Micromechanical analysis of grid-reinforced thin composite generally orthotropic shells

This paper develops a comprehensive micromechanical model for the analysis of periodic thin composite shells with an embedded grid of generally orthotropic reinforcements. The use of generally orthotropic constituents renders the analysis more complicated than with simply isotropic reinforcements, but significantly enhances the applicability of the model. The model is derived on the basis of asymptotic homogenization and allows the determination of the effective elastic stiffnesses (coefficients) of the composite shells. These effective coefficients are only dependent on the structural make-up of the pertinent periodicity unit (referred to as unit cell) of the composite shell, and are completely independent of the global formulation of the problem. As such, they are universal in nature and can be used to study a wide variety of boundary-value problems. In the limiting case in which the shell reduces to a thin flat plate with periodicity in the two in-plane orthogonal directions, the derived model converges to that of previously obtained models. The model is illustrated by means of several examples of practical importance including cylindrical-reinforced shells, multi-layer shells, grid-reinforced plates and single-walled carbon nanotubes

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

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

Asymptotic homogenization modeling of smart composite generally orthotropic grid-reinforced shells: part i - theory

We develop in this paper a comprehensive micromechanical model for the analysis of thin smart composite grid-reinforced shells with an embedded periodic grid of generally orthotropic cylindrical reinforcements that may also exhibit piezoelectric properties. The original boundary value problem which characterizes the thermopiezoelastic behavior of the smart shell is decoupled via the asymptotic homogenization technique into three simpler problems the solution of which permits the determination of the effective elastic, piezoelectric and thermal expansion coefficients. The general orthotropy of the constituent materials is very important from the practical viewpoint and it renders the resulting analysis a lot more complicated. In Part II of this work the model is applied to the analysis of several practically important examples including cylindrical reinforced smart composite shells and multi-layer smart shells

Modeling of the thermopiezoelastic behavior of prismatic smart composite structures made of orthotropic materials

Asymptotic homogenization models for prismatic smart composite structures are derived and the effective elastic, piezoelectric, and thermal expansion coefficients 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 constituents of the smart structures are assumed to exhibit orthotropic characteristics. The original problem for the regularly non-homogeneous smart composite structure reduces to a system of three simpler types of problem, called unit cell problems. It is precisely these unit cell problems that enable the determination of the aforementioned coefficients. These effective coefficients are universal in nature and can be used to study a wide variety of boundary value problems associated with a smart structure of a given geometry

Asymptotic homogenization model for generally orthotropic reinforcing networks in smart composite plates

A general three-dimensional micromechanical model pertaining to smart composite layers with wavy boundaries is applied to the case of thin smart plates reinforced with a network of generally orthotropic bars that may also exhibit piezoelectric behavior. The method used for the development of the structural model is that of asymptotic homogenization, which reduces the original boundary value problem into a set of three decoupled problems, each problem being characterized by two differential equations. These three sets of differential equations, referred to as 'unit cell problems', deal, independently, with the elastic, piezoelectric, and thermal expansion behavior of the network-reinforced smart composite plates. The solution of the unit cell problems yields expressions for effective elastic, piezoelectric and thermal expansion coefficients which, as a consequence of their universal nature, can be used to study a wide variety of boundary value problems associated with a smart structure of a given geometry. The model can be used to customize the effective properties of a smart structure by changing some material or geometric parameters such as the size or nature of the reinforcements. The developed general methodology is applied to smart network-reinforced composite structures with generally orthotropic reinforcements and actuators. As particular examples, spatial rectangular, triangular, and rhombic smart network plates are analyzed. The general orthotropy of materials is very important from the practical viewpoint and this orthotropy makes micromechanical modeling significantly more complex. In the limiting case of isotropic reinforcements and absence of actuators, the above general orthotropic micromechanical model converges to results that are consistent with those of previous models obtained by either asymptotic homogenization, or stress-strain relationships in the isotropic reinforcements

Micromechanics of smart composite plates with periodically embedded actuators and rapidly varying thickness

Asymptotic homogenization models for smart composite plates with periodically arranged embedded actuators and rapidly varying thickness are derived. The formulated models enable the determination of both local fields and effective elastic, actuation, thermal expansion, and hygroscopic expansion coefficients from three-dimensional local unit cell problems. The actuation coefficients, for example piezoelectric or magnetostrictive, characterize the intrinsic transducer nature of active smart materials that can be used to induce strains and stresses in a coordinated fashion. The theory is illustrated by means of examples pertaining to thin smart composite plates of uniform thickness, riband waferreinforced smart composite structures, and sandwich smart composite plates with honeycomb filler

Asymptotic homogenization modeling of smart composite generally orthotropic grid-reinforced shells: part II- applications

A comprehensive micromechanical model for the analysis of thin smart composite grid-reinforced shells with an embedded periodic grid of generally orthotropic cylindrical reinforcements that may also exhibit piezoelectric properties is developed and applied to examples of practical importance. Details on derivation of a general homogenized smart shell model are provided in Part I of this work. The present paper solves the obtained unit cell problems and develops expressions for the effective elastic, piezoelectric and thermal expansion coefficients for the grid reinforced smart composite shell. Thus obtained effective coefficients are universal in nature and can be used to study a wide variety of boundary value problems. The applicability of the model is illustrated by means of several examples including cylindrical reinforced smart composite shells, and multi-layer smart shells. The derived expressions allow tailoring the effective properties of a smart grid-reinforced shell to meet the requirements of a particular application by changing certain geometric or physical parameters

Asymptotic homogenization model for three-dimensional network reinforced composite structures

The method of asymptotic homogenization is used to develop a comprehensive micromechanical model pertaining to three-dimensional composite structures with an embedded periodic network of isotropic reinforcements, the spatial arrangement of which renders the behavior of the given structures macroscopically anisotropic. The model developed in this paper allows the transformation of the original boundary value problem into a simpler one that is characterized by some effective elastic coefficients. These coefficients are calculated from a so-called unit cell or periodicity problem, and are shown to depend solely on the geometric and material characteristics of the unit cell and are completely independent of the global formulation of the boundary-value problem. As such, the effective elastic coefficients are universal in nature and can be used to study a wide variety of boundary value problems. The model is illustrated by means of several examples of a practical importance and it is shown that the effective properties of a given composite structure can be tailored to satisfy the requirements of a particular application by changing certain geometric parameters such as the size or relative orientation of the reinforcements. For the special case in which the reinforcements form only a two-dimensional (in-plane) network, the results converge to those of previous models obtained either by means of asymptotic homogenization or by stress-strain relationships in the reinforcements

Asymptotic homogenization modeling of thin composite network structures

Asymptotic homogenization models for composite plates reinforced with orthotropic bars are developed and the effective elastic coefficients are obtained. The original problem for the regularly non-homogeneous composite structure reduces to a system of two simpler types of problem, called "unit cell" problems. It is precisely these unit cell problems that enable the determination of the aforementioned coefficients. These effective coefficients are universal in nature and can be used to study a wide variety of boundary value problems associated with a composite structure of a given geometry. The derived model is applied to a number of practical cases involving composite plates reinforced with different networks of orthotropic bars. It is shown that the model can be used to tailor the effective properties of a given composite structure to meet the requirements of a particular application by changing some material or geometric parameters. In the limiting case of isotropic reinforcements, the results are shown to converge to those of previous models obtained by means of asymptotic homogenization or stress-strain relationships in the reinforcements