In order to verify the dispersive nature of transverse displacement in a beam, a deep understanding of the governing partial differential equation is developed. Using the finite element method and Newmark’s method, along with Fourier transforms and other methods, the aim is to obtain consistent results across each numerical technique. An analytical solution is also analyzed for the Euler-Bernoulli beam in order to gain confidence in the numerical techniques when used for more advance beam theories that do not have a known analytical solution. Three different beam theories are analyzed in this report: The Euler-Bernoulli beam theory, Rayleigh beam theory and Timoshenko beam theory. A comparison of the results show the difference between each theory and the advantages of using a more advanced beam theory for higher frequency vibrations.

This study employs a finite element method based modeling of cementitious composite microstructure to study the effect of presence of inclusions on the stress distribution and the constitutive response of the composite. A randomized periodic microstructure combined with periodic boundary conditions forms the base of the finite element models. Inclusion properties of quartz and light weight aggregates of size 600μm obtained from literature were made use of to study the effect of their material (including inclusion stiffness, stiffness of interfacial transition zone and matrix stiffening) and geometric properties (volume fraction of inclusion, particle size distribution of inclusion and thickness of the interfacial transition zone) on the composite. Traction-separation relationship was used to incorporate the effect of debonding at the interface of the matrix and the inclusion to study the effect on stress distribution in the microstructure. The stress distributions observed upon conducting a finite element analysis are caused due to the stiffness mismatch in both the quartz and the light weight aggregates as expected. The constitutive response of the composite microstructure is found to be in good conformance with semi-analytical models as well as experimental values. The effect of debonding throws up certain important observations on the stress distributions in the microstructure based on the stress concentrations and relaxations caused by the stiffness of the individual components of the microstructure. The study presented discusses the different micromechanical models employed, their applicability and suitability to correctly predict the composite constitutive response.

The motivation of this work is based on development of new construction products with strain hardening cementitious composites (SHCC) geared towards sustainable residential applications. The proposed research has three main objectives: automation of existing manufacturing systems for SHCC laminates; multi-level characterization of mechanical properties of fiber, matrix, interface and composites phases using servo-hydraulic and digital image correlation techniques. Structural behavior of these systems were predicted using ductility based design procedures using classical laminate theory and structural mechanics. SHCC sections are made up of thin sections of matrix with Portland cement based binder and fine aggregates impregnating continuous one-dimensional fibers in individual or bundle form or two/three dimensional woven, bonded or knitted textiles. Traditional fiber reinforced concrete (FRC) use random dispersed chopped fibers in the matrix at a low volume fractions, typically 1-2% to avoid to avoid fiber agglomeration and balling. In conventional FRC, fracture localization occurs immediately after the first crack, resulting in only minor improvement in toughness and tensile strength. However in SHCC systems, distribution of cracking throughout the specimen is facilitated by the fiber bridging mechanism. Influence of material properties of yarn, composition, geometry and weave patterns of textile in the behavior of laminated SHCC skin composites were investigated. Contribution of the cementitious matrix in the early age and long-term performance of laminated composites was studied with supplementary cementitious materials such as fly ash, silica fume, and wollastonite. A closed form model with classical laminate theory and ply discount method, coupled with a damage evolution model was utilized to simulate the non-linear tensile response of these composite materials. A constitutive material model developed earlier in the group was utilized to characterize and correlate the behavior of these structural composites under uniaxial tension and flexural loading responses. Development and use of analytical models enables optimal design for application of these materials in structural applications. Another area of immediate focus is the development of new construction products from SHCC laminates such as angles, channels, hat sections, closed sections with optimized cross sections. Sandwich composites with stress skin-cellular core concept were also developed to utilize strength and ductility of fabric reinforced skin in addition to thickness, ductility, and thermal benefits of cellular core materials. The proposed structurally efficient and durable sections promise to compete with wood and light gage steel based sections for lightweight construction and panel application

The need for sustainability in construction has encouraged scientists to develop novel environmentally friendly materials. The use of supplementary cementitious materials was one such initiative which aided in enhancing the fresh and hardened concrete properties. This thesis aims to explore the understanding of the early age rheological properties of such cementitious systems.

