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At least 181 records · Page 10

Verification and Validation of a Three-Dimensional Composite Impact Model with Tabulated Input

A material model which incorporates several key capabilities which have been identified by the aerospace community as lacking in the composite impact models currently available in the commercial transient dynamic finite element code LS-DYNA® has been developed. The material model utilizes experimentally based tabulated input to define the evolution of plasticity and damage as opposed to specifying discrete input parameters (such as modulus and strength. The plasticity portion of the orthotropic, three-dimensional, macroscopic composite constitutive model is based on an extension of the Tsai-Wu composite failure model into a generalized yield function with a non-associative flow rule. The capability to account for the rate and temperature dependent deformation response of composites has also been incorporated into the material model. For the damage model, a strain equivalent formulation is utilized to allow for the uncoupling of the deformation and damage analyses. In the damage model, a diagonal damage tensor is defined to account for the directionally dependent variation of damage. However, the terms in the damage matrix are semi-coupled such that the damage in a particular coordinate direction is a function of the stresses and plastic strains in all of the coordinate directions. For the failure model, a tabulated approach is utilized in which a stress or strain based invariant is defined as a function of the location of the current stress state in stress space to define the initiation of failure, which allows an arbitrarily shaped failure surface to be defined. A systematic series of validation and verification studies, at a variety of length scales ranging from single element simulations to simulations of a flat panel impact test, have been performed to fully exercise and evaluate the capabilities of the developed model.

Impact↗

Electro-Optic Modulation Using Metal-Free Perovskites

Electro-optic (EO) modulation is of interest to impart information onto an optical carrier. Inorganic crystals—most notably LiNbO 3 and BaTiO 3 —exhibit EO modulation and good stability, but are difficult to integrate with silicon photonic technology. Solution-processed organic EO materials are readily integrated but suffer from thermal degradation at the temperatures required in operating conditions for accelerated reliability studies. Hybrid organic–inorganic metal halide perovskites have the potential to overcome these limitations; however, these have so far relied on heavy metals such as lead and cadmium. Here, we report linear EO modulation using metal-free perovskites, which maintain the crystalline features of the inorganic EO materials and incorporate the flexible functionality of organic EO chromophores. We find that, by introducing a deficiency of cations, we reduce the symmetry in the perovskite crystal and produce thereby an increased EO response. The best-engineered perovskites reported herein showcase an EO coefficient of 14 pm V –1 at a modulation frequency of 80 kHz, an order of magnitude higher than in the nondefective materials. Furthermore, we observe split peaks in the X-ray diffraction and neutron diffraction patterns of the defective sample, indicating that the crystalline structure has been distorted and the symmetry reduced. Density functional theory (DFT) studies link this decreased symmetry to NH 4 + deficiencies. This demonstration of EO from metal-free perovskites highlights their potential in next-generation optical information transmission.

36 MATERIALS SCIENCE↗

Development of Design Analysis Methods for C/SiC Composite Structures

The stress-strain behavior at room temperature and at 1100 C (2000 F) was measured for two carbon-fiber-reinforced silicon carbide (C/SiC) composite materials: a two-dimensional plain-weave quasi-isotropic laminate and a three-dimensional angle-interlock woven composite. Micromechanics-based material models were developed for predicting the response properties of these two materials. The micromechanics based material models were calibrated by correlating the predicted material property values with the measured values. Four-point beam bending sub-element specimens were fabricated with these two fiber architectures and four-point bending tests were performed at room temperature and at 1100 C. Displacements and strains were measured at various locations along the beam and recorded as a function of load magnitude. The calibrated material models were used in concert with a nonlinear finite element solution to simulate the structural response of these two materials in the four-point beam bending tests. The structural response predicted by the nonlinear analysis method compares favorably with the measured response for both materials and for both test temperatures. Results show that the material models scale up fairly well from coupon to subcomponent level.

