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Processed Gladwin Tensor Strainmeter, Optical Fiber Tensor Strainmeter, and well pressure data from the well 9A injections from July 26 thru November 21, 2022, at the North Avant Field, OK
High energy X-ray diffraction microscopy (HEDM) was employed to index nearly 1000 grains in a polycrystalline Ti specimen and characterize their deformation during an incremental tensile test. For each grain, the positions of its associated diffraction peaks were used for analyzing its evolving crystal orientation and stress tensor. The azimuthal breadth of each peak at different load steps was measured, allowing measurement of initial yielding and providing an estimate of the dislocation density evolution in each grain. Furthermore, the Taylor hardening model was evaluated grain by grain using the above data, indicating that it can represent hardening in most grains. The yield stress and the strain hardening coefficient for all grains were statistically analyzed with respect to grain orientation, grain size, slip systems, and the surrounding neighborhood to examine how the yield stress and hardening are correlated.
Abstract The effective inclusion of a priori knowledge when embedding known data in physics‐based models of dynamical systems can ensure that the reconstructed model respects physical principles, while simultaneously improving the accuracy of the solution in the previously unseen regions of state space. This paper presents a physics‐constrained data‐driven discrepancy modeling method that variationally embeds known data in the modeling framework. The hierarchical structure of the method yields fine scale variational equations that facilitate the derivation of residuals which are comprised of the first‐principles theory and sensor‐based data from the dynamical system. The embedding of the sensor data via residual terms leads to discrepancy‐informed closure models that yield a method which is driven not only by boundary and initial conditions, but also by measurements that are taken at only a few observation points in the target system. Specifically, the data‐embedding term serves as residual‐based least‐squares loss function, thus retaining variational consistency. Another important relation arises from the interpretation of the stabilization tensor as a kernel function, thereby incorporating a priori knowledge of the problem and adding computational intelligence to the modeling framework. Numerical test cases show that when known data is taken into account, the data driven variational (DDV) method can correctly predict the system response in the presence of several types of discrepancies. Specifically, the damped solution and correct energy time histories are recovered by including known data in the undamped situation. Morlet wavelet analyses reveal that the surrogate problem with embedded data recovers the fundamental frequency band of the target system. The enhanced stability and accuracy of the DDV method is manifested via reconstructed displacement and velocity fields that yield time histories of strain and kinetic energies which match the target systems. The proposed DDV method also serves as a procedure for restoring eigenvalues and eigenvectors of a deficient dynamical system when known data is taken into account, as shown in the numerical test cases presented here.
Recent predictions suggest that oxides, such as MgO and CaO, could serve as hosts of spin defects with long coherence times and thus be promising materials for quantum applications. However, in most cases, specific defects have not yet been identified. Here, by using a high-throughput first-principles framework and advanced electronic structure methods, we identify a negatively charged complex between a nitrogen interstitial and a magnesium vacancy in MgO with favorable electronic and optical properties for hybrid quantum technologies. We show that this NV − center has stable triplet ground and excited states, with singlet shelving states enabling optical initialization and spin-dependent readout. We predict several properties, including absorption, emission, and zero-phonon line energies, as well as zero-field splitting tensor, and hyperfine interaction parameters, which can aid in the experimental identification of this defect. Our calculations show that due to a strong pseudo-Jahn Teller effect and low-frequency phonon modes, the NV − center in MgO is subject to a substantial vibronic coupling. We discuss design strategies to reduce such coupling and increase the Debye-Waller factor, including the effect of strain and the localization of the defect states. We propose that the favorable properties of the NV − defect, along with the technological maturity of MgO, could enable hybrid classical-quantum applications, such as spintronic quantum sensors and single qubit gates.