The first phase of the work investigates the influence of supplementary cementitious materials (SCM) in combination with ordinary Portland cement (OPC) on the rheological properties of fresh paste with and without the effect of superplasticizers. Yield stress, plastic viscosity and storage modulus are the rheological parameters which were evaluated for all the design mixtures to fundamentally understand the synergistic effects of the SCM. A time-dependent study was conducted on these blends to explore the structure formation at various time intervals which explains the effect of hydration in conjecture to its physical stiffening. The second phase focuses on the rheological characterization of novel iron powder based binder system.

The results of this work indicate that the rheological characteristics of cementitious suspensions are complex, and strongly dependent on several key parameters including: the solid loading, inter-particle forces, shape of the particle, particle size distribution of the particles, and rheological nature of the media in which the particles are suspended. Chemical composition and reactivity of the material play an important role in the time-dependent rheological study.

A stress plateau method is utilized for the determination of rheological properties of concentrated suspensions, as it better predicts the apparent yield stress and is shown to correlate well with other viscoelastic properties of the suspensions. Plastic viscosity is obtained by calculating the slope of the stress-strain rate curve of ramp down values of shear rates. In oscillatory stress measurements the plateau obtained within the linear visco-elastic region was considered to be the value for storage modulus.

Between the different types of fly ash, class F fly ash indicated a reduction in the rheological parameters as opposed to class C fly ash that is attributable to the enhanced ettringite formation in the latter. Use of superplasticizer led to a huge influence on yield stress and storage modulus of the paste due to the steric hindrance effect.

In the study of iron based binder systems, metakaolin had comparatively higher influence than fly ash on the rheology due to its tendency to agglomerate as opposed to the ball bearing effect observed in the latter. Iron increment above 60% resulted in a decrease in all the parameters of rheology discussed in this thesis. In the OPC-iron binder, the iron behaved as reinforcements yielding higher yield stress and plastic viscosity.

A simplified bilinear moment-curvature model are derived based on the moment-curvature response generated from a parameterized stress-strain response of strain softening and or strain-hardening material by Dr. Barzin Mobasher and Dr. Chote Soranakom. Closed form solutions are developed for deflection calculations of determinate beams subjected to usual loading patterns at any load stage. The solutions are based on a bilinear moment curvature response characterized by the flexural crack initiation and ultimate capacity based on a deflection hardening behavior. Closed form equations for deflection calculation are presented for simply supported beams under three point bending, four point bending, uniform load, concentrated moment at the middle, pure bending, and for cantilever beam under a point load at the end, a point load with an arbitrary distance from the fixed end, and uniform load. These expressions are derived for pre-cracked and post cracked regions. A parametric study is conducted to examine the effects of moment and curvature at the ultimate stage to moment and curvature at the first crack ratios on the deflection. The effectiveness of the simplified closed form solution is demonstrated by comparing the analytical load deflection response and the experimental results for three point and four point bending. The simplified bilinear moment-curvature model is modified by imposing the deflection softening behavior so that it can be widely implemented in the analysis of 2-D panels. The derivations of elastic solutions and yield line approach of 2-D panels are presented. Effectiveness of the proposed moment-curvature model with various types of panels is verified by comparing the simulated data with the experimental data of panel test.

Increased priority on the minimization of environmental impacts of conventional construction materials in recent years has motivated increased use of waste materials or bi-products such as fly ash, blast furnace slag with a view to reduce or eliminate the manufacturing/consumption of ordinary portland cement (OPC) which accounts for approximately 5-7% of global carbon dioxide emission. The current study explores, for the first time, the possibility of carbonating waste metallic iron powder to develop carbon-negative sustainable binder systems for concrete. The fundamental premise of this work is that metallic iron will react with aqueous CO2 under controlled conditions to form complex iron carbonates which have binding capabilities. The compressive and flexural strengths of the chosen iron-based binder systems increase with carbonation duration and the specimens carbonated for 4 days exhibit mechanical properties that are comparable to those of companion ordinary portland cement systems. The optimal mixture proportion and carbonation regime for this non-conventional sustainable binder is established based on the study of carbonation efficiency of a series of mixtures using thermogravimetric analysis. The pore- and micro-structural features of this novel binding material are also evaluated. The fracture response of this novel binder is evaluated using strain energy release rate and measurement of fracture process zone using digital image correlation (DIC). The iron-based binder system exhibits significantly higher strain energy release rates when compared to those of the OPC systems in both the unreinforced and glass fiber reinforced states. The iron-based binder also exhibits higher amount of area of fracture process zone due to its ability to undergo inelastic deformation facilitated by unreacted metallic iron particle inclusions in the microstructure that helps crack bridging /deflection. The intrinsic nano-mechanical properties of carbonate reaction product are explored using statistical nanoindentation technique coupled with a stochastic deconvolution algorithm. Effect of exposure to high temperature (up to 800°C) is also studied. Iron-based binder shows significantly higher residual flexural strength after exposure to high temperatures. Results of this comprehensive study establish the viability of this binder type for concrete as an environment-friendly and economical alternative to OPC.

