# Browsing by Subject "Constitutive modeling"

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Item 3D characterization of ventricular myocardium in health, disease, and treatment(2021-05-07) Li, David Shuen; Sacks, Michael S.; Gorman, Robert C; Rausch, Manuel K; Cosgriff-Hernandez, Elizabeth M; Ravi-Chandar, KrishnaswaShow more Cardiovascular diseases such as myocardial infarction and pulmonary arterial hypertension cause maladaptive remodeling of the heart, which drastically alters its function and progresses toward heart failure. Determining the mechanical drivers of remodeling, as well as therapeutic targets for its amelioration, is hampered by insufficient knowledge of the biomechanical environment of the myocardium at the tissue and cellular scales. Modeling of myocardial behavior has enabled the quantification of its mechanics and the in silico evaluation of cardiac disease therapies, but predictive models that account for full 3D mechanics are still lacking, facing hurdles in terms of (i) available experimental data from which to develop models, and (ii) understanding the complex mechanical behavior and interactions of constituents within the tissue. Clinical treatment strategies also depend on the critical link between organ-level function and the cellular-level microenvironment, necessitating multiscale modeling approaches in order to connect the two. To this end, the research presented in this dissertation focuses on both addressing current challenges in tissue-scale myocardial modeling as well as taking a first step in relating myocardial properties between the tissue and cellular scales. This work combines 3D modeling-driven optimal experimental design, multiaxial mechanical testing, high-resolution imaging, and finite element simulation. Through use of these integrated approaches, we achieve robust characterization of normal and diseased myocardium at the tissue scale within a full 3D framework. Next, we present a multiscale modeling platform for ventricular myocardium to elucidate cellular-scale stress transfer between myofibers and their surroundings, allowing for investigation of fiber-specific microstructural remodeling in response to disease. This research provides a foundation for improved models of myocardium capable of accurate prediction of therapeutic impacts on cell-, tissue-, and organ-level remodeling, ultimately aiding the development of patient-specific interventions and improvement of therapeutic outcomes.Show more Item Constitutive modeling of pseudoelastic NiTi and its application to structural problems(2017-08) Jiang, Dongjie; Kyriakides, S.; Landis, Chad M.; Kovar, Desiderio; Liechti, Kenneth M; Ravi-Chandar, KrishnaswamyShow more Nearly equiatomic NiTi exhibits the unique characteristic of pseudoelasticity, i.e. it can be deformed to strain levels of several percent that is fully recoverable on unloading. Under tension, the phase transformation results in strain of nearly 7% and inhomogeneous deformation while the stress remains essentially constant. By contrast, under compression, transformation occurs at a much higher stress, the induced strain is nearly one-half and deformation is essentially homogeneous. These material nonlinearities interact with structural instabilities to produce hitherto unknown intriguing structural responses. A constitutive modeling framework based on J₂-type kinematic hardening is developed to address the tension/compression asymmetry of pseudoelastic NiTi, including inhomogeneous versus homogeneous deformations. Its performance is then evaluated in the numerical studies of four nonlinear NiTi structures that were previously investigated experimentally. The first problem considered is the buckling and recovery of an axially compressed NiTi tube. The modeling efforts reproduce the major events observed, including onset of axisymmetric wrinkling, collapse by progressive development of buckling lobes with three circumferential waves, erasure of the lobes and recovery of deformation upon unloading. The study shows that the tension/compression asymmetry plays the key role in bringing the calculated response close to the experimental one and addition of plastic deformation further improves the results. The second problem involves a NiTi strip under tension. The constitutive model properly accounting for softening in the tensile response reproduces the closed hysteresis with two stress plateaus with correct levels and extents, as well as localization of deformation into inclined bands that propagate in the specimen. In the third problem, the constitutive model is used to analyze the tension test of a NiTi tube. The simulation reproduces a closed hysteretic response with two stress plateaus close to the measured one. The tubular geometry of the specimen imposes helical and multi-pronged localization patterns. The last problem studied is the bending of a NiTi tube. The simulation reproduces the major features of the experimental results: the hysteretic moment-end rotation response with two plateaus; localization of curvatures; progressive development of diamond patterns of higher strain on the tensioned side and the nearly homogeneous deformation on the compressed side.Show more Item Constitutive modeling of viscoelastic behavior of bituminous materials(2012-12) Motamed, Arash; Bhasin, AmitShow more Asphalt mixtures