View source for Composite Carbon Fiber Reinforced Polymer Concrete Beams

==Introduction==
With the ever increasing demand on our current infrastructure, comes the necessity to find innovative ways to streamline design and, equally as important, preserve the life of our existing large-scale structures. One current issue pertains to the maintenance costs of repairing bridges, buildings, box culverts, etc. that have wear and tear from service loads, corrosion, and accidents. The question of how to effectively handle these issues of maintenance and retrofitting proves to be a difficult one to answer in regards to lightweight design and constructability. With the shift from the older “When in doubt, make it stout” design philosophy of Allowable/Working Stress Design to the new reliability based Load and Resistance Factor Design, came the need for high-strength, lightweight materials. A rising contender in the structural materials market, carbon reinforced polymers, has found its way to all forms of structural design from aerospace engineering and automotive engineering all the way to biomedical engineering. Carbon reinforced polymer new structural asset can show its true value of strength-to-weight ratio in all fields of structural analysis and design, but with  great promise, comes the challenge of accurately modeling behavior as part of a composite material system.

[[Image:FRP Multiscale Modeling Slide.jpg|600px|thumb|right]]

==Downscaling==
To truly understand the inner workings of a fiber reinforced polymer (FRP) system, the modeling approach must be a diligent one approached with a top-down perspective with the end goal in mind: a multi-scale approach. The system under consideration for my research is a composite FRP reinforced concrete beam. While beams are subjected to multiple loading conditions, my focus will be tensile behavior of the FRP system. Much research on FRP wrapped columns subjected to axial loads with eccentricity has shown increased ductility and strength due to the FRP wrap’s ability to keep the concrete confined around steel reinforcement <ref>Kabir, M. Z., Shafei, E. “Plasticity modeling of FRP-confined circular reinforced concrete columns subjected to eccentric axial loading,” Composite Part B, 29B, (2012) 3497-3506</ref>. I believe optimization can be achieved with a multiple length-scale approach.
To approach this system, downscaling from the application (tensile behavior) is key in determining the necessary variables to bridge the length scales. 

==Multiscale Modeling Approach==
===Electronics Scale===
I will start with electronics simulations to begin determining Density Functional Theory (DFT) potentials (interfacial energies) to calculate elastic moduli of the carbon fibers, epoxy, and steel reinforcement. 

===Nanoscale===
DFT potentials can then be passed on to the next length scale to Molecular Dynamics (MD) simulations to calculate dislocation drag coefficients and mobility within the reinforcing steel along with the total energy within the epoxy matrix and carbon fibers. Dislocation mobility is then used to determine the high-rate mechanisms caused by these dislocations within the nanostructure <ref name="Horstemeyer">Horstemeyer, M. F. Integrated Computational Materials Engineering (ICME) For Metals: Using Multiscale Modeling to Invigorate Engineering Design with Science. Hoboken, N.J:WILEY-TMS, 2013</ref>.

===Mesoscale===
My model then proceeds to the mesoscale where damage within each component must be considered. For the FRP system, LS-DYNA can be utilized using material properties determined from the lower length scales as was done by Karim in his constitutive modeling of damage in FRP <ref>Karim, M. R., “CONSTITUTIVE MODELING AND FAILURE CRITERIA OF CARBON-FIBER REINFORCED POLYMERS UNDER HIGH STRAIN RATES,” Dissertation, 2005, pp. 69</ref>. Equally important is the crack growth within the concrete and epoxy matrix as well as the rate of corrosion of the reinforcement. The mechanics of reinforced concrete beams relies upon the transfer of load between the tensioned reinforcement and concrete confining it. Determining the current capacity of the existing beam will greatly depend on the degree of corrosion. The next step in modeling will be simulating crack growth and interaction between concrete and its FRP wrap. 

===Macroscale===
All information is then transferred to the heart of our multi-scale model: the macroscale Internal State Variable (ISV). All of the data gathered from lower length scales will be incorporated into the ISV continuum to truly determine system behavior from the microscale to the macroscale. The FRP system will be modeled at the structural scale via finite element analysis to determine large-scale behavior. 

==Results==
During the multi-scale modeling process, ANOVA, or analysis of variance, will be utilized to find modeling parameters hold the most influence <ref name="Horstemeyer"></ref>. Doing so will ensure that most influential variables are accounted for and the finished model is precise. The resulting system behavior will show the effectiveness and long-term economy that FRP wrapped reinforced concrete beams as well as help pave the way for further research and development of FRP applications.

==References==
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[[Category:Geomaterials]]
[[Category:Civil Engineering Materials]]
[[Category:Polymers]]