Among many kinds of function materials, shape memory alloy is considered as one of the most attractive members. Its existing and potential applications can be widely found in industries such as aerospace, medical, sports and many others. However, high cost is one main limitation of their applications. Even though shape memory alloys have attractive features like shape recovery and hysteresis, they are still not economically efficient enough as structural material, when comparing with conventional materials such as iron, steel and aluminum. As the result, applications of SMAs are mostly in the form of actuators and sensors, and in the fields of aerospace industry and medical industry. Due to the scale and functionality requirements, these fields of application demand deeper understanding of material properties of SMAs. Simulation tools with better accuracy and functionality are required in designing process and production.

Since the establishment of first SMA model in 1980s, computational models about this magic alloy are getting more and more advanced in past years. However, so far SMA computational models are still relatively simple. Essential simulation functions are still not supported in conventional models. Often used functions such as cyclic effect, plasticity and fatigue are still not included. New experimental results have shown more detailed information of shape memory alloys. But those behaviors are rarely considered into conventional models. Considering relatively simple models of SMAs and limited support from commercial FEM software, consistent improvements of SMA numerical model are essentially required.

To meet those needs, this thesis proposes several improvements on legacy SMA models. As most applications of SMA are in the shape of wire or film, numerical studies using improved models are focused on SMA plane frames applications. Those studies cover applications in simple beams, braced frames, as well as complex honeycomb structures, which are low weight, functional structures that have a great potential in smart structure, actuators and sensors. Material level and structural level validation, as well as new discoveries from numerical studies will be discussed in detail.

In this thesis, chapter one is the overall introduction. Brief review about shape memory alloys contributes the first part of this chapter. Martensite phase and austenite phase of SMA, and two variants of martensite phase, the detwinned martensite phase and twinned martensite phase were introduced in this part. Its special features such as shape memory effect, superelasticity, as well as high actuation frequency and energy density were discussed with internal phase transformations. Following its major application examples in aerospace and medical industry, SMA computational models were reviewed. Advantages and disadvantages of each model were discussed. Functionality of each major SMA model was listed and compared with improved model in this thesis. Besides SMA model, SMA honeycomb structure was briefly discussed. Its potential application as smart structure is the major reason of its extensive studies in the following chapters. Finally, purpose of research was discussed. Consistent improvement of SMA model in both accuracy and functionality is always the mission of researcher in this field.

Computational modeling is the topic of chapter two. After a brief review of conventional SMA model by Brinson (1993) and Toi et al. (2004), which is basis of this research, detailed explanation of each improvement could be found in this chapter. Based on the stress strain relationship, kinetics of phase transformation and compressive-tensile asymmetry in conventional SMA model, a new kinetics of phase transformation using logistic sigmoid model was introduced at first. The physical basis, as well as its short demonstration was included. Cyclic effect model dependent on accumulated strain was introduced. Comparison with other two cyclic effect models, its physical meaning and influence factor picking differentiate this model from others. Based on experimental results, model considering twinned martensite phase was introduced. Kinetic of phase transformation from twinned martensite to detwinned martensite as well as its logistic sigmoid function improvement were presented. Embedded plasticity model into superelasticity and quasiplasticity is another major contribution to SMA model improvement. Based on experimental data, different yielding condition for martensite phase and austenite phase was considered. A linear mix rule of yielding was established for martensite-austenite-mixed phase. For shape memory effect, a more stable phase transformation condition was introduced. Finally, FEM models used in this thesis were introduced. Major models are Euler-Bernoulli cubic beam element, finite deformation model and beam layered approach.

Chapter three is about validations of logistic sigmoid function model for phase transformation. Logistic sigmoid function model is a major improvement after introduction of phenomenological models. It combines the widely used framework of Brinson's model and the flexibility of logistic sigmoid type of phase transformation mechanism. Instead of cosine function phase transformation mechanism in the existing model, the new model presented a much better fitting of stress strain relationship about shape memory alloys. The usability of new model was proved in one dimensional testing as material level validation. Structural level validation of this model was performed in an SMA beam four-point bending simulation. Better fittings with experimental data were obtained compared with results from other models.

Chapter four includes material level validation and application of newly developed cyclic effect model. Qualitative validation was performed by comparing with one dimensional cyclic loading experiment. Three major cyclic effects were well reproduced: (1) residual strain increases as cyclic loading continues; (2) critical phase transformation starting and finishing stresses decrease as cyclic loading continues; (3) material parameters' changes convergence as cyclic loading continues. The model was later applied in simulation related to energy absorbing of an SMA-braced frame. Weaker damping capacity of SMA brace was found when considering cyclic effect.

