Piezoelectric Homogenization of the Macro-Fiber Composite with the Mechanics of Structure Genome

Abstract

A convenient and robust way to convert an ordinary structure into a smart one is to adhere a piezoelectric macro-fiber composite (MFC) patch to it. Although the commercialization of the MFC has facilitated numerous sensor and actuator applications, analysis of host structures has mainly relied on homogenized constants that were obtained with various assumptions on the field variables. Here, the newly discovered mechanics of structure genome (MSG) is used to assess the effect of assuming uniform-fields, plane-stress assumptions, and homogeneous layers. First it is shown that MSG can maintain the accuracy of 3D piezoelectric finite element analysis (FEA) but without the need for nine analyses and complex boundary conditions for a full piezoelectric stiffness matrix. With a 3D unit-cell we show how recent reports of the effective in-plane properties of the full MFC have been underpredicted by as much as 30% and transverse shear moduli have been overestimated between 100% and 300%. The implications here are that analyzing host structures with MFCs can proceed with higher accuracy with the effective properties that are obtained without the aforementioned assumptions. The versatility of MSG is demonstrated with a 1D plus 2D homogenization that has improvements in accuracy and completeness over comparable approaches that utilize the homogenous layer assumption. This approach in MSG may provide the best compromise between simplicity and accuracy for performing optimizations and/or case studies on system level performance. Finally, we verify that the ubiquitous uniform-field assumptions are good for homogenizing the fiber layers. However, the plane-stress assumption taken by many researchers at the lamina level should be avoided since it leads to underpredictions of the transverse layer properties by at least 11%. This is especially important when modeling complex systems with many MFCs, off-axis applications, or load-bearing MFCs.