Magnetic shape memory alloys are active materials which deform under the application of a magnetic field or an external stress. Due to their internal friction, recognizable from the strain-stress hysteresis, this new material technology allows the design of multistable actuators. This paper describes and characterizes an innovative airflow control valve whose aperture is proportional to the deformation of the active material and thus controllable by the input voltage. The multistability of the material is partially exploited within an airflow control loop to reduce the energy losses of the valve when a specific airflow value must be hold.

This thesis is concerned with two problems in the Calculus of Variations touching on two central aspects of Materials Science: the structure of solid matter and its dynamic behavior. The problem pertaining to the first aspect is the analysis of the rigidity properties of possibly branched microstructures formed by shape memory alloys undergoing cubic-to-tetragonal transformations. On the basis of a variational model in the framework of linearized elasticity, we derive a non-convex and non-discrete valued differential inclusion describing the local volume fractions of such structures. Our main result shows the inclusion to be rigid without additional regularity assumptions and provides a list of all possible solutions. We give constructions ensuring that the various types of solutions indeed arise from the variational model and quantitatively describe their rigidity via H-measures. Our contribution to the second aspect is a conditional result on the convergence of the Allen-Cahn Equations to multi-phase mean curvature flow, which is a popular model for grain growth in polychrystalline metals. The proof relies on the gradient flow structure of both models and borrows ideas from certain convergence proofs for minimizing movement schemes.:1 Introduction 1.1 Shape memory alloys 1.2 Multi-phase mean curvature flow 2 Branching microstructures in shape memory alloys: Rigidity due to macroscopic compatibility 2.1 The main rigidity theorem 2.2 Outline of the proof 2.3 Proofs 3 Branching microstructures in shape memory alloys: Constructions 3.1 Outline and setup 3.2 Branching in two linearly independent directions 3.3 Combining all mechanisms for varying the volume fractions 4 Branching microstructures in shape memory alloys: Quantitative aspects via H-measures 4.1 Preliminary considerations 4.2 Structure of the H-measures 4.3 The transport property and accuracy of the approximation 4.4 Applications of the transport property 5 Convergence of the Allen-Cahn Equation to multi-phase mean curvature flow 5.1 Main results 5.2 Compactness 5.3 Convergence 5.4 Forces and volume constraints

Magnetic shape memory (MSM) materials are a new class of smart materials which exhibit shape deformation under the influence of an external magnetic field. They are interesting for various types of applications, including actuators, displacement/force sensors, and motion dampers. Due to the huge strain and the magnetic field-driven nature, MSM materials show definite advantages over other smart materials, e.g. conventional thermal shape memory materials, in terms of displacement and speed. The principle behind the magnetic field induced strain (MFIS) is the strong coupling between magnetization and lattice structure. The investigation of both static and dynamic magnetic domain structures in MSM materials is a key step in optimizing the properties for future possible devices. In this work, optical polarization microscopy is applied to investigate the twin boundary and magnetic domain wall motion in bulk NiMnGa single crystals. Surface magnetic domain patterns on adjacent sides of bulk crystals are revealed for the first time providing comprehensive information about the domain arrangement inside the bulk and at the twin boundary. The tilting of the easy axis with respect to the sample surface determines the preferable domain size and leads to spike domain formation on the surface. Out-of-plane surface domains extend into the bulk within a single variant, while a twin boundary mirrors the domain pattern from adjacent variants. Furthermore, magnetic domain evolution during twin boundary motion is observed. The partial absence of domain wall motion throughout the process contradicts currently proposed models. The magnetic state alternates along a moving twin boundary. With the abrupt nucleation of the second variant this leads to the formation of sections of magnetically highly charged head-on domain structures at the twin boundaries. On the other hand, a dynamic actuation experimental setup, which is capable to provide high magnetic fields in a wide range of frequency, was developed in the course of this study. The observation of reversible twin boundary motion up to 600 Hz exhibits the dependence of strain, hysteresis, and twin boundary velocity on the actuation speed. MFIS increases with frequency, while the onset field is similar in all observed cases. Twin boundary mobility enhancement by fast twin boundary motion is proposed to explain the increase in MFIS. The twin boundary velocity is shown to be inversely proportional to the twin boundary density. No limit of twin boundary velocity is observed in the investigated frequency range.

