Architected material analogs for shape memory alloys

Abstract

•Architected material analogs of thermally activated shape memory alloys•ASMAs exhibit superelastic behavior and shape memory effect•ASMAs undergo stress- and temperature-induced phase transformations•We provide a systematic design methodology and demonstrate key behaviors for ASMAs Shape memory alloys (SMAs) are versatile materials that find applications in areas as diverse as non-explosive release bolts for spacecraft, endodontic files, and structural dampers for bridges. However, the widespread use of these materials is limited by their high cost, which is driven by the need for high-purity raw materials and extensive thermo-mechanical processing. We introduce architected material analogs of SMAs (ASMAs), which are periodic cellular materials that exhibit both of the salient behaviors, superelasticity and shape memory, of SMAs. They can be made from a wide variety of polymers, made by many different low-cost production processes as well as 3D printing, and are designed to respond to various stimuli such as heat, magnetic fields, and solvent absorption. ASMAs offer a lower-cost alternative that can expand the design space for SMA-like material behavior to include larger-scale (e.g., self-compacting dunnage) or lower-cost applications (e.g., medical implants). We propose a design for a building block of a periodic cellular material that mimics the salient behaviors, superelasticity and shape memory, exhibited by shape memory alloys (SMAs). The block comprises a sinusoidal beam that is anchored in supports made of a material whose storage modulus decreases at a faster rate with increasing temperature than that of the beam. At low temperatures, the storage moduli of the two constituent materials have comparable magnitudes and the block exhibits two stable configurations. The block can transition elastically from one stable configuration to the other via a snap-through in response to an external load. Above a critical temperature, the storage modulus of the supports is sufficiently low such that the second stable configuration becomes unstable, and the block returns to its first stable configuration without any external load. These responses of the block result in SMA-like material behavior in an ensemble of such blocks. We propose a design for a building block of a periodic cellular material that mimics the salient behaviors, superelasticity and shape memory, exhibited by shape memory alloys (SMAs). The block comprises a sinusoidal beam that is anchored in supports made of a material whose storage modulus decreases at a faster rate with increasing temperature than that of the beam. At low temperatures, the storage moduli of the two constituent materials have comparable magnitudes and the block exhibits two stable configurations. The block can transition elastically from one stable configuration to the other via a snap-through in response to an external load. Above a critical temperature, the storage modulus of the supports is sufficiently low such that the second stable configuration becomes unstable, and the block returns to its first stable configuration without any external load. These responses of the block result in SMA-like material behavior in an ensemble of such blocks. Architected materials derive their constitutive response largely from the topology of their building blocks and the distribution of material within these blocks rather than the chemical composition of their constituent materials.1Zheludev N.I. The road ahead for metamaterials.Science. 2010; 328: 582-583Google Scholar,2Fleck N.A. Deshpande V.S. Ashby M.F. Micro-architectured materials: past, present and future.Proc. R. Soc. A. Math. Phys. Eng. Sci. 2010; 466: 2495-2516Google Scholar Therefore, we can design architected materials that exhibit properties that are not found in naturally occurring bulk materials. Examples of such materials and the exciting applications that they have enabled include negative-refractive-index material for flat loss-less lenses,3Venema L. A lens less ordinary.Nature. 2002; 420: 119-120Google Scholar room-temperature terahertz modulators for ultra-fast wireless communications,4Chen H.T. Padilla W.J. Zide J.M.O. Gossard A.C. Taylor A.J. Averitt R.D. Active terahertz metamaterial devices.Nature. 2006; 444: 597-600Google Scholar and acoustic negative refraction materials for high-resolution medical imaging.5Lu M.H. Feng L. Chen Y.F. Phononic crystals and acoustic metamaterials.Mater. Today. 