes on the elastic waveforms is discussed with respect to the acoustic and optical surfaces featuring the energy spectrum of the material. As final remark, the occurrence of negative refraction phenomena is found to characterize the high-frequency optical surface of the frequency spectrum. (Andrea Bacigalupo) tal lattice, and related its flux density to the particle velocities through the concept of characteristic impedance [3,4]. Almost concurrently, Maurice A. Biot established some general theorems relating the group wave velocity and the energy velocity in anisotropic, non-homogeneous, non-dissipative media [5]. Over the last decades, specific issues related to the transport of mechanical energy have been treated in different monographs concerning anisotropic elastic solids [6], viscoelastic heterogeneous solids and fluids [7], anisotropic, anelastic, porous and electromagnetic materials [8], viscoelastic layered media [9]. Occasional but sharp attention has been specifically devoted to the flow of mechanical energy in periodic systems, including crystal lattices [10,11] and structural assemblies [12,13].The essential idea, shared by the largest majority of literature studies, is that strict formal and substantial analogies can be established between the radiation of electromagnetic energy and the transfer of mechanical energy [14]. According to this standpoint, the well-known Poyn...

“…In order to overcome these drawbacks, multiscale techniques, based on homogenization approaches, are a very valuable tool to gather both a synthetic and thorough description of the complex material behaviour. The investigation of the overall static and dynamic behaviour of periodic elastic composite materials has been performed resorting either to asymptotic approaches (Bakhvalov and Panasenko, 1984;Gambin and Kröner, 1989;Allaire, 1992;Boutin, 1996;Fish and Chen, 2001;Andrianov et al, 2008;Tran et al, 2012;Bacigalupo, 2014), or to variational-asymptotic approaches (Smyshlyaev and Cherednichenko, 2000;Peerlings and Fleck, 2004;Bacigalupo andGambarotta, 2012, 2014), or also to identification techniques, among which computational approaches (Forest and Sab, 1998;Kouznetsova et al, 2004;Kaczmarczyk et al, 2008;Bacigalupo and Gambarotta, 2010;De Bellis and Addessi, 2011;Li et al, 2011;Addessi et al, 2013;Lesičar et al, 2014;Trovalusci et al, 2015;Addessi et al, 2016;Biswas and Poh, 2017;Reccia et al, 2018;Trovalusci et al, 2017) and analytical approaches (Bigoni and Drugan, 2007;Mühlich et al, 2012;Bacca et al, 2013a,b;Bacigalupo and Gambarotta, 2013;Bacigalupo et al, 2017;Hütter, 2017). Generalized homogenization approaches have been proposed to date to handle multi-field problems, ranging from thermo-elastic, thermo-diffusive, to piezoelectric and thermo-piezoelectric problems (Gałka et al, 1996;Pettermann and Suresh, 2000;…”

Section: Introductionmentioning

confidence: 99%

Characterization of hybrid piezoelectric nanogenerators through asymptotic homogenization

Bellis

Computer Methods in Applied Mechanics and Engineering

Zavarise

2019

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In the framework of energy scavenging for applications in flexible/strechable electronics, hybrid piezoelectric nanogenerators, made up with Zinc oxyde nanorods, embedded in a polymeric matrix, and growth on a flexible polymeric support, are investigated. The ZnO nanorods are arranged in clusters, forming nearly regular distributions, so that periodic topologies can be realistically assumed. Focus is on a dynamic multi-field asymptotic homogenization approach, proposed to grasp the overall constitutive behaviour of such complex microstrutcures. A set of applications, both in static and dynamic regime, is proposed to explore different design paradigms, related to nanogenerators based on three working principles. Both extension and bending nanogenerators are, indeed, analysed, considering either extension along the nanorods axis, or orthogonally to it. The study of the wave propagation is, also, exploited to comprehend the main features of such piezoelectric devices in the dynamic regime. 2017;Liu et al., 2018;Askari et al., 2019). Relevant examples concern either the use of piezoelectric zinc oxide (ZnO) nanowire arrays grown on conductive rigid supports (Yi et al., 2005;Wang and Song, 2006), or the adoption of lead zirconate titanate (PZT), polyvinylidene fluoride (PVDF) and barium titanate (BT). An important improvement in the design of ZnO nanorods-based piezoelectric generators has been achieved by adopting flexible substrates made of electro-active polymeric materials. The main advantage is, indeed, the possibility of exploiting relevant flexural mechanisms, besides the standard direct compression of the device. In Fan et al. (2016) different typologies of flexible nanogenerators are presented and critically commented. Also patterned growth of ZnO nanowires can be exploited to enhance the performances of flexible nanogenerators, as discussed in Yang et al. (2017). Further benefits can be obtained by resorting to so-called hybrid nanogenerators, made up by embedding the ZnO nanorods within a polymeric matrix. More specifically, Stassi et al. (2015) propose highly oriented ZnO nanotubes in a porous polycarbonate (PC) matrix. The result is an efficient nanogenerator based on such a highly flexible ZnOPC composite. Moreover, in Choi et al. ( 2017) a hybrid piezoelectric structure made of ZnO nanowires and a matrix of PVDF polymer is investigated in order to obtain a power enhancement. The authors, indeed, find that the ZnO nanowires are able to deliver internal strain to the PVDF, which increase the electrical power output of the hybrid nanogenerator. Based on the aforementioned considerations, with the aim of energy harvesting from green and sustainable energy resources, our focus is on hybrid flexible nanogenerators, made up with clusters of ZnO nanorods embedded into a polymeric matrix and growth on a flexible support. The choice of ZnO nanorods, is motivated by their relatively simple forming processes using low temperature. In particular, by exploiting innovative growth techniques, it is possible to synthesi...