Previous experimental observations have shown that the pseudoelastic response of NiTi shape memory alloys (SMA) is localized in nature and proceeds through nucleation and propagation of localized deformation bands. It has also been observed that the mechanical response of SMAs is strongly affected by loading rate and cyclic degradation. These behaviors significantly limit the accurate modeling of SMA elements used in various devices and applications. The aim of this work is to provide engineers with a constitutive model that can accurately describe the dynamic, unstable pseudoelastic response of SMAs, including their cyclic response, and facilitate the reliable design of SMA elements. A 1-D phenomenological model is developed to simulate the localized phase transformations in NiTi wires during both loading and unloading. In this model, it is assumed that the untransformed particles located close to the transformed regions are less stable than those further away from the transformed regions. By consideration of the thermomechanical coupling among the stress, temperature, and latent heat of transformation, the analysis can account for strain-rate effects. Inspired by the deformation theory of plasticity, the 1-D model is extended to a 3-D macromechanical model of localized unstable pseudoelasticity. An important feature of this model is the reorientation of the transformation strain tensor with changes in stress tensor. Unlike previous modeling efforts, the present model can also capture the propagation of localized deformation during unloading. The constitutive model is implemented within a 2-D finite element framework to allow numerical investigation of the effect of strain rate and boundary conditions on the overall mechanical response and evolution of localized transformation bands in NiTi strips. The model successfully captures the features of the transformation front morphology, and pseudoelastic response of NiTi strip samples observed in previous experiments. The 1-D and 3-D constitutive models are further extended to include the plastic deformation and degradation of material properties as a result of cyclic loading.

Les matériaux granulaires exhibe un spectre très large de propriétés constitutives, le long de chemins de chargement très divers. Développer des modèles constitutifs permettant de reproduire ces caractéristiques a demeuré un réel challenge scientifique au cours des dernières décennies. A cet égard, les approches multi-échelles constituent aujourd’hui une voie très prometteuse. Elles permettent de relier les propriétés macroscopiques à celles observées à l’échelle microscopique.Une investigation a été menée sur la base de simulations numériques discrètes (DEM)d’essais biaxiaux, afin d’identifier les caractéristiques micro-structurelles du matériau granulaire, la manière dont elles évoluent au cours d’un chemin de chargement, et le rôle qu’elles jouent dans l’émergence du comportement macroscopique. A l’échelle mésoscopique,le réseau de transmission de force (chaines de force) et les cellules définies parles vecteurs branches (meso-cycles) apparaissent jouer un rôle de première importance.Les meso-cycles, construits à partir du réseau de contact de l’assemblage, peuvent être caractérisés en fonction du nombre de cotés qu’ils contiennent (topologie). Leur influence sur le comportement volumique de l’échantillon est en effet étroitement liée à ce nombre de contact. En outre, leur interaction avec les chaines de force est également fortement dépendante de leur topologie. Ainsi, les cycles contenant 3 cotés (L3) participent activement à la stabilisation des chaines de force, alors que les cycles contenants au moins6 cotés (L6+) contribuent essentiellement au comportement dilatant de l’échantillon et à l’effondrement des chaines de force. Enfin, l’existence d’une méso-structure unique à l’état critique, au sein de la bande de cisaillement (rupture localisée) ou au sein de l’échantillon (rupture diffuse), est clairement démontrée.viii Sur la base de ces résultats, un modèle constitutif a été développé à partir du modèle H-directionnel (Nicot and Darve, 2011b). La structure du matériau granulaire est décrite par un assemblage d’hexagones (modélisant les cycles L6), orientés dans toutes les directions de l’espace. A partir d’opérations d’homogénéisation, les contraintes et les déformations incrémentales peuvent être reliées à l’échelle de l’assemblage, donnant lieu à un modèle de comportement dont la performance a pu être testée le long de chemins de chargements variés. / Granular materials exhibit a wide spectrum of constitutive features under various loading paths. Developing constitutive models which succeed to characterize these features has been challenging scientists for decades. A promising direction of achieving this can be the multi-scale approach. Through which the constitutive model is formulated in the way that relating material's macroscopic properties to their micro-scale essences, namely, corresponding micro-structure properties.To better characterize the micro-structure and formulate the relation between different scales, a comprehensive investigation have been carried out on the basis of numerical biaxial tests using 2D discrete element method (DEM), in order to ascertain the micro-structure characteristics of the granular material, the way they evolve versus loading and their corresponding rules in the macroscopic behaviors. In a meso-scale, intermediate between the single contact scale and the macro-scale, the force transmission network (force-chains) and area element enclosed by contacts branches (meso-loops) are highlighted in terms of their significant influences on material's macro-scale behavior. Meso-loops herein are tessellated from the whole area of the granular assembly by the contact branch network, and are subsequently categorized according to their side number.The development of meso-loops is observed to be intimately related to material's volumetric evolution, especially the plastic part. Then, the interaction between force-chains and meso-loops and its significance to the global volumetric behavior are revealed. Otherwise, in critical state, an identical meso-structure is found in the failure area of both localized and diffuse failure mode. Meso-loops with 3 sides (L3) appear to be indispensable for the force-chain stability, meanwhile, meso-loops with more than or equal to 6 sides (L6+) contribute much to the volume expansion and accelerate the force-chain buckling. The interplay between L3 and L6+ largely embody, or are representative of, the various mechanical performance of the granular material.A constitutive model has been developed by modifying the H-directional model. In this model, individual hexagons, representatives of L6+, construct the fabric as distributing along different directions in the space. Then multi-scale approach is then used to relate macroscopic properties from local ones, and eventually, to give the constitutive relation. This model is then validated in different loading paths, and eventually proved satisfying.