2009; 12: 34-42Google Scholar Given the wide array of constitutive responses that have been realized by architected materials, it is natural to wonder if we can design architected material analogs for naturally occurring materials. Potential benefits might include a reduction in cost, improvement in performance, and the ability to substitute a readily available material for one that is more difficult to source. In this work, we report the development of an architected material analog for thermally activated shape memory alloys (SMAs). SMAs are a class of metallic alloys that exhibit two interesting behaviors: shape memory effect (SME) and superelasticity (SE).6Wayman C.M. Otsuka K. Shape Memory Alloys. Cambridge University Press, 1998Google Scholar SE behavior is associated with undergoing large, seemingly plastic strains that can be completely recovered upon unloading (see path shown in red curves in Figure 1F). The SE behavior in SMAs has been exploited for applications such as strong-yet-flexible endodontic instruments for root canal treatment7Yoneyama T. Kobayashi C. Endodontic instruments for root canal treatment using Ti–Ni shape memory alloys.in: Yoneyama T. Shuichi M. Shape Memory Alloys for Biomedical Applications. Woodhead Publishing Limited, Cambridge, UK2009: 297-305Google Scholar and damage-tolerant eyeglass frames.8Zider R.B. Krumme J.F. Eyeglass frame including shape memory elements. US patent 4772112A.1988Google Scholar The SE behavior also gives rise to large hysteretic losses during cyclic loading, which results in solid-state energy dissipation. This dissipative behavior has been used to create structural elements with high internal dissipation for stabilizing sensitive structures like bridges9Wilde K. Gardoni P. Fujino Y. Base isolation system with shape memory alloy device for elevated highway bridges.Eng. Struct. 2000; 22: 222-229Google Scholar and buildings.10Song G. Ma N. Li H.N. Applications of shape memory alloys in civil structures.Eng. Struct. 2006; 28: 1266-1274Google Scholar In thermally activated SMAs, SME behavior is associated with an ability to retain a deformed temporary shape for extended periods of time and subsequently recover the original undeformed shape in response to a suitable thermal stimulus (see path shown in blue curves in Figure 1F). The SME has been used to create deployable structures such as implantable blood clot filters that can be folded into a compact configuration for delivery through a catheter, and subsequently be unfurled at the proper location in the body just by letting it reach the body temperature.11Duerig T. Pelton A. Stöckel D. An overview of nitinol medical of applications.Mater. Sci. Eng. A. 1999; 273–275: 149-160Google Scholar SME behavior also enables SMAs to do work against an external load. The ability to do external work has led to applications such as a non-explosive release device for safer spacecraft deployment12Johnson A.D. No-explosive separation device, US patent 5119555.1992Google Scholar and highly dexterous endoscopes for in-vivo exploration.13Ikuta, K., Tsukamoto, M., and Hirose, S. (1988). Shape Memory Alloy Servo Actuator System with Electric Resistance Feedback and Application for Active Endoscope. In 1988 IEEE International Conference on Robotics and Automation, pp. 427–430.Google Scholar Both SE and SME arise from solid-state, diffusionless phase transformations between the two dominant solid-state phases in the material. The phase transformations can be driven by stress, temperature, or a combination thereof. The complexity of the thermo-mechanical response exhibited by SMAs makes it challenging to mimic the behavior of SMAs. A literature survey shows that researchers have demonstrated architected materials that can mimic some aspects of SMA behavior. Architected materials whose building blocks comprise structural elements with very different coefficients of linear thermal expansion (CLTE) have been used to create materials with embedded thermal actuation by exploiting differential thermal expansion at the building block level.14Hopkins J.B. Lange K.J. Spadaccini C.M. Designing microstructural architectures with thermally actuated properties using freedom, actuation, and constraint topologies.J. Mech. Des. Trans. ASME. 2013; 135: 061004Google Scholar, 15Xu H. Farag A. Ma R. Pasini D. Thermally actuated hierarchical lattices with large linear and rotational expansion.J. Appl. Mech. 2019; 86: 1-12Google Scholar, 16Taniker S. Celli P. Pasini D. Hofmann D.C. Daraio C. Temperature-induced shape morphing of bi-metallic structures.Int. J. Sol. Struct. 2020; 190: 22-32Google Scholar The same idea has also led to architected materials that exhibit near-zero or negative CLTE.17Lakes R. Cellular solid structures with unbounded thermal expansion.J. Mater. Sci. Lett. 1996; 15: 475-477Google Scholar, 18Steeves C.A. dos Santos e Lucato S.L. He M. Antinucci E. Hutchinson J.W. Evans A.G. Concepts for structurally robust materials that combine low thermal expansion with high stiffness.J. Mech. Phys. Sol. 2007; 55: 1803-1822Google Scholar, 19Lehman J. Lakes R. Stiff lattices with zero thermal expansion.J. Intell. Mater. Syst. Struct. 2012; 23: 1263-1268Google Scholar, 20Wei K. Chen H. Pei Y. Fang D. Planar lattices with tailorable coefficient of thermal expansion and high stiffness based on dual-material triangle unit.J. Mech. Phys. Sol. 2016; 86: 173-191Google Scholar, 21Boatti E. Vasios N. Bertoldi K. Origami metamaterials for tunable thermal expansion.Adv. Mater. 