The significantly different properties between normal type honeycomb structure and low shear stiffness honeycomb structure have determined their potential applications. Low shear stiffness honeycomb structure using shape memory alloy shows its potential in applications such as actuator, sensor and adaptive structure. Under proper control, functions including actuating, shape controlling could be achieved. External stimulus includes temperature change could induce phase transformation inside honeycomb structure. Macroscopic deformation due to phase transformation is the reason for its actuating and shape controlling. Besides, deformation induced phase transformation inside SMA honeycomb structure could lead to latent heat or electrical resistance change. By taking advantage of this feature, sensoring function of SMA honeycomb structure could also be achieved.

Considering attractive potentials of SMA honeycomb structures in functional structures, their thermomechanical behaviors were extensively studied in following three chapters. Chapter five implemented accuracy improved model into in-plane tensile behavior of SMA honeycomb structures. This model takes consideration of different material properties between twinned martensite phase and detwinned martensite phase. Two kinds of honeycomb structures were examined in simulations: OX type honeycomb structure, which has a positive Poisson's ratio and auxetic type honeycomb structure, which has a negative Poisson's ratio. Simple tension behaviors of these two types of honeycomb structures were compared with experimental result by Hassan et al. (2009). Qualitative agreement was proved. Full cycle tension loading simulation was performed afterward. Localized deformation due to bifurcation of OX type honeycomb structure was discovered, which demonstrates less stability of OX type honeycomb structure than auxetic type. This phenomenon was due to stress concentration in particular regions. High stress level induced phase transformation, which largely weakened stiffness. Similar localized deformation was not observed for the same structure under smaller tensile loading, or the same structure made of elastic material. Critical stress to induce bifurcation for this specific OX type honeycomb structure was also calculated.

Further studies related to in-plane behavior of SMA honeycombs could be found in chapter six. Newly developed plasticity model was applied in simulations of this chapter. This new model embedded plasticity model into superelasticity and shape memory effect. Different yielding conditions for austenite phase and martensite phase, as well as mixed phase were taken into consideration. Qualitative agreement was proved by comparing with simulation data from Michailidis et al. (2009). Then this model was applied in full cycle loading, coupling of plasticity and superelasticity induced permanent deformation in simulation. On the other hand, imperfection of honeycomb structures was another topic in this chapter. Simulations show no obvious instability of imperfect honeycomb structures than perfect ones. However, lower stiffness was observed.

Low shear stiffness type SMA honeycombs is considered as ideal candidate for smart structures. After extensive fundamental studies of this type in chapter five and chapter six, application about this type of structures as actuator is simulated in chapter seven. As one of the latest proposed smart structure, honeycomb core actuator by Okabe [Sugiyama (2009), Okabe et al. (2011)] was extensively studied. It is a temperature induced actuator. Its actuation process includes a forced shear deformation process and a heating process. Reasonable fitting with experimental results could be found in two aspects. Similar cell shape deformation between simulation and experiment could be proved as a qualitative validation. The quantitative validation could be found in comparison of actuating range, as well as its dependence to temperature. Besides, more detailed information was provided by simulation program such as stress, martensite phase distribution inside actuator. This could be considered as pioneering computational tool for advanced design of SMA honeycomb core actuators.

As more and more applications related to shape memory alloys come out every day, lacking of widely accepted numerical model becomes an urgent topic for researchers in this field. This thesis provided several major improvements on the conventional phenomenological model, aiming for a highly reliable model for shape memory alloy simulation. Models in this thesis are more accurate, more flexible and more adaptive for industrial needs. Experiments have validated its reliability in several aspects. With the validations and application examples, we have enough confidence to apply this model in broader fields. More applications using this model are expected in the future.

最も魅力的な機能材料の一種である形状記憶合金(SMA)は、航空宇宙、医療などの産業分野で応用され、多くの新たな可能性を秘めている。これらの応用を進めるためには、SMAの材料特性に対する深い理解が必要であり、開発設計のためには、より高い精度と機能を有する計算ツールが求められている。1980年代以降、SMAの計算モデルは発展し続けてきたが、実験的に観察される複雑な挙動を表現するためには未だ単純であり、精密化が必要である。