Previous experimental observations have shown that the pseudoelastic response of NiTi shape memory alloys (SMA) is localized in nature and proceeds through nucleation and propagation of localized deformation bands. It has also been observed that the mechanical response of SMAs is strongly affected by loading rate and cyclic degradation. These behaviors significantly limit the accurate modeling of SMA elements used in various devices and applications. The aim of this work is to provide engineers with a constitutive model that can accurately describe the dynamic, unstable pseudoelastic response of SMAs, including their cyclic response, and facilitate the reliable design of SMA elements. A 1-D phenomenological model is developed to simulate the localized phase transformations in NiTi wires during both loading and unloading. In this model, it is assumed that the untransformed particles located close to the transformed regions are less stable than those further away from the transformed regions. By consideration of the thermomechanical coupling among the stress, temperature, and latent heat of transformation, the analysis can account for strain-rate effects. Inspired by the deformation theory of plasticity, the 1-D model is extended to a 3-D macromechanical model of localized unstable pseudoelasticity. An important feature of this model is the reorientation of the transformation strain tensor with changes in stress tensor. Unlike previous modeling efforts, the present model can also capture the propagation of localized deformation during unloading. The constitutive model is implemented within a 2-D finite element framework to allow numerical investigation of the effect of strain rate and boundary conditions on the overall mechanical response and evolution of localized transformation bands in NiTi strips. The model successfully captures the features of the transformation front morphology, and pseudoelastic response of NiTi strip samples observed in previous experiments. The 1-D and 3-D constitutive models are further extended to include the plastic deformation and degradation of material properties as a result of cyclic loading. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

This study provides an overview of the implementation of a nonlinear microstructural constitutive model in ABAQUS employing a user subroutine at the level of the biomedical engineer. Two different element formulations are employed: a continuum incompressible and a plane stress incompressible. All examples are validated by performing a number of deformations on 2D and 3D square elements and comparing the analytical formulation in a programming language and the user subroutine in ABAQUS. Application models will be presented that provide a deeper look into the impacts of soft tissue deformation, damage, and fracture. Additionally, we investigate the mechanical behavior of skin layers in terms of the nominal stress-strain curve using uniaxial and cyclic loading tests on porcine skin specimens in two forms: dermis integrating epidermis and hypodermis. Experiments were performed on specimens from the belly and breast of the pigs and under both orthogonal orientations with respect to the spine direction. All tests were carried out at room temperature with cyclic loading at a constant strain rate and increasing stretch increments. Finally, data is fitted using microstructural constitutive model.