2017; 29Google Scholar, 22Xu H. Farag A. Pasini D. Multilevel hierarchy in bi-material lattices with high specific stiffness and unbounded thermal expansion.Acta Mater. 2017; 134: 155-166Google Scholar Like Invar, which is an alloy of iron and nickel (64FeNi) that exhibits nearly zero CLTE, these architected analogs of Invar can be used in precision scientific instruments and other applications where dimensional stability of structural parts is needed to counteract large variations in the operating temperature. The large recoverable deformations and solid-state energy dissipation associated with SE behavior have been demonstrated in phase-transforming cellular materials (PXCMs). PXCMs are periodic cellular materials whose unit cells exhibit a snap-through instability.23Restrepo D. Mankame N.D. Zavattieri P.D. Phase transforming cellular materials.Extrem. Mech. Lett. 2015; 4: 52-60Google Scholar When an element of a building block in the material transforms under external load, some of the strain energy stored in the material is released as kinetic energy. This gives rise to oscillatory waves that dissipate the released energy, which eventually ends up as heat.24Findeisen C. Hohe J. Kadic M. Gumbsch P. Characteristics of mechanical metamaterials based on buckling elements.J. Mech. Phys. Sol. 2017; 102: 151-164Google Scholar If the building blocks in PXCMs are sized properly, the material can remain in the elastic regime during the loading and unloading steps. The quasi-static behavior of these materials in response to cyclic loads,23Restrepo D. Mankame N.D. Zavattieri P.D. Phase transforming cellular materials.Extrem. Mech. Lett. 2015; 4: 52-60Google Scholar, 24Findeisen C. Hohe J. Kadic M. Gumbsch P. Characteristics of mechanical metamaterials based on buckling elements.J. Mech. Phys. Sol. 2017; 102: 151-164Google Scholar, 25Correa D.M. Seepersad C.C. Haberman M.R. Mechanical design of negative stiffness honeycomb materials.Integr. Mater. Manuf. Innov. 2015; 4: 8Google Scholar high strain rate monotonic loads,26Shan S. Kang S.H. Raney J.R. Wang P. Fang L. Candido F. Lewis J.A. Bertoldi K. Multistable architected materials for trapping elastic strain energy.Adv. Mater. 2015; 27: 4296-4301Google Scholar and impact loads27Ha C.S. Lakes R.S. Plesha M.E. Design, fabrication and analysis of lattice exhibiting energy absorption via snap-through behavior.Mater. Des. 2018; 141: 426-437Google Scholar,28Debeau D.A. Seepersad C.C. Haberman M.R. Impact behavior of negative stiffness honeycomb materials.J. Mater. Res. 2018; 33: 290-299Google Scholar has been studied via analytical, computational, and experimental means in recent years. PXCMs can exhibit solid-state energy dissipation and undergo large elastically recoverable deformations like SE in SMAs, but, unlike SMAs, they cannot retain a temporary shape and recover a permanent one in response to an external stimulus. The architected materials referenced in the works referenced above can mimic either the ability of SMAs to do work against an external resistance or their SE behavior, but not both. Moreover, none of these materials exhibit SME behavior. In this work, we build on the previous research23Restrepo D. Mankame N.D. Zavattieri P.D. Phase transforming cellular materials.Extrem. Mech. Lett. 2015; 4: 52-60Google Scholar, 24Findeisen C. Hohe J. Kadic M. Gumbsch P. Characteristics of mechanical metamaterials based on buckling elements.J. Mech. Phys. Sol. 2017; 102: 151-164Google Scholar, 25Correa D.M. Seepersad C.C. Haberman M.R. Mechanical design of negative stiffness honeycomb materials.Integr. Mater. Manuf. Innov. 2015; 4: 8Google Scholar, 26Shan S. Kang S.H. Raney J.R. Wang P. Fang L. Candido F. Lewis J.A. Bertoldi K. Multistable architected materials for trapping elastic strain energy.Adv. Mater. 2015; 27: 4296-4301Google Scholar, 27Ha C.S. Lakes R.S. Plesha M.E. Design, fabrication and analysis of lattice exhibiting energy absorption via snap-through behavior.Mater. Des. 2018; 141: 426-437Google Scholar, 28Debeau D.A. Seepersad C.C. Haberman M.R. Impact behavior of negative stiffness honeycomb materials.J. Mater. Res. 2018; 33: 290-299Google Scholar to develop a periodic cellular material that can do work against an external resistance and mimic both salient behaviors (SE and SME) seen in SMAs. We use the term architected material analogs for SMAs (ASMAs) to refer to these materials. References to content provided as a part of supplemental information carry the prefix S. We refer readers to section S1.1 for a list of abbreviations and symbols used in this work. In this section, we describe how a basic PXCM design can be modified by the introduction of a second material into the building block to create an ASMA building block. A PXCM is a periodic cellular material whose building block comprises one or two sinusoidal beams that are clamped at each end (see Figure 1A). This block can have