Alexander L. Kalamkarov

Asymptotic Homogenization of Composite Materials and Structures

The present paper provides details on the new trends in application of asymptotic homogenization techniques to the analysis of composite materials and thin-walled composite structures and their effective properties. The problems under consideration are important from both fundamental and applied points of view. We review a state-of-the-art in asymptotic homogenization of composites by presenting the variety of existing methods, by pointing out their advantages and shortcomings, and by discussing their applications. In addition to the review of existing results, some new original approaches are also introduced. In particular, we analyze a possibility of analytical solution of the unit cell problems obtained as a result of the homogenization procedure. Asymptotic homogenization of 3D thin-walled composite reinforced structures is considered, and the general homogenization model for a composite shell is introduced. In particular, analytical formulas for the effective stiffness moduli of wafer-reinforced shell and sandwich composite shell with a honeycomb filler are presented. We also consider random composites; use of two-point Pade approximants and asymptotically equivalent functions; correlation between conductivity and elastic properties of composites; and strength, damage, and boundary effects in composites. This article is based on a review of 205 references. DOI: 10.1115/1.3090830

Strain measurement in a concrete beam by use of the Brillouin-scattering-based distributed fiber sensor with single-mode fibers embedded in glass fiber reinforced polymer rods and bonded to steel reinforcing bars

The strain measurement of a 1.65-m reinforced concrete beam by use of a distributed fiber strain sensor with a 50-cm spatial resolution and 5-cm readout resolution is reported. The strain-measurement accuracy is +/-15 microepsilon (microm/m) according to the system calibration in the laboratory environment with non-uniform-distributed strain and +/-5 microepsilon with uniform strain distribution. The strain distribution has been measured for one-point and two-point loading patterns for optical fibers embedded in pultruded glass fiber reinforced polymer (GFRP) rods and those bonded to steel reinforcing bars. In the one-point loading case, the strain deviations are +/-7 and +/-15 microepsilon for fibers embedded in the GFRP rods and fibers bonded to steel reinforcing bars, respectively, whereas the strain deviation is +/-20 microepsilon for the two-point loading case.

The use of Fabry Perot fiber optic sensors to monitor residual strains during pultrusion of FRP composites

Abstract This paper describes the use of an embedded optical sensor to measure the process induced strain in pultruded carbon fiber reinforced composite rods. The survivability of Fabry Perot optical sensors in the pultrusion process, real time strain monitoring during the pultrusion process and residual strain measurements within the composite rods, were the three objectives of the research. Strain profiles were recorded for individual experiments as the sensors traveled through the pultrusion die, and for the cool down period after the sensor had exited the die. For the total pultrusion process, the residual strain after cooling was found to present somewhat of a problem. For several experiments, the residual strain after exiting the pultrusion die was in the range of +200 to 400 microstrain, after which the sensors ceased to function. Calculations indicated that the radial shrinkage of the carbon fiber rods was sufficient to cause failure of the glass capillary portion of the Fabry Perot sensors. A novel method of reinforcing the Fabry Perot sensors before being pultruded was successful in allowing the sensors to survive the total process with only a slightly negative residual strain.

A new asymptotic model for a composite piezoelastic plate

A new asymptotic homogenization piezoelastic composite plate model is obtained. Derivation is based on a modified two-scale asymptotic homogenization technique applied to a rigorously formulated piezoelectric problem for a three-dimensional thin composite layer of a periodic structure. The obtained model makes it possible to determine both local fields and the effective properties of piezoelectric plate by means of solution of the obtained three-dimensional local unit cell problems and a global two-dimensional piezoelastic problem for a homogenized anisotropic plate. It is shown, in particular that the effective stiffnesses generally depend on the local piezoelectric constants of the material. The general symmetry properties of the effective stiffnesses and piezoelectric coefficients of the homogenized plate are derived. The general model is applied to a practically important case of a laminated anisotropic piezoelastic plate, for which the analytical formulas for the effective stiffnesses, piezoelectric and dielectric coefficients are obtained. Theory is illustrated by a numerical example of a piezoelectric laminated plate of a specific structure.