Composite materials are finally providing uses hitherto reserved for metals in structural systems applications – airframes and engine containment systems, wraps for repair and rehabilitation, and ballistic/blast mitigation systems. They have high strength-to-weight ratios, are durable and resistant to environmental effects, have high impact strength, and can be manufactured in a variety of shapes. Generalized constitutive models are being developed to accurately model composite systems so they can be used in implicit and explicit finite element analysis. These models require extensive characterization of the composite material as input. The particular constitutive model of interest for this research is a three-dimensional orthotropic elasto-plastic composite material model that requires a total of 12 experimental stress-strain curves, yield stresses, and Young’s Modulus and Poisson’s ratio in the material directions as input. Sometimes it is not possible to carry out reliable experimental tests needed to characterize the composite material. One solution is using virtual testing to fill the gaps in available experimental data. A Virtual Testing Software System (VTSS) has been developed to address the need for a less restrictive method to characterize a three-dimensional orthotropic composite material. The system takes in the material properties of the constituents and completes all 12 of the necessary characterization tests using finite element (FE) models. Verification and validation test cases demonstrate the capabilities of the VTSS.

Laminated composite materials are used in aerospace, civil and mechanical structural systems due to their superior material properties compared to the constituent materials as well as in comparison to traditional materials such as metals. Laminate structures are composed of multiple orthotropic material layers bonded together to form a single performing part. As such, the layup design of the material largely influences the structural performance. Optimization techniques such as the Genetic Algorithm (GA), Differential Evolution (DE), the Method of Feasible Directions (MFD), and others can be used to determine the optimal laminate composite material layup. In this thesis, sizing, shape and topology design optimization of laminated composites is carried out. Sizing optimization, such as the layer thickness, topology optimization, such as the layer orientation and material and the number of layers present, and shape optimization of the overall composite part contribute to the design optimization process of laminates. An optimization host program written in C++ has been developed to implement the optimization methodology of both population based and numerical gradient based methods. The performance of the composite structural system is evaluated through explicit finite element analysis of shell elements carried out using LS-DYNA. Results from numerical examples demonstrate that optimization design processes can significantly improve composite part performance through implementation of optimum material layup and part shape.

The main objective of this study is to investigate drying properties and plastic shrinkage cracking resistance of fresh cement-based pastes reinforced with fibers and textiles. Naturally occurring mineral wollastonite has been studied independently as well as in combination with AR-glass textile. A series of blended mixes with Portland cement and wollastonite nano-fibers were developed and tested under low vacuum conditions to simulate severe evaporation conditions and expedite the drying process causing plastic shrinkage cracks. Cumulative moisture loss, evaporation rates, and diffusivity were analyzed by means of a 2-stage diffusion simulation approach, developed previously in Arizona State University. Effect of fiber-matrix interaction on the transport properties of the composite were evaluated using the existing approach. Morphology of the cracked surface was investigated by the means of image analysis wherein length, width, area and density of the cracks were computed to help characterize the contribution of fiber and textile in the cracking phenomenon. Additionally, correlation between cumulative moisture loss and crack propagation was attempted. The testing procedures and associated analytical methods were applied to evaluate effectiveness of four wollastonite fiber sizes and also a hybrid reinforcement system with alkali-resistant glass (ARG) textile in improving shrinkage cracking related parameters. Furthermore, the experimental and analytical approach was extended to magnified version of the existing shrinkage testing set-up to study the size effect of these composites when subjected to matching drying conditions. Different restraining mechanisms were used to study the simulation of the cracking phenomena on a larger specimen. Paste and mortar formulations were developed to investigate size effect on shrinkage resistance of cementitious composites.