two stable configurations. The undeformed stable configuration will be referred to as C1 in this paper. When the beam is loaded at the center as shown in the figure, it undergoes a snap-through. The stable configuration attained after the snap-through is referred to as C2 in this paper. According to Qiu29Qiu J. An Electrothermally-Actuated Bistable MEMS Relay for Power Applications. Massachusetts Inst. Technol., 2003: 94Google Scholar,30Qiu J. Lang J.H. Slocum A.H. A curved-beam bistable mechanism.J. Microelectromech. Syst. 2004; 13: 137-146Google Scholar a single parameter Q, the ratio of the amplitude to the thickness of a sinusoidal beam, controls the stability of C2. Q > 2.31 yields a bistable building block where C2 is stable and the block can persist indefinitely in this configuration in the absence of an external load seeking to reverse its deformation as shown in the top row of Figure 1A. Q ∊ [1.23, 2.31] leads to a metastable building block where C2 is unstable, and the block reverts to C1 when the external load is removed, as seen in the bottom row of Figure 1A. Q < 1.23 gives a simple nonlinear spring response with no snap-through. The force (F)-deflection (d) responses for a stack of many such blocks (bistable or metastable) connected mechanically in series show a loading and an unloading plateau. The separation between the loading and unloading plateaus in the F-d response for a stack of these blocks is a consequence of solid-state energy dissipation in these materials. The beam in a building block experiences axial compression and bending during its deformation. The length of the beam shortens during its deformation as it moves toward a straight line joining its ends, and its length increases as the beam moves away from this line. The stability of C2 is determined by the interplay between two competing sources of strain energy stored in the deformed beam.29Qiu J. An Electrothermally-Actuated Bistable MEMS Relay for Power Applications. Massachusetts Inst. Technol., 2003: 94Google Scholar, 30Qiu J. Lang J.H. Slocum A.H. A curved-beam bistable mechanism.J. Microelectromech. Syst. 2004; 13: 137-146Google Scholar, 31Liu M. Gomez M. Vella D. Delayed bifurcation in elastic snap-through instabilities.J. Mech. Phys. Sol. 2021; 151: 104386Google Scholar The strain energy (Ua) associated with axial compression of the sinusoidal beam varies non-monotonically with the deflection of the beam and serves to stabilize C2 (see Figure S1). On the other hand, the strain energy (Ub) associated with the bending of the beam varies monotonically with the deflection of the beam and is the primary driver for restoring the C1 configuration of the beam. Thus, Ua promotes bistability while Ub favors metastability in the building block. The compliance of the end supports for the beam is a key determinant of Ua. Varying the support compliance provides a means to modulate Ua, and thus to modulate the stability of C2. We exploit this observation to propose a two-material variation of the single material PXCM building block design; this variation is the building block for an ASMA material. A building block for the proposed ASMA is shown in Figure 1B along with a comparable one for a PXCM.23Restrepo D. Mankame N.D. Zavattieri P.D. Phase transforming cellular materials.Extrem. Mech. Lett. 2015; 4: 52-60Google Scholar The geometry of both blocks is identical. The building block for the PXCM is made entirely of material m1. The building block for the ASMA is made almost entirely of m1 as well; however, the supports are made of a different material (m2). These two materials have similar storage moduli (E) at low temperatures (TL), but E(m1) ≫ E(m2) at higher temperatures (Th) as seen schematically in Figure 1C. The mechanical behaviors of the two building blocks at the two salient temperatures are shown in Figure 1D (PXCM) and Figure 1E (ASMA). As Q > 2.31 for both blocks, they both exhibit a bistable response at Tl. However, as the temperature increases, the modulus of the support material (m2) in the ASMA building block reduces at a faster rate than the modulus for the sinusoidal beam material (m1). This relaxes the axial constraint on the sinusoidal beam, and consequently reduces Ua for the beam. As discussed earlier, a reduction in Ua leads to a reduction in the stability of C2 for the building block. When the temperature rises above a critical transition value (Tt), the relaxation of the axial constraint is sufficient to switch the response of the building block from bistable to metastable. The behavior of the PXCM building block changes quantitatively (e.g., the peak force reduces at Th because of the reduction in E), but the stability of C2 remains unchanged, whereas the behavior of the ASMA building block changes quantitatively as well as qualitatively (C2 becomes unstable) above a critical transition temperature (Th > Tt). Unlike the PXCM building block whose mechanical response was completely determined by a single geometric