Sullivan, Roy M.↗

Fast Photoactuation Driven by Supramolecular Polymers Integrated into Covalent Networks

Abstract The design of robotic soft matter capable of emulating the complex movements of living organisms such as mechanical actuation, shape transformation, and autonomous translation remains a grand challenge in soft materials science. Functionalized hydrogels are excellent candidates for such materials since they can operate in water and are highly responsive to their environment, but their response times can be slow. This work investigates fast photoactuation of hybrid bonding hydrogels composed of peptide amphiphile (PA) supramolecular nanofibers bonded covalently to merocyanine‐based (MCH + ) photoresponsive networks. By incorporating ionizable acrylic acid (AA) co‐monomers in these networks, photoactuation at nearly neutral pH is observed, which in turn enables a new mechanism to accelerate the response by triggering the bundling of supramolecular nanofibers by rapid proton exchange reactions. Furthermore, this rapid response and its consequent large shape transformations lead to hydrogels capable of spontaneously tracking external light sources inspired by pedicellariae, defensive organs present in echinoderms like the starfish and the sea urchin. This work suggests that hybrid bonding polymers (HBPs), which leverage the interplay between supramolecular assemblies and covalent networks, offer novel strategies to design rapidly actuating soft robotic materials.

Cezan, S. Doruk↗

Ultrathin films as photomechanical transducers

In order to investigate the photomechanical effect in ultrathin films, several commercially available polymers of various structure and properties have been studied experimentally below the glass transition temperature. In the experiments using an Instron test machine equipped with a 200-g load cell and a microscope stage illuminator as the light source, the load at the fixed strain was recorded as a function of time. Plots of the steady-state change in stress as a function of the intensity of the incident radiation are presented for several of the materials studied. The response is found to be linear; the greater the intensity of the incident radiation, the greater is the change in stress.

Sarbolouki, M. N.↗

A predictive model for failure properties of thermoset resins

A predictive model for the three-dimensional failure behavior of engineering polymers has been developed in a recent NASA-sponsored research program. This model acknowledges the underlying molecular deformation mechanisms and thus accounts for the effects of different chemical compositions, crosslink density, functionality of the curing agent, etc., on the complete nonlinear stress-strain response including yield. The material parameters required by the model can be determined from test-tube quantities of a new resin in only a few days. Thus, we can obtain a first-order prediction of the applicability of a new resin for an advanced aerospace application without synthesizing the large quantities of material needed for failure testing. This technology will effect order-of-magnitude reductions in the time and expense required to develop new engineering polymers.

Caruthers, James M.↗

Computational Implementation of a Thermodynamically Based Work Potential Model For Progressive Microdamage and Transverse Cracking in Fiber-Reinforced Laminates

A continuum-level, dual internal state variable, thermodynamically based, work potential model, Schapery Theory, is used capture the effects of two matrix damage mechanisms in a fiber-reinforced laminated composite: microdamage and transverse cracking. Matrix microdamage accrues primarily in the form of shear microcracks between the fibers of the composite. Whereas, larger transverse matrix cracks typically span the thickness of a lamina and run parallel to the fibers. Schapery Theory uses the energy potential required to advance structural changes, associated with the damage mechanisms, to govern damage growth through a set of internal state variables. These state variables are used to quantify the stiffness degradation resulting from damage growth. The transverse and shear stiffness of the lamina are related to the internal state variables through a set of measurable damage functions. Additionally, the damage variables for a given strain state can be calculated from a set of evolution equations. These evolution equations and damage functions are implemented into the finite element method and used to govern the constitutive response of the material points in the model. Additionally, an axial failure criterion is included in the model. The response of a center-notched, buffer strip-stiffened panel subjected to uniaxial tension is investigated and results are compared to experiment.

Pineda, Evan J.↗

Higher-Order Theory for Functionally Graded Materials

This paper presents the full generalization of the Cartesian coordinate-based higher-order theory for functionally graded materials developed by the authors during the past several years. This theory circumvents the problematic use of the standard micromechanical approach, based on the concept of a representative volume element, commonly employed in the analysis of functionally graded composites by explicitly coupling the local (microstructural) and global (macrostructural) responses. The theoretical framework is based on volumetric averaging of the various field quantities, together with imposition of boundary and interfacial conditions in an average sense between the subvolumes used to characterize the composite's functionally graded microstructure. The generalization outlined herein involves extension of the theoretical framework to enable the analysis of materials characterized by spatially variable microstructures in three directions. Specialization of the generalized theoretical framework to previously published versions of the higher-order theory for materials functionally graded in one and two directions is demonstrated. In the applications part of the paper we summarize the major findings obtained with the one-directional and two-directional versions of the higher-order theory. The results illustrate both the fundamental issues related to the influence of microstructure on microscopic and macroscopic quantities governing the response of composites and the technologically important applications. A major issue addressed herein is the applicability of the classical homogenization schemes in the analysis of functionally graded materials. The technologically important applications illustrate the utility of functionally graded microstructures in tailoring the response of structural components in a variety of applications involving uniform and gradient thermomechanical loading.