This study examines the use of embedded shape memory alloy (SMA)actuators for adaptive control of the themomechanical response of composite structures. Control of static and dynamic responses are demonstrated including thermal buckling, thermal post-buckling, vibration, sonic fatigue, and acoustic transmission. A thermomechanical model is presented for analyzing such shape memory alloy hybrid composite (SMAHC) structures exposed to thermal and mechanical loads. Also presented are (1) fabrication procedures for SMAHC specimens, (2) characterization of the constituent materials for model quantification, (3) development of the test apparatus for conducting static and dynamic experiments on specimens with and without SMA, (4) discussion of the experimental results, and (5) validation of the analytical and numerical tools developed in the study. The constitutive model developed to describe the mechanics of a SMAHC lamina captures the material nonlinearity with temperature of the SMA and matrix material if necessary. It is in a form that is amenable to commercial finite element (FE) code implementation. The model is valid for constrained, restrained, or free recovery configurations with appropriate measurements of fundamental engineering properties. This constitutive model is used along with classical lamination theory and the FE method to formulate the equations of motion for panel-type structures subjected to steady-state thermal and dynamic mechanical loads. Mechanical loads that are considered include acoustic pressure, inertial (base acceleration), and concentrated forces. Four solution types are developed from the governing equations including thermal buckling, thermal post-buckling, dynamic response, and acoustic transmission/radiation. These solution procedures are compared with closed-form and/or other known solutions to benchmark the numerical tools developed in this study. Practical solutions for overcoming fabrication issues and obtaining repeatable specimens are demonstrated. Results from characterization of the SMA constituent are highlighted with regard to their impact on thermomechanical modeling. Results from static and dynamic tests on a SMAHC beam specimen are presented, which demonstrate the enormous control authority of the SMA actuators. Excellent agreement is achieved between the predicted and measured responses including thermal buckling, thermal post-buckling, and dynamic response due to inertial loading. The validated model and thermomechanical analysis tools are used to demonstrate a variety of static and dynamic response behaviors associated with SMAHC structures. Topics of discussion include the fundamental mechanics of SMAHC structures, control of static (thermal buckling and post-buckling) and dynamic responses (vibration, sonic fatigue, and acoustic transmission), and SMAHC design considerations for these applications. The dynamic response performance of a SMAHC panel specimen is compared to conventional response abatement approaches. SMAHCs are shown to have significant advantages for vibration, sonic fatigue, and noise control. / Ph. D.

Over recent decades, the public tendency toward using the structural composite lumber (SCL), a common composite of wood made of wood strands or veneers glued and compressed together, as structural members (especially the main load bearing members such as beams and columns) has risen considerably. In contrast to the fast-paced market growth of these products, development is slow. The experimental development is gradual and time-consuming and the computational development is even slower. The objective of this project is to introduce appropriate numerical models for limit state analysis of a certain type of SCL material called PSL. Parallel strand lumber (PSL), has mesostructures characterized by the presence of voids that renders the mesostructure highly heterogeneous. In addition to material phase aberrations such as grain angle variations and defects, void heterogeneities play an important role in determining the failure modes and strength of PSL. In this study, virtual void structures were defined to form part of the input to finite element analysis of PSL for the purpose of investigating the sensitivity of strength to the void structure. Assuming the wood phase to be homogeneous and orthotropic, the following 2D and 3D characteristics of voids were investigated: volume fraction, volume, alignment and moments of inertia of voids, as well as second moment properties, lineal path function and chord length functions of the two phase mesostructure. In addition, a method was developed to generate virtual voids in order to simulate PSL and investigate the possible effects of the void distribution on material strength. An experimental program along with a statistical survey was conducted to quantify the mentioned characteristics of the voids in two 133 mm * 133 mm * 610 mm 2.0 E Eastern Species PSL billets. As expected, most of the voids lie on the longitudinal direction of the specimen and have approximately an ellipsoidal shape. Based on this shape data, the characteristics of the ellipsoids which best t the voids were calculated. Using the statistical data of the fitted ellipsoids, a random field of virtual ellipsoid shaped voids to simulate the mesostructure of PSL was generated. In this study, the simulation of PSL material is based on two simplifying assumptions: 1) The wood phase is continuum, homogeneous and orthotropic. While in reality, the wood phase consists of glued wood strands that are heterogeneous due to their mechanical variability and only roughly orthotropic on a macro scale as a result of the varying fiber angle; 2) Voids are the mere source of uncertainty. The linear elastic analysis of carefully defined (in mesostructural aspect) PSL models can be the first step of mechanical study of the material. The effective modulus of elasticity of material in presence of voids and the distribution of conventional, principal and effective stresses considering the effect of volume fraction and shape of the voids are the target of this preliminary study. Linear elastic uniaxial analyses showed good mechanical consistency between the models including actual void shapes and the models including ellipsoidal void representations. Also, they showed that the stress mutliaxiality at the tip of the voids is negligible. The study of mechanics of PSL is incomplete unless the question of material anisotropy is taken into consideration. PSL is brittle in tension and ductile in compression. The material heterogeneity increases the complexity of the problem by affecting the stress distribution in the member. A detailed nonlinear approach has been proposed in order to investigate the mechanical behavior of PSL structural members under different uniaxial loading scenarios. This approach introduces proper constitutive models for the wood phase along with good void generation techniques. In other words, this approach suggests what models should be used for the continuum-assumed wood phase to simulate its brittle behavior in tension and ductile behavior in compression; and moreover, tests the applicability and accuracy of ellipsoidal void representation. The models are calibrated using the results of experiments on PSL material. Because of the brittle behavior, all wood products show significant mechanical dependency to the member's size under tensile loading. Once good constitutive model and mesostructural simulation is found for tensile loading, it is easy to make and analyze PSL models with different sizes and investigate the effect of size on mechanical behavior. The simulation results have been compared to the available results of a previously done experimental study.