Im Legierungssytem Ni-Mn-Ga tritt bei Zusammensetzungen nahe der stöchiometrischen Zusammensetzung Ni2MnGa der magnetische Formgedächtniseffekt auf. Darunter versteht man die Dehnung durch Bewegung von Zwillingsgrenzen im Magnetfeld. Einkristalle aus Ni-Mn-Ga mit einer tetragonalen 5M-Martensitstruktur zeigen magnetisch erzeugbare Dehnungen von bis zu 6 %. Diese großen Dehnungen verbunden mit der schnellen Schaltfrequenz von Magnetfeldern machen den Effekt interessant für technische Anwendungen z. B. als Aktoren. Derartige Einkristalle sind schwierig und teuer herzustellen, weshalb für technische Anwendung Polykristalle von Interesse sind. Diese lassen sich im Allgemeinen leichter und preiswerter herstellen. Um den magnetischen Formgedächtniseffekt in Polykristalle einzustellen, werden grobkörnige, texturierte Proben mittels des Verfahrens der gerichteten Erstarrung hergestellt. Die Gefügeuntersuchungen erfolgen mit metallographischen Schliffen und die Kornorientierungen werden mit der EBSD-Technik bestimmt. Um das Gefüge zu vergröbern, werden Glühungen nach einer aufgebrachten Warmverformung untersucht. Zur Verringerung der für die Bewegung der Zwillingsgrenzen notwendigen Spannung (Zwillingsspannung) werden die Proben im Druckversuch mechanisch trainiert. Dabei kann die Zwillingsspannung teilweise unter die magnetisch erzeugbare Spannung auf die Zwillingsgrenzen (Magnetospannung) abgesenkt werden. Eine weitere Absenkung der Zwillingsspannung wird durch eine plattenförmige Probengeometrie mit Dicken im Bereich der Korndurchmesser erreicht. An derartigen Proben wird magnetisch rückstellbare freie Dehnung durch Zwillingsgrenzenbewegung erzielt.

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Shape memory alloys when deformed can produce strains as high as 8%. Heating results in a phase transformation and associated recovery of all the accumulated strain, a phenomenon known as shape memory. This strain recovery can occur against large forces, resulting in their use as actuators. The goal of this project is to lower the operating temperature range of shape memory alloys in order for them to be used in cryogenic switches, seals, valves, fluid-line repair and self-healing gaskets for space related technologies. The Ni-Ti-Fe alloy system, previously used in Grumman F-14 aircrafts and activated at 120 K, is further developed through arc-melting a range of compositions and subsequent thermo-mechanical processing. A controlled atmosphere arc-melting facility and vertical vacuum quench furnace facility was commissioned to fabricate these alloys. The facility can create a vacuum of 10-7 Torr and heat treat samples up to 977 °C. High purity powders of Ni, Ti and Fe in varying ratios were mixed and arc-melted into small buttons weighing 0.010 kg to 0.025 kg. The alloys were subjected to solutionizing and aging treatments. A combination of rolling, electro-discharge machining and low-speed cutting techniques were used to produce strips. Successful rolling experiments highlighted the workability of these alloys. The shape memory effect was successfully demonstrated at liquid nitrogen temperatures through a constrained recovery experiment that generated stresses of over 40 MPa. Differential scanning calorimetry (DSC) and a dilatometry setup was used to characterize the fabricated materials and determine relationships between composition, thermo-mechanical processing parameters and transformation temperatures.