Aboudi, Jacob↗

Synergizing a Large Ordinary Nernst Effect and Axis‐Dependent Conduction Polarity in Flat Band KMgBi Crystals

The exploration of quantum materials in which an applied thermo/electrical/magnetic field along one crystallographic direction produces an anisotropic response has led to unique functionalities. Along these lines, KMgBi is a layered, narrow gap semiconductor near a critical state between multiple Dirac phases due to the presence of a flat band near the Fermi level. The valence band is highly anisotropic with minimal cross-plane dispersion, which, in combination with an isotropic conduction band, enables axis-dependent conduction polarity. Thermopower and Hall measurements indicate dominant p-type conduction along the cross-plane direction, and n-type conduction along the in-plane direction, leading to a significant zero-field transverse thermoelectric response when the heat flux is at an angle to the principal crystallographic directions. Additionally, a large Ordinary Nernst effect (ONE) is observed with an applied field. It arises from the ambipolar term in the Nernst effect, whereby the Lorentz force on electrons and holes makes them drift in opposite directions so that the resulting Nernst voltage becomes a function of the difference between their partial thermopowers, greatly enhancing the ONE. It is proven that axis-dependent polarity can synergistically enhance the ONE, in addition to leading to a zero-field transverse thermoelectric performance.

36 MATERIALS SCIENCE↗

Charge Transfer Plasmonics in Bespoke Graphene/α-RuCl 3 Cavities

Surface plasmon polaritons (SPPs) provide a window into the nano-optical, electrodynamic response of their host material and its dielectric environment. Graphene/α-RuCl 3 serves as an ideal model system for imaging SPPs since the large work function difference between these two layers facilitates charge transfer that hole dopes graphene with n ~ 10 13 cm –2 free carriers. In this work, we study the emergent THz response of graphene/α-RuCl 3 heterostructures using our home-built cryogenic scanning near-field optical microscope. Using phase-resolved imaging, we clearly observe long wavelength, heavily damped THz SPPs in a series of variable-size graphene cavities. From this, we extract the plasmonic wavelength and scattering rate in the graphene/α-RuCl 3 heterostructures. We determine that the measured plasmon wavelength and electronic scattering rate match our heterostructures’ theoretically predicted values. Here, our results demonstrate that shaping graphene into bespoke cavity structures enables observation and quantification of SPPs in heavily doped graphene that are largely not addressable with other experimental techniques. Moreover, the manifest lack of metallicity observed in the adjacent doped α-RuCl 3 layer provides significant constraints on the nature of the interfacial charge transfer in this 2D heterostructure.

