Magnetic shape memory alloys (MSMAs) are a class of active materials that de- form under magnetic and mechanical loading conditions. This work is concerned with the modeling of MSMAs constitutive responses. The hysteretic magneto-mechanical responses of such materials are governed by two major mechanisms which are variant reorientation and field induced phase transformation (FIPT). The most widely used material for variant reorientation is Ni2 MnGa which can produce up to 6% magnetic field induced strain (MFIS) under 5 MPa actuation stress. The major drawback of this material is a low blocking stress, which is overcome in the NiMnCoIn material system through FIPT. This magnetic alloy can exhibit 5% MFIS under 125 MPa actuation stress. The focus of this work is to capture the key magneto-thermo-mechanical responses of such mechanisms through phenomenological modeling. In this work a detailed thermodynamic framework for the electromagnetic interaction within a continuum solid is presented. A Gibbs free energy function is postulated after identifying the external and internal state variables. Material symmetry restrictions are imposed on the Gibbs free energy and on the evolution equations of the internal state variables. Discrete symmetry is considered for single crystals whereas continuous symmetry is considered for polycrystalline materials. The constitutive equations are derived in a thermodynamically consistent way. A specific form of Gibbs free energy for FIPT is proposed and the explicit form of the constitutive equations is derived from the generalized formulation. The model is calibrated from experimental data and different predictions of magneto-thermo-mechanical loading conditions are presented. The generalized constitutive equations are then reduced to capture variant reorientation. A coupled magneto-mechanical boundary value problem (BVP) is solved that accounts for variant reorientation to investigate the influence of the demagnetization effect on the magnetic field and the effect of Maxwell stress on the Cauchy stress. The BVP, which mimics a real experiment, provides a methodology to correlate the difference between the externally measured magnetic data and internal magnetic field of the specimen due to the demagnetization effect. The numerical results show that localization zones appear inside the material between a certain ranges of applied magnetic field. Stability analysis is performed for variant reorientation to analyze these numerical observations. Detailed numerical and analytical analysis is presented to investigate these localization zones. Magnetostatic stability analysis reveals that the MSMA material system becomes unstable when localizations appear due to non-linear magnetization response. Coupled magneto-mechanical stability analysis shows that magnetically induced localization creates stress-localizations in the unstable zones. A parametric study is performed to show the constraints on material parameters for stable and unstable material responses.

As explosive blasts continue to cause casualties in both civil and military environments, there is a need for increased understanding of the mechanisms of blast trauma at the organ level and a need for a more detailed predictive methodology. A fundamental understanding of blast injury will lead to the development of improved protective equipment and ultimately reduce the severity of injury. Models capable of predicting injury to varied blast loading will also reduce the emphasis on animal blast testing. To provide some historical context, this research was begun shortly after the U.S. led invasion of Iraq, and came to a close while there continues to be daily loss of life from blast injuries in the Middle East, as well as continued threats of terrorism throughout the world. In addition to industrial accidents, it is clear that blast injury is far more than just a military concern. Simplified finite element models of the human and sheep thoraces were created in order to provide practical and flexible models for the prediction of primary blast injury in simple and complex blast environments, and subsequently for the development of improved protective equipment. The models were created based on actual human and sheep geometries and published material properties. The fluid-structure interaction of the models compared well with experimental blast studies carried out during the course of the research, as shown by comparing actual and predicted overpressures in the free field and at the thorax. By comparing the models to published experimental data from simple blasts, trends in the results were verified and peak lung pressure was proposed as a trauma criterion. Local extent of injury in the lung is correlated to the peak pressure measured in each finite element, categorized as no injury (< 60 kPa), trace (60-100 kPa), slight (100-140 kPa), moderate (140-240 kPa) and severe (> 240 kPa). The calculation of the mean value of the peak lung pressures of all of the finite elements allows for an overall estimate of the injury level, with 35 kPa predicting threshold damage, 129 kPa for one percent lethality, and 186 kPa for fifty percent lethality. The simple blast results also compared well to the predictions of two previously validated mathematical models. Variation of predicted injury within a given loading severity was 15%, which is comparable to the model by Stuhmiller that had a variation of 20%. The model by Axelsson had very little variation (1.4%), but the differences between levels of severity were quite small, and often difficult to decipher. In addition to predicting consistent levels of injury, the finite element models were able to provide insight into the trauma mechanism, map the extent of injury through the lungs, and validate a local injury criterion. The models were then applied to predict injury under complex blast loading by subjecting the human finite element torso to a threshold level blast while located at varying distances from a wall or a corner. The results compared well to the validated mathematical models, showing a sharp increase in injury severity as the model approached the reflecting surface. When directly against the wall, the mean of the peak lung pressure values was 57 kPa, and in the corner, the mean value reached 69 kPa. Although these values did not reach the level representing one percent lethality, they do represent a significant increase in injury above threshold as a direct result of the surrounding geometry. Once again, the finite element models correctly showed injury trends and lung injury patterns reported in experiments. The models predicted the level of injury and were able to predict the time varying pattern of injury, which is something existing models cannot do. Having designed the models from physical principals, and having validated the models against published results, they can now be used in the continued development of protective equipment. Acknowledging that this model was the first iteration, the author believes that improvements in material properties, mesh refinement, and the investigation of other possible parameters for the prediction of injury will lead to substantial advances in the understanding of primary blast injury.