are complex composites that comprise aggregate, asphalt binder, and air. Several research studies have shown that the mechanical behavior of the asphalt mixture is strongly influenced by the matrix, i.e. the asphalt binder. Therefore, accurate constitutive models for the asphalt binders are critical to ensure accurate performance predictions at a material and structural level. However, researchers who use computational methods to model the micromechanics of asphalt mixtures typically assume that (i) asphalt binders behave linearly in shear, and (ii) either bulk modulus or Poisson’s ratio of asphalt binders is not time dependent. This research develops an approach to measure and model the shear and bulk behavior of asphalt binders at intermediate temperatures. First, this research presents the findings from a systematic investigation into the nature of the linear and nonlinear response of asphalt binders subjected to shear using a Dynamic Shear Rheometer (DSR). The DSR test results showed that under certain conditions a compressive normal force was generated in an axially constrained specimen subjected to cyclic torque histories. This normal force could not be solely attributed to the Poynting effect and was also related to the tendency of the asphalt binder to dilate when subjected to shear loads. The generated normal force changed the state of stress and interacted with the shear behavior of asphalt binder. This effect was considered to be an “interaction nonlinearity” or “three dimensional effect”. A constitutive model was identified to accommodate this effect. The model was successfully validated for several different loading histories. Finally, this study investigated the time-dependence of the bulk modulus of asphalt binders. To this end, poker-chip geometries with high aspect ratios were used. The boundary value problem for the poker-chip geometry under step displacement loading was solved to determine the bulk modulus and Poisson’s ratio of asphalt binders as a function of time. The findings from this research not only improve the understanding of asphaltic materials behavior, but also provide tools required to accurately predict pavement performance.Show more Item Histomechanical characterization and microstructure-based modeling of right ventricular myocardium(2023-12) Kakaletsis, Sotirios; Rausch, Manuel Karl; Huang, Rui; Dortdivanlioglu, Berkin; Lejeune, Emma; Ravi-Chandar, KrishnaswamyShow more Right ventricular histomechanics have been historically overlooked, thus limiting our ability to describe the mechanisms underlying severe pathological conditions of the right heart. In this dissertation we set out to investigate the histomechanics of the right ventricular myocardium both in health and disease (pulmonary arterial hypertension), using a large animal (ovine) model. To this end, we combine mechanical testing, histology analysis, magnetic resonance imaging and microstructure-based modeling. Our computational approach is threefold, involving established homogenized models, novel machine learning metamodels and the use of embedded, discrete fiber networks. First, we found that the right ventricular myocardium in health exhibits nonlinear, anisotropic mechanical response. The homogenized models successfully captured this behavior at the cost of considerable computational time, subsequently accelerated by the machine learning metamodels. Moreover, we found that pulmonary arterial hypertension induced extracellular collagen deposition, spatially-dependent wall thickening, and increased stiffness at the low strain regime. Our embedded fiber network approach was able to account for these remodeling effects. Finally, throughout this work we have been making our experimental data and computational implementations publicly available, establishing for the first time a complete pipeline for the characterization of the right ventricular myocardium.Show more Item Localization instabilities in pseudoelastic NiTi tubes under multiaxial stress states(2022-07-01) Kazinakis, Karlos Thomas Leonidas; Kyriakides, S.; Landis, Chad M.; Kovar, Desiderio; Liechti, Kenneth M.; Ravi-Chandar, KrishnaswamyShow more Nearly equiatomic NiTi has a unique property called pseudoelasticity in that strain of several percent is recoverable at room temperatures. This characteristic is attainable due to solid-state transformations between the austenite and martensite phases. It is well established that the transformation in tension is associated with localization during the loading/unloading stress plateaus of its hysteresis. By contrast, the transformation in compression is essentially homogeneous and occurs at much higher stresses and lower strains. Recently conducted biaxial experiments on NiTi tubes revealed, in addition to tension/compression asymmetry, an inherent anisotropic behavior. The interaction of these material nonlinearities with geometric instabilities results in challenging structural problems and the need for adept constitutive models is vital. Hence, a J₂-type kinematic hardening model was developed by our group, which incorporates asymmetry and is now extended to include anisotropy. Two numerical studies of NiTi tubular structures incorporate this framework within a finite element analysis aiming to reproduce the experimental responses and the transformation-induced strain