Asymptotic homogenization model for 3D grid-reinforced composite structures with generally orthotropic reinforcements

The asymptotic homogenization method is used to develop a comprehensive micromechanical model pertaining to three-dimensional composite structures with an embedded periodic grid of generally orthotropic reinforcements. The model developed transforms the original boundary-value problem into a simpler one characterized by some effective elastic coefficients. These effective coefficients are shown to depend only on the geometric and material parameters of the unit cell and are free from the periodicity complications that characterize their original material counterparts. As a consequence they can be used to study a wide variety of boundary-value problems associated with the composite of a given microstructure. The developed model is applied to different examples of orthotropic composite structures with cubic, conical and diagonal reinforcement orientations. It is shown in these examples that the model allows for complete flexibility in designing a grid-reinforced composite structure with desirable elastic coefficients to conform to any engineering application by changing some material and/or geometric parameter of interest. It is also shown in this work that in the limiting particular case of 2D grid-reinforced structure with isotropic reinforcements our results converge to the earlier published results

Micromechanical analysis of magneto-electro-thermo-elastic composite materials with applications to multilayered structures

The method of asymptotic homogenization was used to analyze a periodic magnetoelectric smart composite structure consisting of piezoelectric and piezomagnetic phases. The asymptotic homogenization model is derived, the governing equations are determined and subsequently general expressions called unit-cell problems that can be used to determine the effective elastic, piezoelectric, piezomagnetic, thermal expansion, dielectric, magnetic permeability, magnetoelectric, pyroelectric and pyromagnetic coefficients are presented. The latter three sets of coefficients are particularly interesting in the sense that they represent product or cross-properties; they are generated in the macroscopic composite via the interaction of the different phases, but may be absent from the constituents themselves. The derived expressions pertaining to the unit-cell problems and the resultant effective coefficients are very general and are valid for any 3-D geometry of the unit cell. The model is illustrated by means of longitudinally-layered smart composites consisting of piezoelectric (Barium Titanate) and piezomagnetic (Cobalt Ferrite) constituents. Closed-form expressions for the effective properties are derived and the results are plotted vs. the volume fraction of the piezoelectric phase. Pertaining to the product properties of this particular magnetoelectric laminate, it is observed that the effective pyroelectric and pyromagnetic coefficients attain a maximum value at a BaTiO3 volume fraction of 0.5 and maximum values for the magnetoelectric coefficients at a BaTiO 3 volume fraction of 0.4. Likewise, the maximum value of a magnetoelectric figure of merit (characterizing efficiency of energy conversion in longitudinal direction) is also attained at a volume fraction of 0.4

Modeling of smart composites on account of actuation, thermal conductivity and hygroscopic absorption

The asymptotic homogenization models for smart composite materials are derived and effective elastic, actuation, thermal expansion and hygroscopic expansion coefficients for smart structures are obtained. The actuation coefficients characterize the intrinsic transducer nature of active smart materials that can be used to induce strains and stresses in a coordinated fashion. Examples of such actuators employed with smart composite material systems are derived from piezoelectric, magnetostrictive, and some other materials. The pertinent mathematical framework is that of asymptotic homogenization. The objective is to transform a general anisotropic composite material with a regular array of reinforcements and/or actuators into a simpler one that is characterized by some effective coefficients; it is implicit, of course, that the physical problem based on these homogenized coefficients should give predictions differing as little as possible from those of the original problem. The effectiveness of the derived models is illustrated by means of two- and three-dimensional examples

Micromechanical modeling of smart composite materials with a periodic structure

Comprehensive micromechanical models for smart composite materials with a periodic structure are derived and effective elastic, actuation, thermal expansion and hygroscopic expansion coefficients pertaining to these structures are obtained. The actuation coefficients characterize the intrinsic nature of adaptive structures that can be used to induce strains and stresses in a controlled manner. The effective coefficients replace the rapidly oscillating coefficients inherent to the differential equations that govern the behavior of smart anisotropic materials with a regular array of reinforcements and actuators. The mathematical framework employed is that of asymptotic homogenization that permits the determination of the effective coefficients through solution of unit cell problems. The unit cell problems are shown to be independent of the global boundary value problem. It is implicit of course that the physical model based on these coefficients should give predictions differing as little as possible from those of the original problem. Once determined, the effective coefficients can be utilized in studying different types of boundary value problems associated with a given structure. The effectiveness of the derived models and the use of the effective coefficients is illustrated by means of various two- and three-dimensional examples associated with periodic laminates