The stress-state within individual grains in a polycrystal determine the fate of the aggregate including mechanical failure. By tracking the evolution of the stress tensor throughout the elastoplastic transition, large rotations of the stress-state, which have long been theorized to occur, are observed experimentally for the first time. These stress rotations (~15°) are more than an order of magnitude larger than the concomitant crystallographic lattice reorientations (~0.9°) well-known to occur during metal plasticity. Furthermore, these rotations are accompanied by a decrease in stress triaxiality within certain grains, promote strain softening, and set the stage for failure at an early stage of deformation. Finally, these results provide a completely new perspective through which to contemplate the question of “hot-spots” responsible for failure of high-performance structural materials.
TReactMech couples geomechanical processes (poroelasticity, failure, and inelastic strain) with multiphase nonisothermal flow (derived from TOUGH2) and reactive geochemical transport. At its core is the reactive-transport code TOUGHREACT v4.13. TReactMech is an efficient hybrid parallel simulator, solving the geomechanics using finite elements and MPI/PetSc, the multiphase flow using integrated finite difference and MPI/PETSc, and the reactive chemistry using OpenMP. The advantages of TReactMech are in its multiphase flow capabilities (e.g., supercritical CO2, supercritical water, air) and parallel geomechanics including full 3-D stress tensor, shear and tensile failure, coupled to porosity and permeability changes. It is backwardly compatible with TOUGH2 and TOUGHREACT v4.13, allowing for easier transitions between the codes. TReactMech can be used to simulate many natural and engineered subsurface systems, including geothermal reservoirs, borehole heat exchangers, geologic carbon sequestration, geologic storage of nuclear waste, groundwater resources, weathering, sediment diagenesis, seafloor hydrothermal circulation, hydrofracturing in unconventional reservoirs, and injection/production-induced surface deformation.
This study leverages high-resolution differential-aperture X-ray structural microscopy (DAXM) to probe the local dislocation structure in deformed 304L-stainless steel at small strain, by measuring the lattice rotation and deviatoric elastic strain with a sub-micron resolution. For a single grain in a polycrystalline specimen, the measured lattice rotation field over the measured volume exhibited a multimodal distribution while the deviatoric elastic strain showed a single-mode distribution. An unsupervised Cauchy mixture machine learning model was developed to resolve the multimodal distribution of the lattice rotation. By mapping the lattice rotation data associated with each Cauchy peak in the model back onto the measured volume, we identify contiguous regions of the crystal rotated near the average values corresponding to the peaks of the overall rotation distribution. These regions represent the grain subdivision in the microstructure. Finally, the dislocation density tensor was also computed and its norm was laid over the rotation field to detect the subgrain boundaries. This step provided a validation of the Cauchy mixture model for the analysis of the lattice rotation distribution. The current study highlights the integration of advanced X-ray microscopy techniques with data-driven analysis methods to uncover detailed microstructure scales in deformed crystals.
Efficient computation and visualization of elastic and mechanical properties are crucial in the selection of materials and the design of new materials. Here, the ElasTool v3.0 toolkit marks a significant advancement in the computational analysis and visualization of elastic and mechanical properties of materials, essential in material selection and design. This enhanced version extends beyond standard calculations like elastic tensor, Young's modulus, bulk modulus, and Poisson's ratio. It introduces capabilities for computing minimum thermal conductivity, linear compressibility, rendering the Christoffel equation, and elastic energy density. Notably, it integrates advanced visualization tools, including compatibility with Plotly and Elate web platforms for interactive web-based property exploration. A key feature of ElasTool v3.0 is the implementation of second-order elastic constants (SOECs) for tubular 2D-based nanostructures and nanotubes. Leveraging high-efficiency strain-matrix sets (OHESS), the toolkit now facilitates efficient computation of elastic constants and mechanical properties at both zero and finite temperatures for 1D, 2D, and 3D dimensions. ElasTool is openly accessible on GitHub: https://github.com/gmp007/elastool.