36 MATERIALS SCIENCE↗

Recent Advancements in the PATO Material Response Code

Introduction: Predicting the complicated multiphysics phenomena during atmospheric entry requires high-fidelity modeling tools to refine estimates of mission risks during entry. To this end, new capabilities are being added to the Porous-material Analysis Toolbox based on OpenFOAM (PATO). PATO is an open-source software for Computational Material Response (CMR) of reactive porous materials submitted to high-temperature environments. The objective of this work is to highlight current efforts to add to and improve upon the modeling capabilities of PATO. These include efforts to loosely couple PATO with other discipline specialized codes including hypersonic Computational Fluid Dynamics (CFD), to assess the interaction effects between pyrolysis gas blowing and the boundary layer, and Computational Solid Mechanics (CSM), to address modeling of mechanical erosion. Other refinements include surface phenomena modeling capabilities to address the effects of silicone-based coatings applied to the TPS during flight preparation, and a unified multiphase solver for a mixed porous-material and plain-fluid domain. Coupling CMR with CFD (CMR/CFD): A loose coupling between PATO and the Data Parallel Line Relaxation (DPLR) CFD code has been achieved by making use of a blowing boundary condition at the heatshield surface available in DPLR. Starting with heat flux estimates with no pyrolysis gas blowing at the surface, blowing gases are computed by the CMR and passed to the CFD such that aerothermal properties of the environment can be recomputed for a new CMR computation. This leads to an iterative process which is supplemented with an estimate of the radiative heat flux using the Nonequilibrium air radiation (NEQAIR) program. The entire iterative process is illustrated in Figure 1. This coupling strategy has been utilized in computing the MSL material response. The goal is to compare the coupled CMR/CFD results with material response results obtained using traditional blowing corrections. Coupling CMS with CMR: A mechanical erosion model is currently being implemented in PATO to account for the additional mass removal induced by high shear conditions. The modeling process at each timestep consists of updating the mechanical properties as a function of temperature and computing the stress tensor and displacement fields of the material. Then, a failure criteria model determines the regions in which the stress exceeds the ultimate strength values resulting in mesh movement to account for mass removal. This model allows the material response simulation to compute the recession due to both oxidation and shear-induced erosion. The model is demonstrated by computing material response of sphere-cone arc jet samples. Surface Modeling Capabilities: NuSil, a silicone-based coating, was sprayed onto the MSL and Mars 2020 heatshields to mitigate shedding of phenolic dust. To better understand the effects of the NuSil coating on the material response, a novel model has been implemented in PATO. In this model, the equilibrium of the charred NuSil surface is modeled as pure silica, and a constant offset, inspired by the classical spallation model, is added to the the char blowing rate and wall enthalpy to reproduce HyMETS experimental results. The model has also been used to estimate the 3D material response of the MSL heatshield. Unified Solver: In addition to the iterative loose coupling approach mentioned above, a multiphase unified solver is being developed to couple the environment (plain-fluid phase) and the porous-material phase. The solver is based on the volume averaged conservation of mass, momentum, and energy for the macroscale with closure models which include microscale effects through effective physicochemical properties. The unified solver has been used to compute flow through a porous plug and solve the Beavers and Joseph problem. Since the strong coupling between phases is inherent to this solver, modeling assumptions present in other coupling methods of material response are mitigated. This strategy also makes it feasible to capture the competition between surface and volume ablation in the same computational domain, which is usually not possible with other coupling approaches.

Material Response↗

Recent Advancements in the PATO Material Response Code

Introduction: Predicting the complicated multiphysics phenomena during atmospheric entry requires high-fidelity modeling tools to refine estimates of mission risks during entry. To this end, new capabilities are being added to the Porous-material Analysis Toolbox based on OpenFOAM (PATO) [1,2,3]. PATO is an open-source software for Computational Material Response (CMR) of reactive porous materials submitted to high-temperature environments. The objective of this work is to highlight current efforts to add to and improve upon the modeling capabilities of PATO. These include efforts to loosely couple PATO with other discipline specialized codes including hypersonic Computational Fluid Dynamics (CFD), to assess the interaction effects between pyrolysis gas blowing and the boundary layer, and Computational Solid Mechanics (CSM), to address modeling of mechanical erosion. Other refinements include surface phenomena modeling capabilities to address the effects of silicone-based coatings applied to the TPS during flight preparation, and a unified multiphase solver for a mixed porous-material and plain-fluid domain. Coupling CMR with CFD (CMR/CFD): A loose coupling between PATO and the Data Parallel Line Relaxation (DPLR) [4] CFD code has been achieved by making use of a blowing boundary condition at the heatshield surface available in DPLR. Starting with heat flux estimates with no pyrolysis gas blowing at the surface, blowing gases are computed by the CMR and passed to the CFD such that aerothermal properties of the environment can be recomputed for a new CMR computation. This leads to an iterative process which is supplemented with an estimate of the radiative heat flux using the Nonequilibrium air radiation (NEQAIR) [5] program. The entire iterative process is illustrated in Figure 1. This coupling strategy has been utilized in computing the MSL material response. The goal is to compare the coupled CMR/CFD results with material response results obtained using traditional blowing corrections. Coupling CMS with CMR: A mechanical erosion model is currently being implemented in PATO to account for the additional mass removal induced by high shear conditions. The modeling process at each timestep consists of updating the mechanical properties as a function of temperature and computing the stress tensor and displacement fields of the material. Then, a failure criteria model determines the regions in which the stress exceeds the ultimate strength values resulting in mesh movement to account for mass removal. This model allows the material response simulation to compute the recession due to both oxidation and shear-induced erosion. The model is demonstrated by computing material response of sphere-cone arc jet samples. Surface Modeling Capabilities: NuSil, a silicone-based coating, was sprayed onto the MSL and Mars 2020 heatshields to mitigate shedding of phenolic dust. To better understand the effects of the NuSil coating on the material response, a novel model has been implemented in PATO. In this model, the equilibrium of the charred NuSil surface is modeled as pure silica, and a constant offset, inspired by the classical spallation model, is added to the the char blowing rate and wall enthalpy to reproduce HyMETS experimental results. The model has also been used to estimate the 3D material response of the MSL heatshield [6]. Unified Solver: In addition to the iterative loose coupling approach mentioned above, a multiphase unified solver is being developed to couple the environment (plain-fluid phase) and the porous-material phase. The solver is based on the volume averaged conservation of mass, momentum, and energy for the macroscale with closure models which include microscale effects through effective physicochemical properties. The unified solver has been used to compute flow through a porous plug and solve the Beavers and Joseph problem [7]. Since the strong coupling between phases is inherent to this solver, modeling assumptions present in other coupling methods of material response are mitigated. This strategy also makes it feasible to capture the competition between surface and volume ablation in the same computational domain, which is usually not possible with other coupling approaches.