No description available.

While traumatic aortic injury (TAI) and rupture (TAR) continue to be a major cause of morbidity and mortality in motor vehicle accidents, its underlying mechanisms are still not well understood. Different mechanisms such as increase in intraluminal pressure, relative movement of aorta with respect to mediastinal structures, direct impact to bony structures have been proposed as contributing factors to TAI/TAR. At the tissue level, TAI is assumed to be the result of a complex state of supra-physiological, high rate, and multi-axial loading. A major step to gain insight into the mechanisms of TAI is a characterization of the aortic tissue mechanical and failure properties under loading conditions that resemble traumatic events. While the mechanical behavior of arteries in physiological conditions have been investigated by many researchers, this dissertation was motivated by the scarcity of reported data on supra-physiological and high rate loading conditions of aorta. Material properties of the porcine aortic tissue were characterized and a Fung-type constitutive model was developed based on ex-vivo inflation-extension of aortic segments with intraluminal pressures covering a range from physiological to supra-physiological (70 kPa). The convexity of the material constitutive model was preserved to ensure numerical stability. The increase in ë_è from physiological pressure (13 kPa) to 70 kPa was 13% at the outer wall and 22% at the inner wall while in this pressure range, the longitudinal stretch ratio ë_z increased 20%. A significant nonlinearity in the material behavior was observed as in the same pressure range, the circumferential and longitudinal Cauchy stresses at the inner wall were increased 16 and 18 times respectively. The effect of strain-rate on the mechanical behavior and failure properties of the tissue was characterized using uniaxial extension experiments in circumferential and longitudinal directions at nominal strain rates of 0.3, 3, 30 and 400 s-1. Two distinct states of failure initiation (FI) and ultimate tensile strength (UTS) were identified at both directions. Explicit direct relationships were derived between FI and UTS stresses and strain rate. On the other hand, FI and UTS strains were rate independent and therefore strain was proposed as the main mechanism of failure. On average, engineering strain at FI was 0.85±0.03 for circumferential direction and 0.58±0.02 for longitudinal direction. The engineering strain at UTS was not different between the two directions and reached 0.89±0.03 on average. Tissue pre-failure linear moduli showed an average of 60% increase over the range of strain rates. Using the developed material model, mechanical stability of aorta was studied by varying the loading parameters for two boundary conditions, namely pinned-pinned boundary condition (PPBC) and clamped-clamped boundary condition (CCBC). The critical pressure for CCBC was three times higher than PPBC. It was shown that the relatively free segment of aorta at the isthmus region may become unstable before reaching the peak intraluminal pressures that occur during a trauma. The mechanical instability mechanism was proposed as a contributing factor to TAI, where elevations in tissue stresses and strains due to buckling may increase the risk of injury. / Mechanical Engineering