Spontaneous polarization as large as ~28 μC/cm 2 was recently observed around the dislocation cores in non-polar SrTiO 3 bulk crystals, and its origin was attributed to the flexoelectric effect, i.e., polarization induced by strain gradients. However, the roles of flexoelectricity, relative to other electromechanical contributions, and the nature of dislocations, i.e., edge vs screw dislocations in the induced polarization, are not well understood. In this work, we study the role of flexoelectricity in inducing polarization around three types of dislocation cores in SrTiO 3 : b= a(100) edge dislocation, b= a(110) edge dislocation, and b= a(010) screw dislocation, where b is the Burgers vector. For the edge dislocations, polarization can be induced by electrostriction alone, while flexoelectricity is essential for stabilizing the symmetric polarization pattern. The shear component of the flexoelectric tensor has a dominant effect on the magnitude and spatial distribution of the flexoelectric polarization. In contrast, no polarization is induced around the b= a(010) screw dislocation through either electrostriction or flexoelectricity. Finally, our findings provide an in-depth understanding of the role of flexoelectricity in inducing polarization around dislocation cores and offer insights into the defect engineering of dielectric/ferroelectric materials.
Crack growth in ductile single crystals (DuSCs) is orientation dependent due to the anisotropies of crystal plasticity and elastic tensor. This study develops a phase-field model incorporating both crystal plasticity and crack growth and proposes a general method to decompose the elastic energy into compressive and tensile parts to prevent crack growth under compression in the phase-field description. The phase-field model, in combination with three Euler angles, is employed to simulate orientation-dependent crack growth in DuSCs. The contributions from crystal plasticity and anisotropic elasticity are compared, and the former is found to dominate in the anisotropy of crack growth in copper single crystals. Furthermore, the simulation results demonstrate that crystal orientation strongly affects the heterogeneous distribution of plastic strain and the interaction between plastic strain and crack growth. High-throughput phase-field simulations are performed with exhaustive crystal orientations, and the results are explained based on the anisotropy of the Taylor factor.
The 10 September 2025 M w 4.1 earthquake in northeastern Utah, United States, had a focal depth 68 km beneath sea level, which is ∼20–25 km greater than estimates of local crustal thickness, making it a rare example of a continental mantle earthquake (CME). The focal depth is well resolved from arrival-time inversion (nearest station ∼13 km away) and moment tensor inversion of regional waveforms. Similar to other CMEs in the Intermountain West, there were no obvious aftershocks or foreshocks, and the waveforms were enriched in high-frequency energy. Spectral modeling gives a stress drop of ∼80 MPa and a radiation efficiency of ∼0.08, albeit with large uncertainties. The high stress drop and low radiation efficiency are consistent with a dissipative source process such as thermal runaway. Also similar to previous Intermountain West CMEs, the event occurred along the boundary of the Archean Wyoming craton, where pressure–temperature conditions favor ductile deformation. We hypothesize that edge-driven or regional-scale mantle convection produces increased strain rates near the craton boundary that make either conventional brittle failure or thermal runaway feasible at relatively high pressure–temperature conditions. High conductivity inferred around the edge of the craton may suggest that fluids also contribute to CME occurrence.
A deep convolutional neural network (DCNN) was used for microstructure reconstruction using artificial intelligence (MR-AI) by predicting local average fiber orientation distributions (FOD) in a 3D prepreg platelet molded composite (PPMC) pin bracket. To train the MR-AI model, surface strain fields from residual stresses simulated in PPMC plates were used as the input to the DCNN. A training dataset included PPMC plates with various degrees of global fiber alignment, based on the information obtained from high-fidelity flow simulation of a pin bracket. Further, the MR-AI model was then deployed to analyze FOD in the 3D pin bracket by conducting thermo-elastic residual stress analysis. Initially, the MR-AI model was established entirely on the synthetic simulation data. Then, a μCT scan of a physically molded pin bracket was used to create a finite element model that provided data for additional validation of the DCNN model. For the μCT scan finite element pin bracket the MR-AI model predicted the distribution of fiber orientation tensor components with MAE of 0.10 indicating a global prediction error of 10%. For the flow simulated pin bracket, the MR-AI model predicted the distribution of fiber orientation tensor components with a global prediction error of 11%. The MR-AI model showed the ability to predict regions of varying alignment in the base and flange of the pin bracket. The proposed MR-AI methodology allows for rapid prediction of FOD in geometrically complex parts and offers a promising path to detecting unique fiber orientation states in molded components.