patterns. The first problem investigates the buckling and collapse of a thin-walled NiTi tube under pure bending. The analysis captures the moment-end rotation response and the distinct diamond patterns that develop demonstrating how their interaction with ovalization leads to buckling and collapse. Parametric sensitivity studies illustrate the roles of the diameter-to-thickness ratio, geometric imperfections, and some key aspects of the model to the stability of the structure. The second problem examines thin-walled NiTi tubes under combined axial force and internal pressure. The simulations reproduce well the stress-average strain responses and the transformation stress loci, while for hoop dominant stress paths the extents of the transformation strains are somewhat overpredicted. The evolution of localization in the form of high or low strain helical bands, the variation of helix angles with the stress ratio, and the dissipated energy compare favorably. The hardening response and essentially homogeneous deformation exhibited in the neighborhood of the equibiaxial stress state is reproduced, but with reduced hardening and weak deformation patterns. The special case of equibiaxial tension is studied further as it highlights the effects of asymmetry and anisotropy in the constitutive model on structural behaviorsShow more Item Lüders banding and its effects on structures under tension/compression and cyclic bending loads(2023-12) Zhang, Weihan, Ph. D.; Kyriakides, S.; Hallai, Julian F.; Liechti, Kenneth M.; Ravi-Chandar, Krishnaswamy; Huang, RuiShow more Lüders banding is a material instability that leads to localized deformation during the initial yielding of the material. This research project investigates how this material instability affects the response of tubular structures under bending and cyclic bending. Tension/compression experiments are first performed on steel rods exhibiting Lüders banding. Special attention is given to how a specimen behaves when the initial loading is interrupted with part of it Lüders deformed and the rest of the specimen still remaining elastic. Digital image correlation reveals that both sections unload elastically, but upon reverse loading, the previously elastic zone develops Lüders strain of the opposite sign, while the plastically deformed zone traces Bauschinger rounding. A custom constitutive model is developed to capture this complex behavior, encompassing a J2-type softening material response and nonlinear kinematic hardening for reverse loading. The constitutive model is subsequently used to study the effect of Lüders banding on tubes under cyclic bending. Under bending, tubes progressively develop inclined bands of higher strain organized in periodic diamond-shaped patterns. Upon unloading, the diamond patterns gradually disappear, but simultaneously local secondary patterns of higher strain develop in the hitherto elastic zones between the original diamonds. When completing the cycle, the secondary patterns are progressively erased and the diamond patterns reappear. The sensitivity of this structural behavior to several problem variables including the extent of Lüders strain, the level of Lüders stress, and diameter-to-thickness ratio of the tube is examined in parametric studies. The constitutive model is subsequently implemented in a large-scale numerical analysis of the winding/unwinding of a pipeline with Lüders bands on a large diameter reel. During winding, inclined Lüders bands organize into clusters separated by elastic sections. During unwinding and straightening, the intensity of Lüders patterns is gradually reduced and secondary patterns develop in the previously undeformed zones. This appearance, erasure, and reappearance of Lüders patterns is repeated in subsequent wind/unwind cycles. Ovality accumulates during each cycle and may lead to local buckling and collapse. The effect of problem variables such as the level of back tension, reel diameter, extent of Lüders strain, steel yield strength and diameter-to-thickness ratio is examined in a parametric study.Show more Item Phenomenological constitutive modeling and numerical analysis of fracture toughness for shape memory alloys(2022-05-02) Alsawalhi, Mohammed Yousuf; Landis, Chad M.; Foster, John T; Ravi-Chandar, Krishnaswamy Ravi; Mear, Mark E; Kyriakides, SteliosShow more Nickel titanium (NiTi) alloys possess unique characteristics that provide them the ability to recover large mechanical strains up to 8%. Pseudoelasticity and the shape memory effect are phenomena associated with SMA behavior. Shape recovery is driven by thermomechanical loading/unloading during the martensitic phase transformation. NiTi behavior also exhibits the property of asymmetry in transformation stress and transformation strain between the tension and compression responses as a result of forward and reverse phase transformations, as well as the reorientation and detwinning of the martensite phase. Furthermore, the process of heat generation during phase transformation near a crack tip effects the local temperature variations and thus the fracture toughness of the material. A new thermomechanical constitutive modeling approach for shape memory alloys (SMAs) that undergo a martensite to austenite phase transformation is presented. The novelty of this new formulation is that a single transformation