The uterosacral ligament (USL) and cardinal ligament (CL) are the two major suspensory tissues of the uterus, cervix, and vagina. These supportive structures can be weakened or damaged, leading to the development of pelvic floor disorders (PFDs) such as urinary incontinence, fecal incontinence, and pelvic organ prolapse. In the surgical treatment for PFDs, the USL and CL are extensively used as anchor structures to restore the normal position of the prolapsed organs. Therefore, the mechanical properties of the USL and CL may be critical for the development of new surgical reconstruction strategies for PFDs. In chapter 1, we present the first histo-mechanical characterization of the swine USL and CL using histological analysis, scanning electron microscopy and quasi-static uniaxial tensile tests. Our results suggest that the histological and uniaxial tensile properties of the swine CL and USL are very similar to those in humans. The swine is found to be a suitable animal model for studying the mechanical properties of these ligaments. To capture both the active and passive mechanical responses of biological tissues containing SMCs such as the USL and CL, a new structural constitutive model is proposed in chapter 2. The deformation of the active component in such tissues during isometric and isotonic contractions is described using an evolution law. This model is tested with published active and passive, uniaxial and biaxial, experimental data on pig arteries due to lack of data on the active properties of the USL and CL. Subjected to constant forces in-vivo, the structure and length of the USL and CL are sig- nificantly altered over time. In chapter 3, we present the first rigorous characterization of the fiber microstructure and creep properties of the USL/CL complex by using scanning electron microscopy and planar biaxial testing. Fibers are found to be oriented primarily along the main in-vivo loading direction. In such direction, the creep proceeds significantly faster under lower load. Overall, our experimental findings advance our knowledge about the passive elastic and viscoelastic properties of the USL/CL complex. The novel structural constitutive model proposed enhances our understanding of the active mechanical behavior of biological tissues containing SMCs. Knowledge about the mechanical behavior of the USL and CL from experimental and theoretical studies such as those presented here will help to improve, in the long term, the medical treatment for PFDs. / Ph. D.

Deep soil mixing to construct stiff columns is one of the methods used today to improve performance of loose ground and remediate liquefaction problems. This research adopts a numerical approach to study seismic performance of soil-cement columnar reinforcements in loose sandy profiles. Different constitutive models were investigated in order to find a model that can properly predict soil behavior during seismic excitations. These models included NorSand, Dafalias-Manzari, Plasticity Model for Sands (PM4Sand) and Pressure-Dependent-Multi-Yield-02 (PDMY02) model. They were employed to predict behavior of soils with different relative densities and under different confining pressures during monotonic and cyclic loading. PDMY02 was identified as the most suitable model to represent soil seismic behavior for the system studied herein. The numerical aspects of the finite element approach were investigated to minimize the unintended numerical miscalculations. The focus was put on convergence tolerance, solver time-step, constraint definition, and, integration, material and Rayleigh damping. This resulted in forming a robust numerical configuration for 3-D nonlinear models that were later used for studying behavior of the reinforced grounds. Nonlinear finite element models were developed to capture the seismic response of columnar reinforced ground during dynamic centrifuge testing. The models were calibrated with results from tests with unreinforced profiles. Thereafter, they were implemented to predict the response of two reinforced profiles during seismic excitations with different intensities and liquefaction triggering. Model predictions were compared with recordings and the possible effects from the reinforcements were discussed. Finally, parametric studies were performed to further evaluate the efficiency of the reinforcements with different extension depths and area replacement ratios. The results collectively showed that the stiff elements, if constructed appropriately, can withstand seismic excitations with different intensities, and provide a firm base for overlying structures. However, the presence of the stiff elements within the loose ground resulted in stronger seismic intensities on the soil surface. The columns were not able to considerably reduce pore water pressure generation, nor prevent liquefaction triggering. The reinforced profiles, comparing to the free-field profiles, had larger settlements on the soil surface but smaller settlements on the columns. The results concluded that utilization of the columnar reinforcements requires great attention as these reinforcements may result in larger seismic intensities at the ground surface, while not considerably reducing the ground deformations. / Ph. D.