A new model for the multiphase fiber–matrix composite materials

Abstract A new model for a multiphase fiber–matrix composite material is proposed and the corresponding constitutive equations are derived. The matrix in the composite material is considered to be an isotropic continuous medium, and the reinforcing fibers are modeled by equivalent fibers using statistical averaging. The equivalent fibers are divided into those homogeneously distributed and oriented in the matrix and those having a preferred orientation. Based on the assumption of homogeneous deformation, a meso-constitutive equation for the multiphase fiber–matrix composite material is derived. The constitutive equation can be applied to the cases of isotropic, transversely isotropic or generally anisotropic properties of composite materials. As examples, several fiber–matrix composite material structures with isotropic and transversely isotropic characteristics are constructed, and the corresponding constitutive equations are obtained and analyzed.

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.

Reliability assessment of pultruded FRP reinforcements with embedded fiber optic sensors

Fiber optic strain sensors are successfully embedded in glass and carbon fiber reinforced polymer (GFRP and CFRP) reinforcements during pultrusion. The specific application is the use of the smart composite reinforcements for strain monitoring of innovative civil engineering structures. A comprehensive reliability assessment of the pultruded smart FRP rods with embedded sensors is performed, encompassing mechanical tests at room temperature as well as under conditions of low and high temperatures. In these tests, the strain output from the embedded fiber optic sensors was in good agreement with the output from surface mounted extensometers. The fatigue and short-term creep behavior of the smart composite rods is also examined. Finally, the long-term performance of the smart composites under sustained loads in alkaline environments simulating conditions encountered in concrete structures is assessed. The experiments conducted showed that the strain from the embedded fiber optic sensors conformed well with the corresponding output from the extensometers or foil gages.

Two-phase potentials in the analysis of smart composites having piezoelectrical components

Abstract The piezoelectric smart composite material consisting of two discrete phases of hexagonal piezoelectric crystals is subjected to mechanical and electric loads causing out-of-plane displacement and in-plane electric field. The two-phase potential method is introduced to linear piezoelectricity and worked out for the case of the antiplane deformation of a piezoelectric composite. It is shown that only two holomorphic functions (two-phase potentials) are sufficient to fully describe the field variables of the corresponding piezoelectric problem. The power of the method is exhibited by finding the two-phase potential solution to several piezoelectric problems of micromechanics of smart composites.

The mechanical performance of pultruded composite rods with embedded fiber-optic sensors

Abstract Fiber-optic strain sensors are successfully embedded in glass- and carbon-fiber-reinforced polymer (GFRP and CFRP) tendons during pultrusion. The study of the performance of the embedded Fabry-Perot fiber-optic sensors under conditions of static and dynamic loading when exposed to both low and high temperature extremes, is presented. The experiments entailed subjecting the GFRP and CFRP tendons to sinusoidal and trapezoidal load waveforms of about 11 kN magnitude inside a temperature chamber. The temperature in the chamber was varied from −40 to 60°C in increments of 20°C. The strain output from the embedded sensors was compared to that from externally mounted extensometers as well as to theoretical strain values. It was determined that the performance of the Fabry-Perot sensors was not affected by ambient temperatures falling within the range of −40 to +60°C and the sensor readings conformed very well with the corresponding extensometer and theoretical readings.

On the processing and evaluation of pultruded smart composites

The use of the pultrusion process for the manufacture of fiber reinforced polymer (FRP) composites with embedded fiber optic sensors are discussed. The specific application is the use of smart composite reinforcements for strain monitoring in innovative bridges and structures. The Bragg Grating and Fabry Perot fiber optic sensors are successfully embedded during the pultrusion of FRP rods. The behavior of optic sensors during pultrusion was assessed, and the effect of the embedment of optical fibers and their surface coatings on the mechanical properties of the composite was investigated. Monitoring of the output of embedded fiber optic strain sensors during the pultrusion of composite rods may provide useful information about the formation of process-induced strains within the composite. To verify the operation of the optic sensors embedded in the smart pultruded tendons, mechanical tests were conducted and the output of the fiber optic sensors was compared to that of an extensometer during quasi-static and cyclic tensile tests.