parameter (Q), the response of the ASMA building block is dependent on two parameters: Q and temperature (T). This allows us to endow ASMAs with the ability to mimic both salient constitutive responses (SE and SME) that are observed in SMAs. We note that this is not the only building block design that results in ASMA behavior; two alternative designs are presented in section “Designing ASMAs for constrained recovery.” In this section, we explore the similarities between SMAs and ASMAs. We begin by establishing an equivalence between the various phases in these two materials and then proceed to show how the thermo-mechanical response of ASMAs can mimic that of SMAs. We use NiTiNOL, a family of SMA materials with nearly equi-atomic fractions of Ni and Ti, as the canonical SMA material in this paper. In NiTiNOL, the SE and SME behaviors arise from reversible solid-state phase transformations between two dominant material phases. The austenite (A) phase has a high-symmetry unit cell (cubic, B2) and is stable at high temperatures (T > Af, the austenite finish temperature). The martensite phase has a lower-symmetry unit cell (monoclinic, B19') and is stable at low temperatures (T < Mf, the martensite finish temperature), or at higher temperatures (T > As, the austenite start temperature) under high stress. As mentioned earlier, the transformations between these two phases are diffusionless; i.e., there is no long-range migration of atoms, rather the transition from one type of unit cell to the other takes place by small but coordinated movements in a large number of atoms. In NiTiNOL, martensite has two main varieties: thermal or unstrained martensite (denoted as M+/-) and de-twinned or oriented martensite (M+). Thermal martensite is a self-accommodating mixture of several energetically equivalent variants that is obtained by cooling the material in a stress-free condition from austenite. Oriented martensite comprises almost exclusively the variant that is energetically favored by the applied load.32Shaw, J.A., Churchill, C.B., Lagoudas, D.C., and Kumar, P. (2010). Shape memory alloys. 1–20. 10.1002/9780470686652.EAE232.Google Scholar A PXCM is an ensemble of many building blocks comprising sinusoidal beams arranged in a periodic manner. When a beam transitions from C1 to C2, the topology of the building block remains unchanged but there is a cooperative rearrangement of the structural elements of the building block. The rearrangement is repeated throughout the material when all beams in a sample transition from C1 to C2. This is reminiscent of the non-diffusive rearrangement of atoms during solid-state diffusionless phase transformations in NiTiNOL. The mechanical response of the beam in C2 may or may not be significantly different from that in C1 depending on the design parameters, but the specific volume of material is much smaller when all constituent beams are in C2 than when they are in C1 because the beams are packed more closely together in the former case. Thus, a PXCM sample that has all beams in C1 has a different physical behavior than one that has all beams in C2. The sample can transition from having all beams in C1 to having all beams in C2 (or vice versa) under the application (or removal) of an external load. These transitions are accompanied by a jump in a specific volume and involve an exchange of energy with the environment. Based on these observations, we propose the following interpretation for phases in PXCMs. When all sinusoidal beams in a part of a PXCM sample are in C1 (or C2), that part of the PXCM is said to be in phase 1 (or 2 respectively). If the underlying block is bistable, we use the prefix B for the phase name; e.g., phase B1 comprises entirely bistable blocks in the configuration C1. Similarly, if the underlying block is metastable, we use the prefix M for the phase name; e.g., M2 has all metastable beams in C2. A transformation from B1 (or M1) to B2 (or M2 respectively) is called the forward transformation, and a transformation in the opposite direction is called the reverse transformation. Figure 1F is a schematic showing the paths for the SE (red lines) and SME (blue lines) behaviors in SMAs and their equivalents for ASMAs, in the stress-strain-temperature space. Salient points in the diagram are numbered, and these numbers are referenced in the discussion below. The different phases for the SMA and ASMA materials at different points along the two paths are juxtaposed in Figure 1F to emphasize their equivalence. As discussed earlier, NiTiNOL exists in a stable and stress-free austenite (A) phase at temperatures above Af. When a stress-free NiTiNOL wire (point ① in Figure 1F) is loaded in uniaxial tension at T > Af, initially, we observe a nominally linear elastic response until a threshold value of stress is reached at ②. Beyond this stress level, the de-twinned martensite (M+) phase is thermodynamically more favorable, and hence, a stress-induced A to M+ transformation