As explosive blasts continue to cause casualties in both civil and military environments, there is a need for increased understanding of the mechanisms of blast trauma at the organ level and a need for a more detailed predictive methodology. A fundamental understanding of blast injury will lead to the development of improved protective equipment and ultimately reduce the severity of injury. Models capable of predicting injury to varied blast loading will also reduce the emphasis on animal blast testing. To provide some historical context, this research was begun shortly after the U.S. led invasion of Iraq, and came to a close while there continues to be daily loss of life from blast injuries in the Middle East, as well as continued threats of terrorism throughout the world. In addition to industrial accidents, it is clear that blast injury is far more than just a military concern. Simplified finite element models of the human and sheep thoraces were created in order to provide practical and flexible models for the prediction of primary blast injury in simple and complex blast environments, and subsequently for the development of improved protective equipment. The models were created based on actual human and sheep geometries and published material properties. The fluid-structure interaction of the models compared well with experimental blast studies carried out during the course of the research, as shown by comparing actual and predicted overpressures in the free field and at the thorax. By comparing the models to published experimental data from simple blasts, trends in the results were verified and peak lung pressure was proposed as a trauma criterion. Local extent of injury in the lung is correlated to the peak pressure measured in each finite element, categorized as no injury (< 60 kPa), trace (60-100 kPa), slight (100-140 kPa), moderate (140-240 kPa) and severe (> 240 kPa). The calculation of the mean value of the peak lung pressures of all of the finite elements allows for an overall estimate of the injury level, with 35 kPa predicting threshold damage, 129 kPa for one percent lethality, and 186 kPa for fifty percent lethality. The simple blast results also compared well to the predictions of two previously validated mathematical models. Variation of predicted injury within a given loading severity was 15%, which is comparable to the model by Stuhmiller that had a variation of 20%. The model by Axelsson had very little variation (1.4%), but the differences between levels of severity were quite small, and often difficult to decipher. In addition to predicting consistent levels of injury, the finite element models were able to provide insight into the trauma mechanism, map the extent of injury through the lungs, and validate a local injury criterion. The models were then applied to predict injury under complex blast loading by subjecting the human finite element torso to a threshold level blast while located at varying distances from a wall or a corner. The results compared well to the validated mathematical models, showing a sharp increase in injury severity as the model approached the reflecting surface. When directly against the wall, the mean of the peak lung pressure values was 57 kPa, and in the corner, the mean value reached 69 kPa. Although these values did not reach the level representing one percent lethality, they do represent a significant increase in injury above threshold as a direct result of the surrounding geometry. Once again, the finite element models correctly showed injury trends and lung injury patterns reported in experiments. The models predicted the level of injury and were able to predict the time varying pattern of injury, which is something existing models cannot do. Having designed the models from physical principals, and having validated the models against published results, they can now be used in the continued development of protective equipment. Acknowledging that this model was the first iteration, the author believes that improvements in material properties, mesh refinement, and the investigation of other possible parameters for the prediction of injury will lead to substantial advances in the understanding of primary blast injury.