surface is implemented in order to capture the main aspects of SMAs including forward transformation, reverse transformation, and martensite reorientation. Specific forms for the transformation surface and the transformation potential are devised and results for the behaviors captured by the model are provided for a range of thermomechanical loadings. The validity of the model is assessed with experimental studies of complex thermomechanical proportional and non proportional load paths at different temperatures using numerical simulations. The phenomenological constitutive model is implemented in finite element calculations and applied to the pseudoelastic and shape memory effects of a beam in pure bending. Fracture analysis is implemented within finite element computations to model the toughening due to the austenite to martensite phase transformation and martensite reorientation during steady mode I crack growth. Several dimensionless parameters relating the thermomechanical parameters of the constitutive model, the crack growth velocity, and the prevailing sample temperature are identified and applied to study the thermomechanical crack tip fields and the toughening enhancement due to the forward and reverse phase transformations in the vicinity of the crack tip. The first part of this dissertation involves validation of the model by comparisons of numerical simulations with experimental data and by developing consistent tangent moduli and applying the model to simple structural analysis of pure beam bending. First, uniaxial tensile and compressive stress-strain responses are simulated at four different temperatures: below the martensite finish temperature, between the martensite start and austenite start temperatures, between the austenite start and austenite finish temperatures, and above the austenite finish temperature. The numerical model reproduces the major aspects of the experimental measurements including the stress and strain levels. The transformation stress and transformation strain asymmetry between the tensile and compressive responses is also implemented in the model. The second problem investigates the performance of the model for a NiTi tube under a square axial-shear strain load path. The asymmetric model outperforms the symmetric model by reproducing the main features observed in the experiments. However, there is a notable difference in the magnitudes of stresses, mainly the shear stress, due to the anisotropy of the SMA material which is not accounted for in this model. The third problem examines the behavior of the constitutive model for tension-torsion of SMA wires for temperatures at the martensite and austenite phases. Again, the asymmetric model performs better than the symmetric model in terms of fitting the model response to the experimental measurements. The exclusion of anisotropy from the constitutive model has noticeable impact on the axial strain behavior at high temperatures. Lastly, the final problem investigates the pseudoelastic and shape memory behaviors of a beam under pure bending. The analysis in each case captures the moment-curvature and the temperature-curvature responses, as well as the axial stress distribution through the cross-section of the beam. The asymmetric model produced asymmetry in the axial stress distribution that fits the behavior of real SMAs. The second part of this dissertation involves fracture computations to analyze the toughening due to the stress-induced martensitic transformation and martensite reorientation during steady mode I crack growth. First, analyses are performed on the sizes and shapes of the various transformed zones near the crack tip for a range of temperatures analyzed. Secondly, the uniaxial stress-strain response is impacted by the thermomechanical parameters in the constitutive model which results in a relatively strong dependence of the transformation toughening on the material parameters. Next, numerical simulations are used to illustrate the effects of crack growth speed and heat capacity on the toughening. Finally, different sample temperatures show the strong impact on the toughness enhancement due to phase transformation. The last part of this dissertation discusses different approaches for material modeling, including different formulations associated with the transformation potentials and the associated integration routines. The first approach introduces a new internal variable that is a function of the other two in an attempt to control the pure shear stress-strain response as being a mixture between the tensile and compressive responses. The second approach introduces two stress invariants that are a linear or non-linear combination of the strain invariant. Here the objective is to control how fast the strain invariant goes towards uniaxial tension in a pure shear loading in order to allow the pure shear response to be a controlled mixture between the tensile and compressive responses as opposed to having similar behavior to the tensile response. The last approach for the integration algorithm utilizes a classical elastic prediction-transformation correction return mapping. This method simplifies the number of unknowns solved in the integration routine to just one. Therefore, a 1-D Newton-Raphson (NR) scheme is used which allows for more robust numerical calculations.Show more