このような要求に答えるため、本論文では既存のSMAモデルに様々な改良を加えている。応用されるSMAの大部分はワイヤあるいはフィルム形状であるため、改良された計算モデルによる数値解析はSMA平面骨組への応用を念頭に置く。すなわち、単純はり、ブレース付き骨組、さらにはより複雑なハニカム構造を対象とする。ハニカム構造は、スマート構造、アクチュエータなどへの応用において大きな可能性を有する軽量・高機能構造である。材料レベル、構造レベルの検証、および数値解析による新しい知見について詳細に論じている。

本論文の1章は序論である。まず、SMAの物理的性質を説明している。航空宇宙、医療分野における応用例の紹介に続いて、SMAの計算モデルのレビューを行う。ハニカム構造についても簡単に論ずる。最後に研究目的を述べている。

2章では、SMAの計算モデルについて述べている。本研究のベースとなるBrinsonおよびToiらによるSMAモデルについて概説した後、改良点のそれぞれについて、検証も含め詳細に説明する。まず、相変態発展方程式に対するロジスティックシグモイド関数モデル、累積ひずみに依存する繰返し効果を導入する。続いて、双晶マルテンサイト相を考慮したモデリング、塑性を考慮した超弾性あるいは準塑性モデリング、形状記憶効果におけるより安定的な相変態アルゴリズムを導入した。最後に、層分割型Bernoulli-Euler3次はり要素を用いた有限変形FEM増分解析の定式化を示している。

3章では、相変態に対するロジスティックシグモイド関数モデルの数値的検証を行っている。広く使われているBrinsonモデルの枠組とロジスティックシグモイド型の相変態メカニズムを組み合わせる。既存モデルにおけるコサイン型の表現と比較して、新モデルはSMAの応力・ひずみ曲線の材料試験結果と非常に良好に対応することを確認した。また、SMAはりの4点曲げ解析結果を実験結果と対比することにより、構造レベルにおける妥当性も検証している。

4章では、新しい繰返し効果モデルの材料レベルの検証と構造解析への応用を行っている。まず、繰返し材料試験結果と比較して、妥当性を検証した。主な特徴は次の3点である。繰返しとともに、(1)最大残留ひずみが増加する。(2)変態開始および終了限界応力が低減する。(3)材料パラメータの変動が収束する。続いてこのモデルをSMAブレース付き骨組のエネルギー吸収に関するシミュレーションに適用し、繰返し効果を考慮するとSMAブレースのエネルギー吸収能が低下することを見出した。

標準ハニカム構造と低せん断剛性ハニカム構造は著しく異なった特性を有しており、後者はSMAを用いることにより、アクチュエータ、センサ、アダプティブ構造としての応用可能性が広がる。続く3つの章では、機能構造としてのSMAハニカム構造の力学挙動について論じている。

5章では、双晶および非双晶マルテンサイト相に異なる材料特性を仮定したモデルを、SMAハニカム構造の面内引張挙動の解析に適用している。正のポアソン比を示すOXハニカムと負のポアソン比を示すAuxeticハニカムの単純引張挙動を解析し、Hassanらの実験結果と定性的に対応することを確認した。除荷を含むフルサイクル解析からは、OXハニカムにおいて分岐挙動に起因する変形の局所化が起こることを見出した。荷重レベルが低い場合は起こらない。

6章では、OXハニカムとAuxeticハニカムの面内圧縮挙動を解析している。OXハニカムに対するMichailidisらの実験結果との比較により定性的妥当性を確認した。続いて行った塑性と超弾性の連成を考慮した解析では、永久変形が観察された。他方、10%程度の形状初期不整を仮定した解析では、剛性低下は見られたものの、顕著な不安定性は観察されなかった。

7章では、Okabeらにより提案された低せん断剛性型のSMAハニカムを利用したアクチュエータに対し、形状記憶効果におけるより安定的な相変態アルゴリズムを援用したシミュレーションを行っている。アクチュエーションは強制的なせん断変形と引き続く加熱過程より成る。各ハニカムセルの変形形状、作動変位の温度変化が実験結果と良好に対応した。また、応力分布、マルテンサイト相体積率分布などの詳細を把握することができ、SMAハニカムコアアクチュエータに対する先駆的な計算ツールとしての有用性を検証している。

8章は結論である。本論文は、今後ますます広範な応用が期待されるSMAに対する既存の現象論的モデルに対し、より信頼度の高いシミュレーションを可能とするために、様々な観点からの改良を加えており、より精確、柔軟かつ順応的な計算モデルを提供している。実験との対比などによるモデルの検証とともに、SMAハニカム構造などに対する多彩な数値例により、いくつかの物理的知見も得ており、本提案モデルの工学的有用性を立証している。

よって本論文は博士(工学)の学位請求論文として合格と認められる。