Thermal Protection Systems↗

Incorporation of Damage and Failure into an Orthotropic Elasto-Plastic Three-Dimensional Model with Tabulated Input Suitable for Use in Composite Impact Problems

A material model which incorporates several key capabilities which have been identified by the aerospace community as lacking in the composite impact models currently available in LS-DYNA(Registered Trademark) is under development. In particular, the material model, which is being implemented as MAT 213 into a tailored version of LS-DYNA being jointly developed by the FAA and NASA, incorporates both plasticity and damage within the material model, utilizes experimentally based tabulated input to define the evolution of plasticity and damage as opposed to specifying discrete input parameters (such as modulus and strength), and is able to analyze the response of composites composed with a variety of fiber architectures. The plasticity portion of the orthotropic, three-dimensional, macroscopic composite constitutive model is based on an extension of the Tsai-Wu composite failure model into a generalized yield function with a non-associative flow rule. The capability to account for the rate and temperature dependent deformation response of composites has also been incorporated into the material model. For the damage model, a strain equivalent formulation is utilized to allow for the uncoupling of the deformation and damage analyses. In the damage model, a diagonal damage tensor is defined to account for the directionally dependent variation of damage. However, in composites it has been found that loading in one direction can lead to damage in multiple coordinate directions. To account for this phenomena, the terms in the damage matrix are semi-coupled such that the damage in a particular coordinate direction is a function of the stresses and plastic strains in all of the coordinate directions. The onset of material failure, and thus element deletion, is being developed to be a function of the stresses and plastic strains in the various coordinate directions. Systematic procedures are being developed to generate the required input parameters based on the results of experimental tests.

Finite Element Method↗

Satellite Hyperspectral Imaging Simulation

Simulation of generic pushbroom satellite hyperspectral sensors have been performed to evaluate the potential performance and validation techniques for satellite systems such as COIS(NEMO), Warfighter-1(OrbView-4) and Hyperion(EO-1). The simulations start with a generation of synthetic scenes from material maps of studied terrain. Scene-reflected radiance is corrected for atmospheric effects and convolved with sensor spectral response using MODTRAN 4 radiance and transmissions calculations. Scene images are further convolved with point spread functions derived from Optical Transfer Functions (OTF's) of the sensor system. Photon noise and etectorr/electronics noise are added to the simulated images, which are also finally quantized to the sensor bit resolution. Studied scenes include bridges and straight roads used for evaluation of sensor spatial resolution, as well as fields of minerals, vegetation and manmade materials used for evaluation of sensor radiometric response and sensitivity. The scenes are simulated with various seasons and weather conditions. Signal-to-noise ratios and expected performance are estimated for typical satellite system specifications and are discussed for all the scenes.