This work focuses on the thermomechanical characterization and constitutive model calibration of shape memory polymers (SMPs). These polymers have the ability to recover seemingly permanent large deformations under the appropriate thermomechanical load path. In this work, a contribution is made to both existing experimental and modeling efforts. First, an experimental investigation is conducted which subjects SMPs to a thermomechanical load path that includes varying the value of applied deformations and temperature rates. Specifically, SMPs are deformed to tensile extensions of 10% to 100% at temperature rates varying from 1 degree C /min to 5 degree C/min, and the complete shape recovery profile is captured. The results from this experimental investigation show that the SMP in question can recover approximately 95% of the value of the applied deformation, independent of the temperature rate during the test. The data obtained in the experimental investigation are then used to calibrate, in one-dimension, two constitutive models which have been developed to describe and predict the material response of SMPs. The models include a model in terms of general deformation gradients, thus making it capable of handling large deformations. In addition, the data are used to calibrate a linearized version of the constitutive model for small deformations. The material properties required for calibrating the constitutive models are derived from portions of the experimental results, and the model is then used to predict the shape memory effect for an SMP undergoing various levels of deformation. The model predictions are shown to match well with the experimental data.

The focus of this dissertation is on constant displacment rate experiments on asphalt concrete and on developing continuum models in a general thermo-mechanical setting which will corroborate with the experimental results. Modeling asphalt concrete and predicting its response is of great importance to the pavement industry. More than 90 percent of the US Highways uses asphalt concrete as a pavement material. Asphalt concrete exhibits nonlinear response even at small strains and the response of asphalt concrete to different types of loading is quite different. The properties of asphalt concrete are highly in&#64258;uenced by the type and amount of the aggregates and the asphalt used. The internal structure of asphalt concrete keeps on evolving during the loading process. This is due to the in&#64258;uence of different kinds of activities at the microlevel and also due to the interaction with the environment. The properties of asphalt concrete depend on its internal structure. Hence we need to take the evolution of the internal structure in modeling the response of asphalt concrete. Experiments were carried out at different con&#64257;nement pressures and displacement rates on cylindrical samples of asphalt concrete. Two different aggregates were used to make the sample -limestone and granite. The samples were tested at a constant displacement rate at a given con&#64257;nement pressure. The force required to maintain this constant displacement rate is measured and recorded. The frame-work has been developed using the idea of multiple natural con&#64257;gurations that was introduced recently to study a variety of non-linear dissipative response of materials. By specifying the forms of the stored energy and rate of dissipation function of the material, speci&#64257;c models were developed using this frame work. In this work both a compressible and an incompressible model were developed by choosing appropriate forms of stored energy and rate of dissipation function. Finally the veracity of the models were tested by corroborating with the experimental results. It is anticipated that the present work will aid in the development of better constitutive equations which in turn will accurately model asphalt concrete in laboratory and in &#64257;eld.

The disturbed state concept (DSC) based constitutive model is the focus of this research. It is applied for characterizing two problems; thermomechanical reliability analysis of electronic packages, and prediction of glacial motion. A new procedure for construction of static yield surface for materials is proposed. Further, a modified DSC model to include effect of rate of loading on material behavior is proposed.The DSC is applied to characterize the behavior of Sn-3.9Ag-0.6Cu (SAC) lead free solder alloy used in electronic packages. Proposed procedure of construction of static curve and rate dependent DSC model is applied for prediction of creep and rate dependent behavior of the SAC alloy. Laboratory test data is adopted from the literature and material parameters are determined. The DSC model is validated using the derived material parameters. A finite element analysis of the BGA 225 package is performed under cyclic thermomechanical loading. Analysis results are compared with available test data. A failure criterion for prediction of number of cycles to failure for BGA 225 is then derived.The second application of DSC discussed in this work is prediction of glacial motion. Mechanical behavior of glacial till and its contribution to overall ice movement is characterized using DSC. Two regionally significant tills are chosen and samples are collected from field. A series of laboratory tests are conducted on samples. Tests results are used for model calibration and validation. A numerical simulation of an idealized ice - till system under gravity loading is performed. Two such analyses are performed with DSC and Mohr Coulomb models and the results are compared.The DSC predicts failure when a significant portion of the material reaches a critical disturbance whereas the Mohr Coulomb model predicts failure based on peak stress. DSC predicts a gradual progression to failure whereas the Mohr Coulomb model predicts early catastrophic failure. According to DSC, the material undergoes considerable plastic strains before it reaches failure whereas the Mohr Coulomb predicts failure at very low elastic strains. In general the DSC is considered to provide a more realistic and general constitutive model for glacial tills.

