Analytical and numerical modeling for 3D smart orthotropic grid-reinforced composite structures

Abstract

A new comprehensive micromechanical modeling of a periodic smart composite structures reinforced with a 3D grid of orthotropic reinforcements and actuators is undertaken to fully determine effective piezoelectric and thermal expansion properties. Two different modeling techniques are presented; one is based on the asymptotic homogenization method (AHM) and the other is a numerical model based on the finite element analysis (FEA). The AHM transforms the original boundary value problem into a simpler one characterized by effective coefficients which are shown to depend only on geometric and material parameters of a periodicity cell. The developed models can be applied to various 3D smart grid-reinforced composite structures with generally orthotropic constituents. Analytical formulae for the effective piezoelectric and thermal expansion coefficients are derived and a finite element analysis is subsequently developed and used to examine the aforementioned periodic grid-reinforced orthotropic structures. The electro-thermo-mechanical deformation responses from the finite element simulations are used to extract the homogenized piezoelectric and thermal expansion coefficients. The results of the FEA are compared to those pertaining to their AHM counterparts using a varying volume fractions and different poling directions. A very good agreement is shown between these two modeling techniques. The prediction of the effective properties of 3D grid-reinforced smart composites is important for design and manufacturing of composite parts using such structures.