takes place as we move from ② to ③. This transformation is completed at ③ and the wire comprises entirely the M+ phase at this stage. If the wire is unloaded at ③, the M+ phase persists until another (lower) stress threshold is crossed at ⑤. The A phase becomes thermodynamically more stable at this lower stress at this temperature. Hence, we observe an M+ to A phase transformation during the segment ⑤–⑥ of the SE path. This transformation is completed at ⑥, and further unloading of the wire results in a nominally linear elastic recovery of the material over the segment ⑥–⑦. If the material was not overloaded during this cycle, there is no irreversible deformation of the wire. Consequently, the end state ⑦ is identical to the starting state ① of this path. The ASMA building block shown in Figure 1B exhibits metastable behavior at temperatures above Tt. Consider a stress-free ASMA sample that comprises building blocks all of which are in the M1 phase at a temperature Th (Th > Tt as shown in Figure 1F). This is shown schematically at point ① in the figure. When this sample is subjected to uniaxial compression along the axis of symmetry of the block, we initially see a nominally linear rise in stress during the segment ①–② as all of the beams in the sample deform elastically starting from the C1 configuration. At ②, one row of blocks transitions to C2. This transition causes a small jump in the global strain accompanied by a drop in the stress experienced by the remaining rows that are still in M1. As the load increases again and reaches the level at ②, another row snaps through. This sequence ripples through the whole sample as we move from ② to ③. At ③, the forward phase transformation is complete, and the sample comprises entirely the M2 phase at this stage. If we continue loading the sample beyond ③ (e.g. along ③–④), the sample will exhibit the mechanical response associated with elastic deformation of the M2 phase. Unloading from ③ yields a nominally linear drop in stress as the deformed beams start retracting elastically from their deformed C2 configurations. This process continues until we reach point ⑤, at which point one row of beams transitions back from C2 to C1. The reverse phase transformation of the entire sample takes place as we move from ⑤ to ⑥ in a manner similar to the forward transformation. If the beams are designed properly23Restrepo D. Mankame N.D. Zavattieri P.D. Phase transforming cellular materials.Extrem. Mech. Lett. 2015; 4: 52-60Google Scholar,29Qiu J. An Electrothermally-Actuated Bistable MEMS Relay for Power Applications. Massachusetts Inst. Technol., 2003: 94Google Scholar,30Qiu J. Lang J.H. Slocum A.H. A curved-beam bistable mechanism.J. Microelectromech. Syst. 2004; 13: 137-146Google Scholar and the sample is not overloaded during the load-unload cycle, there is no irreversible deformation of the sample during this process. Further unloading of the sample results in a nominally linear response as all of the beams in the sample revert elastically back to the stress-free C1 configuration at ⑦, which is identical to the configuration at ①. The snap-through of each row in the sample is associated with a serration in the mechanical response that is caused by the jump in strain and the concomitant drop in stress. In a sample with a large number of rows, the size of the serration is small relative to the global stress at points ② and ⑤, and, hence, these serrations are not easily visible in the overall stress-strain response.23Restrepo D. Mankame N.D. Zavattieri P.D. Phase transforming cellular materials.Extrem. Mech. Lett. 2015; 4: 52-60Google Scholar In the absence of any residual strains, NiTiNOL exists in the stress-free state (point ⑧ in Figure 1F) at temperatures below Mf in the thermal martensite (M+/-) phase. Uniaxial loading from this state results in a nominally linear stress-strain response due to elastic straining of the thermal martensite until we reach ⑨. The externally applied stress alters the energy landscape in the material to favor the martensite variants that are aligned with the external stress. At the stress corresponding to ⑨, martensite variants oriented in other directions start reorienting to align with the applied stress via a process called de-twinning. This process is completed at point ⑩, where the material exists entirely as de-twinned martensite (M+). If we continue to load past ⑩ (e.g., along ⑩–⑪), we see another linear regime that corresponds to elastic deformation of the M+ phase. If we unload the sample at ⑩, we see an elastic strain recovery until the sample is completely stress free at ⑫. Unlike at ⑧, where the sample was also stress free but it existed entirely in the M+/- phase, it exists entirely in the M+ phase at ⑫. There is a residual strain in the sample at ⑫, which is due to the accumulation of strain during the reorientation of the martensite variants throughout the sample during the de-twinning process. If the material is loaded again st