Multifield asymptotic homogenization of thermo-pi

Multifield asymptotic homogenization of thermo-piezoelectric materials with periodic microstructure


Figure 2: (a) Heterogeneous model and homogenized one subject to L-periodic volume forces bi(x1), free charge densities ρe(x1), and heat sources r(x1); (b)Periodic cell A with characteristic size ε made of FR4 and a ceramic PZT inclusion.
The analytical solution of the homogenized model in terms of macro displacement U(x), electric potential Φ(x), and temperature Θ(x) is compared with the results provided by a finite element analysis of the corresponding heterogeneous model. The periodic cell A of the considered thermo-piezoelectric material is a 10mm× 10mm cell with a 5mm× 5mm inclusion (see figure 2(b)). The two different phases constituting the periodic cell are assumed to be homogeneous. The geometry of such periodic cell reproduces the one of a pyroelectric cell typically used as an energy harvester and organized in array of elements (Hsiao and Jia-Wai, 2015; Hsiao et al., 2015). The inclusion is made of a material like the Lead Zirconate Titanate (PZT-5H) which has marked piezoelectric and pyroelectric properties. Such a material is characterized by the following constitutive tensors

https://arxiv.org/pdf/1701.03361v1.pdf

Towards David D. conversation we had at the last shareholder meeting this goes with your off the chip incorporated thinking. IMO with the molecular measurements that are now available and the ability to trace energy transfer in a number of different dimensions.....damn it looks like we are getting real close!