In the field of control systems, testbeds are a pivotal step in the validation and improvement of new algorithms for different applications. They provide a safe, controlled environment typically having a significantly lower cost of failure than the final application. Vision systems provide nonintrusive methods of measurement that can be easily implemented for various setups and applications. This work presents methods for modeling, removing distortion, calibrating, and rectifying single and two camera systems, as well as, two very different applications of vision-based control system testbeds: deflection control of shape memory polymers and trajectory planning for mobile robots. First, a testbed for the modeling and control of shape memory polymers (SMP) is designed. Red-green-blue (RGB) thresholding is used to assist in the webcam-based, 3D reconstruction of points of interest. A PID based controller is designed and shown to work with SMP samples, while state space models were identified from step input responses. Models were used to develop a linear quadratic regulator that is shown to work in simulation. Also, a simple to use graphical interface is designed for fast and simple testing of a series of samples. Second a robot testbed is designed to test new trajectory planning algorithms. A templatebased predictive search algorithm is investigated to process the images obtained through a lowcost webcam vision system, which is used to monitor the testbed environment. Also a userfriendly graphical interface is developed such that the functionalities of the webcam, robots, and optimizations are automated. The testbeds are used to demonstrate a wavefront-enhanced, Bspline augmented virtual motion camouflage algorithm for single or multiple robots to navigate through an obstacle dense and changing environment, while considering inter-vehicle conflicts, iv obstacle avoidance, nonlinear dynamics, and different constraints. In addition, it is expected that this testbed can be used to test different vehicle motion planning and control algorithms.

Smart materials are intelligent materials that change their structural, chemical, mechanical, or thermal properties in response to an external stimulus such as heat, light, and magnetic and electric fields. With the increase in usage of smart materials in many sensitive applications, the need for a remote, wireless, efficient, and biologically safe stimulus has become crucial. This dissertation addresses this requirement by using high intensity focused ultrasound (HIFU) as the external trigger. HIFU has a unique capability of maintaining both spatial and temporal control and propagating over long distances with reduced losses, to achieve the desired response of the smart material. Two categories of smart materials are investigated in this research; shape memory polymers (SMPs) and piezoelectric materials. SMPs have the ability to store a temporary shape and returning to their permanent or original shape when subjected to an external trigger. On the other hand, piezoelectric materials have the ability to convert mechanical energy to electrical energy and vice versa. Due to these extraordinary properties, these materials are being used in several industries including biomedical, robotic, noise-control, and aerospace. This work introduces two novel concepts: First, HIFU actuation of SMP-based drug delivery capsules as an alternative way of achieving controlled drug delivery. This concept exploits the pre-determined shape changing capabilities of SMPs under localized HIFU exposure to achieve the desired drug delivery rate. Second, solving the existing challenge of low efficiency by focusing the acoustic energy on piezoelectric receivers to transfer power wirelessly. The fundamental physics underlying these two concepts is explored by developing comprehensive mathematical models that provide an in-depth analysis of individual parameters affecting the HIFU-smart material systems, for the first time in literature. Many physical factors such as acoustic, material and dynamical nonlinearities, acoustic standing waves, and mechanical behavior of materials are explored to increase the developed models' accuracy. These mathematical frameworks are designed with the aim of serving as a basic groundwork for building more complex smart material-based systems under HIFU exposure. / Doctor of Philosophy / Smart materials are a type of intelligent materials that have the ability to respond to external stimuli such as heat, light, and magnetic fields. When these materials respond, they can change their structural, thermodynamical, mechanical or chemical nature. Due to this extraordinary property, smart materials are being used in many applications including biomedical, robotic, space, microelectronics, and automobile industry. However, due to increased sensitivity and need for safety in many applications, a biologically safe, wireless, and efficient trigger is required to actuate these materials. In this dissertation, sound is used as an external trigger to actuate two types of smart materials: shape memory polymers (SMPs) and piezoelectric materials. SMPs have an ability to store a temporary (arbitrarily deformed) shape and return to their permanent shape when exposed to a trigger. In this dissertation, focused sound induced thermal energy acts as a trigger for these polymers. A novel concept of focused ultrasound actuation of SMP-based drug delivery capsules is proposed as a means to solve some of the challenges being faced in the field of controlled drug delivery. Piezoelectric materials have an ability to generate electric power when an external mechanical force is applied and vice versa. In this study, sound pressure waves supply the external force required to produce electric current in piezoelectric disks, as a method for achieving power transfer wirelessly. This study aims to solve the current problem of low efficiency in acoustic power transfer systems by focusing sound waves. This dissertation addresses the fundamental physics of high intensity focused ultrasound actuation of smart materials by developing comprehensive mathematical models and systematic experimental investigations, that have not been performed till now. The developed models enable an in-depth analysis of individual parameters including nonlinear material behavior, acoustic nonlinearity and resonance phenomena that affect the functioning of these smart systems. These mathematical frameworks also serve as groundwork for developing more complex systems.