Design of thermo-piezoelectric microstructured bending actuators via multi-field asymptotic homogenization

Abstract

The use of integrated MicroElectroMechanical systems (MEMS) is recently spread thanks to their improved sensitivity, accuracy and reliability. Accurate preliminary computations born from the need of high precision in the manufacturing process of such devices. Piezoelectric materials are broadly employed in this field as direct converters between mechanical and electrical signals and some of these piezoelectric materials show pyroelectric features, which involve thermo-electrical interactions. Pyroelectric bending actuators are analyzed in the present study in plane conditions. They consists of active PZT layers with in-plane polarization and a microstructured composite layer characterized by a periodic microstructure where PZT fibers with an out of plane polarization are immersed in a polymeric matrix. The constitutive law of the composite layer at the macroscale has been determined by means of a multi-field asymptotic homogenization technique, recently developed for thermo-piezoelectric materials. Overall constitutive equations characterizing the behavior of the microstructured layer at the macroscale have been derived and the closed form of the overall constitutive tensors has been provided for the equivalent first-order (Cauchy) homogenized continuum. Deflection of unimorph and bimorph bender actuators has been investigated in relation to their geometrical features, exploiting the out of plane piezoelectric properties of the composite layer, which modify the stiffness of the entire bender. An accurate description of benders behavior at the structural length scale is of fundamental importance in order to design devices with high performances. In this regard, the influence of the microstructure on the global response of the actuator is investigated in the present study in order to understand how the composite material can be tailored to meet specific design requirements.

A phase field approach for damage propagation in periodic microstructured materials

“…It is worth mentioning that variability of source terms acting on the medium has to be much greater than the microstructural length scale ε, in order to preserve the scales separability principle. If volume forces are L-periodic, then macroscopic displacement U(x) will be L-periodic too, otherwise suitable boundary conditions should be taken into account in order to determine the macroscopic field (Fantoni et al, 2017(Fantoni et al, , 2018.…”

“…Homogenization techniques have been a matter of intensive research within the last decades. In general sense, the local and/or nonlocal homogenization methods can be classified with respect to the underlying fundamental hypotheses as: the asymptotic techniques (Bensoussan et al, 1978;Bakhvalov and Panasenko, 1984;Gambin and Kröner, 1989;Hubert and Palencia, 1992;Allaire, 1992;Meguid and Kalamkarov, 1994;Boutin, 1996;Andrianov et al, 2008;Panasenko, 2009;Tran et al, 2012;Bacigalupo, 2014;Fantoni et al, 2017Fantoni et al, , 2018, the variational-asymptotic techniques (Willis, 1981;Smyshlyaev and Cherednichenko, 2000;Smyshlyaev, 2009;Bacigalupo and Gambarotta, 2014a,b;Bacigalupo et al, 2014;Del Toro et al, 2019) and many identification approaches, involving the analytical (Sevostianov et al, 2005;Bigoni and Drugan, 2007;Bacca et al, 2013a,b,c;Bacigalupo and Gambarotta, 2013;Sevostianov and Giraud, 2013;Rizzi et al, 2019a,b), and the computational techniques (Forest and Sab, 1998;Ostoja-Starzewski et al, 1999;Kouznetsova et al, 2002;Forest, 2002;Feyel, 2003;Kouznetsova et al, 2004;Kaczmarczyk et al, 2008;Yuan et al, 2008;Bacigalupo and Gambarotta, 2010;De Bellis and Addessi, 2011;Forest and Trinh, 2011;Addessi et al, 2013;Trovalusci et...…”

The generalized Floquet-Bloch spectrum for periodic thermodiffusive layered materials

“…Homogenization techniques, in fact, allow to take into account the role of the microstructure upon the overall constitutive behaviour of composite materials in a concise, but accurate way. They have been a matter of extremely intensive research within the last decades and, in a general sense, homogenization procedures can be classified in asymptotic techniques (Bakhvalov and Panasenko, 1984) togheter with their extension to multi-field phenomena (Fantoni et al, 2017(Fantoni et al, , 2018(Fantoni et al, , 2019, variational-asymptotic techniques (Smyshlyaev and Cherednichenko, 2000), and different identification approaches, involving the analytical (Bigoni and Drugan, 2007;Bacca et al, 2013a,b) and computational techniques (Forest, 2002;Lew et al, 2004;Scarpa et al, 2009;De Bellis and Addessi, 2011;Forest and Trinh, 2011;Wang et al, 2017;Yvonnet et al, 2020). Furthermore, dynamic homogenization schemes, useful to approximate frequency band structure of periodic media at high frequencies, can be found in (Zhikov, 2000;Smyshlyaev, 2009;Craster et al, 2010;Bacigalupo and Lepidi, 2016;Sridhar et al, 2018;Kamotski and Smyshlyaev, 2019;Bacigalupo and Gambarotta, 2019).…”

Wave propagation modeling in periodic elasto-thermo-diffusive materials via multifield asymptotic homogenization

“…The application of homogenization methods and multiscale modelings allows avoiding the demanding numerical computation of the whole heterogeneous medium leading to the identification of effective macroscopic properties for the equivalent continuum. In order to study the overall properties of composite materials, numerous homogenization approaches have been provided over the last decades, which can be divided in asymptotic techniques (Sanchez-Palencia, 1974;Bensoussan et al, 1978;Bakhvalov and Panasenko, 1984;Gambin and Kröner, 1989;Allaire, 1992;Bacigalupo, 2014;Fantoni et al, 2017Fantoni et al, , 2018, variational-asymptotic techniques (Smyshlyaev and Cherednichenko, 2000;Peerlings and Fleck, 2004;Bacigalupo and Gambarotta, 2014), and numerous identification approaches including the analytical (Bigoni and Drugan, 2007;Milton and Willis, 2007;Bacca et al, 2013a,b,c;Nassar et al, 2015;Bacigalupo et al, 2018) and computational methods (Forest and Sab, 1998;Ostoja-Starzewski et al, 1999;Feyel and Chaboche, 2000;Kouznetsova et al, 2002;Forest, 2002;Feyel, 2003;Kouznetsova et al, 2004;Lew et al, 2004;Kaczmarczyk et al, 2008;Yuan et al, 2008;Scarpa et al, 2009;Bacigalupo and Gambarotta, 2010;Forest and Trinh, 2011;De Bellis and Addessi, 2011;Addessi et al, 2013;Zäh and Miehe, 2013;Salvadori et al, 2014;Trovalusci et al, 2015). The present study is devoted to provide a multifield asymptotic homogenization technique ...…”