Horizontal directional drilling is increasingly used to install pipes without costs and disruptions associated with conventional ‘cut and cover’ installations. This technique, which was developed by industrial innovators, feature complex soil and pipe response which is not well understood. The success of this operation depends on knowledge of the pulling forces applied, level of ground disturbance, ground expansion or fracture from mud pressure, and the effect of the pulling operation on the pipes. Tensile stresses in the pipe vary with time during and after installation, and along the pipe. This applies especially to polymer pipes where the stresses during insertion and those over the service life of the pipe may influence its performance. The main objective of this study is to model the short term and long term response of pipes installed using horizontal directional drilling and to investigate the effect of the time dependent behaviour of polymer pipes, as well as other installation variables on the performance of the pipe during and after installation. The mechanical behaviour of high density polyethylene used to manufacture a significant portion of pipes installed using horizontal directional drilling is investigated and two sophisticated constitutive models are developed to simulate the time-dependent behaviour of high density polyethylene. The interaction between the pipe and the surrounding soil during horizontal directional drilling installations is also investigated and modelled. A FORTRAN algorithm is developed to calculate the short and long term response of elastic and polymeric pipes installed using horizontal directional drilling. The program uses the HDPE constitutive models as well as the pipe-soil interaction model developed in the study. After evaluation, the developed program is employed in a parametric study on the sensitivity of short term and long term pipe response to different parameters, including the effect of overstressing the pipe during installation. As Multiaxial modeling is necessary for accurate analysis of some applications including the swagelining method, a uniaxial constitutive model developed in the current study is generalized to a multi-axial model that can simulate the response to biaxial stress-strain fields. The multi-axial model is implemented in a finite element code and its performance in simulating multiaxial stress-strain fields is evaluated. / Thesis (Ph.D, Civil Engineering) -- Queen's University, 2008-06-12 18:03:43.501

Time- and rate-dependent materials such as polymers, bituminous materials, and soft materials clearly display all four fundamental responses (i.e. viscoelasticity, viscoplasticity, viscodamage, and healing) where contribution of each response strongly depends on the temperature and loading conditions. This study proposes a new general thermodynamic-based framework to specifically derive thermo-viscoelastic, thermo-viscoplastic, thermo-viscodamage, and micro-damage healing constitutive models for bituminous materials and asphalt mixes. The developed thermodynamic-based framework is general and can be applied for constitutive modeling of different materials such as bituminous materials, soft materials, polymers, and biomaterials. This framework is build on the basis of assuming a form for the Helmohelotz free energy function (i.e. knowing how the material stores energy) and a form for the rate of entropy production (i.e. knowing how the material dissipates energy). However, the focus in this work is placed on constitutive modeling of bituminous materials and asphalt mixes. A viscoplastic softening model is proposed to model the distinct viscoplastic softening response of asphalt mixes subjected to cyclic loading conditions. A systematic procedure for identification of the constitutive model parameters based on optimized experimental effort is proposed. It is shown that this procedure is simple and straightforward and yields unique values for the model material parameters. Subsequently, the proposed model is validated against an extensive experimental data including creep, creep-recovery, repeated creep-recovery, dynamic modulus, constant strain rate, cyclic stress controlled, and cyclic strain controlled tests in both tension and compression and over a wide range of temperatures, stress levels, strain rates, loading/unloading periods, loading frequencies, and confinement levels. It is shown that the model is capable of predicting time-, rate-, and temperature-dependent of asphalt mixes subjected to different loading conditions.

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