Zanoni, Vicki↗

Satellite Hyperspectral Imaging Simulation

Simulations of generic pushbroom satellite hyperspetral sensors have been performed to evaluate the potential performance and validation techniques for satellite systems such as COIS (NEMO), Warfighter-1 (OrbView-4), and Hyperion (EO-1). The simulaitons start with a generation of synthetic scenes form material maps of studied terrain. Scene-reflected radiance is corrected for atmospheric effects and convolved with sensor spectral response uwing MODTRAN 4 radiance and transmission calculations. Scene images are further convolved with point spread functions derived from Optical Transfer Functions (OTF's) of the sensor system. Photon noise and detector/electronics noise are added to the simulated images, which are also finally quantized to the sensor bit resolution. Studied scenes include bridges and straight roads used for evaluation of sensor spatial resolution, as well as fields of minerals, vegetation, and manmade materials used for evaluation of sensor radiometric response and sensitivity. The scenes are simulated with various seasons and weather conditions. Signal-to-noise ratos and expected performance are estimated for typica satellite system specifications and are discussed for all the scenes.

Zanoni, Vicki↗

Smart Droplets Stabilized by Designer Surfactants: From Biomimicry to Active Motion to Materials Healing

The science and technologies of emulsion droplets have been a long‐term focus of extensive research endeavors for their practical utility across a breadth of industries, including pharmaceutical products, oil recovery processes, and the food sciences. However, with advances in materials chemistry and characterization tools, new emerging areas are arising with a focus on “smart droplets”. The versatility of emulsion droplets across is based on their ability to partition and create isolated systems with properties defined by the liquid–liquid interface, while preparative routes allow manipulation of droplet size, stability, and encapsulated contents. As described in this article, significant efforts are being devoted to creating new types of droplets by “activating” this interface through the incorporation of reactive structures that trigger droplet response to applied or environmental stimuli (e.g., pH, temperature, salt, or external fields). Moreover, parallels between droplets and live cells inspire efforts to conceive systems that resemble biological motifs or that can produce cellular behaviors that imitate biology (e.g., swarming, communication, or motion). Here, the authors highlight recent advances in smart droplets, with emphasis on organic, polymer, and/or particle surfactants that give rise to inter‐droplet communication (via aggregation, fusion, division, or mass transfer), droplet vehicles for controlled delivery, autonomous droplet motion, and tunable emulsion inversion. Especially emphasized is the macromolecular design to produce reactive and functional surfactants, which are crucial to responsive droplet behavior and their underlying mechanisms. More generally, the exquisite interplay between materials science and biology inspires the review of this research area that provides unique opportunities for insight and inspiration into the capabilities of new droplet designs.

36 MATERIALS SCIENCE↗

Twinning-mediated anomalous alignment of rutile films revealed by synchrotron X-ray nanodiffraction

Nanotwin structures in materials engender fascinating exotic properties. However, twinning usually alter the crystal orientation, resulting in random orientation and limited performances. Here, we report a well-aligned rutile TiO 2 nanotwin film with superior preferential orientation than its isostructural substrate. By means of the synchrotron X-ray Laue nanodiffraction technique, the crystal orientation, twin boundaries, and deviatoric stresses of the film were quantitatively imaged at unprecedented spatial resolution to unravel the underlying mechanism of this anomalous alignment. Massive {101}-type rutile nanotwins were observed, and a crystallographic relationship of the heteroepitaxy was proposed. The rapid twinning and twin-controlled heteroepitaxy are responsible for the texture improvement. This work would open up opportunities for rational design of better twin-based functional materials, and implies the powerful capabilities of X-ray nanodiffraction technique for multidisciplinary applications.

36 MATERIALS SCIENCE↗

M PX 3 van der Waals magnets under pressure ( M = Mn, Ni, V, Fe, Co, Cd; X = S, Se)

van der Waals antiferromagnets with chemical formula MPX 3 (M = V, Mn, Fe, Co, Ni, Cd; X = S, Se) are superb platforms for exploring the fundamental properties of complex chalcogenides, revealing their structure-property relations and unraveling the physics of confinement. Pressure is extremely effective as an external stimulus, able to tune properties and drive new states of matter. In this review, we summarize experimental and theoretical progress to date with special emphasis on the structural, magnetic, and optical properties of the MPX 3 family of materials. Under compression, these compounds host inter-layer sliding and insulator-to-metal transitions accompanied by dramatic volume reduction and spin state collapse, piezochromism, possible polar metal and orbital Mott phases, as well as superconductivity. Some responses are already providing the basis for spintronic, magneto-optic, and thermoelectric devices. We propose that strain may drive similar functionality in these materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