Browsing by Subject "Constitutive Modeling"
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Item A phenomenological constitutive model for magnetic shape memory alloys(Texas A&M University, 2007-04-25) Kiefer, BjoernA thermodynamics-based constitutive model is derived which predicts the nonlinear strain and magnetization response that magnetic shape memory alloys (MSMAs) exhibit when subjected to mechanical and magnetic loads. The model development is conducted on the basis of an extended thermo-magneto-mechanical framework. A novel free energy function for MSMAs is proposed, from which the constitutive equations are derived in a thermodynamically-consistent manner. The nonlinear and hysteretic nature of the macroscopic material behavior is captured through the evolution of internal state variables which are motivated by the crystallographic and magnetic microstructures of MSMAs. Model predictions are presented for different relevant loading cases and analyzed in detail. Finally, magnetostatic boundary value problems for MSMAs are considered and numerically solved using the finite element method. For these computations the developed constitutive model provides the nonlinear magnetic properties of the MSMA. The knowledge of the magnetic field distribution in the computational domain as a function of the applied field, which results from this magnetostatic analysis, is useful for the proper interpretation of experimental results as well as the design of experiments and applications.Item Constant displacement rate experiments and constitutive modeling of asphalt mixtures(Texas A&M University, 2006-04-12) Hariharakumar, PradeepThe 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 influenced 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 influence 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 confinement 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 confinement 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 configurations 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, specific 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 field.Item Magneto-Thermo-Mechanical Coupling, Stability Analysis and Phenomenological Constitutive Modeling of Magnetic Shape Memory Alloys(2012-12-06) Haldar, Krishnendu 1978-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.Item Thermo-Viscoelastic-Viscoplastic-Viscodamage-Healing Modeling of Bituminous Materials: Theory and Computation(2012-10-19) Darabi Konartakhteh, MasoudTime- 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.Item Thermomechanical Characterization and Modeling of Shape Memory Polymers(2010-01-16) Volk, Brent L.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.