Although atomistic simulations have contributed significantly to our understanding of twin boundary structure and migration in metals and alloys with hexagonal close packed (HCP) crystal structures, few direct atomistic studies of twinning have been conducted for other types of low symmetry materials, in large part due to a lack of reliable interatomic potentials. In this work, we examine twin boundary structure and migration in a tetragonal material, β-Sn, comparing high resolution Transmission Electron Microscopy (TEM) images of deformation twins in β-Sn to the results of direct atomistic simulations using multiple interatomic potentials. ML-based potentials developed in this work are found to give results consistent with our experimental data, revealing faceted twin boundary structures formed by the nucleation and motion of twinning disconnections. We use bicrystallographic methods in combination with atomistic simulations to analyze the structure, energy and shear coupled migration of observed twin facets in β-Sn. In analogy to Prismatic-Basal (PB/BP) interfaces in HCP metals, we discover low energy asymmetric Prismatic-A-plane (PA/AP) interfaces important to twin growth in β-Sn. Finally, a Moment Tensor Potential (MTP) and Rapid Artificial Neural Network (RANN) interatomic potential suitable for studying twinning and phase transformations in Sn are made publicly available as part of this work.
The 2023 smooth Lagrangian Crack-Band Model (slCBM), inspired by the 2020 invention of the gap test, prevented spurious damage localization during fracture growth by introducing the second gradient of the displacement field vector, named the “sprain,” as the localization limiter. The key idea was that, in the finite element implementation, the displacement vector and its gradient should be treated as independent fields with the lowest ( C 0 ) continuity, constrained by a second-order Lagrange multiplier tensor. Coupled with a realistic constitutive law for triaxial softening damage, such as microplane model M7, the known limitations of the classical Crack Band Model were eliminated. Here, we show that the slCBM closely reproduces the size effect revealed by the gap test at various crack-parallel stresses. To describe it, we present an approximate corrective formula, although a strong loading-path dependence limits its applicability. Except for the rare case of zero crack-parallel stresses, the fracture predictions of the line crack models (linear elastic fracture mechanics, phase-field, extended finite element method (XFEM), cohesive crack models) can be as much as 100% in error. We argue that the localization limiter concept must be extended by including the resistance to material rotation gradients. We also show that, without this resistance, the existing strain-gradient damage theories may predict a wrong fracture pattern and have, for Mode II and III fractures, a load capacity error as much as 55%. Finally, we argue that the crack-parallel stress effect must occur in all materials, ranging from concrete to atomistically sharp cracks in crystals.
The Nye tensor, which quantifies the density of Burgers vector for a given dislocation line direction, can be effectively used to characterize dislocation content in bulk crystals from atomic-resolution transmission electron microscopy images. The Nye tensor can be calculated from these images, in part because the reference state is simply defined by the lattice of the perfect crystal. The application of the Nye tensor to interfacial line defects, for which the natural reference state is the dichromatic pattern of the two grains in their reference orientation, poses additional challenges. In this work, we present a method that employs the Nye tensor to characterize the edge dislocation content of line defects at grain boundaries from atomic-resolution images. This approach enables us to rapidly characterize all edge dislocation content along a grain boundary. Additionally, the Nye tensor provides information about line defect core structure. Finally, we demonstrate this method on two exemplar defects: a twin boundary disconnection and a facet junction in face-centered cubic Au.
The nature and Equation of State (EOS) of dense neutron-rich matter are still very poorly known, while they have broad impacts on many interesting issues in both astrophysics and nuclear physics. In particular, the nuclear symmetry energy $E_{\textrm{sym}}(\rho )$ encoding the cost to make nuclear matter more neutron-rich has been the most uncertain component of the EOS of dense neutron-rich nucleonic matter. It significantly affects the radii, tidal deformations, cooling rates, and frequencies of various oscillation modes of isolated neutron stars as well as the strain amplitude and frequencies of gravitational waves from their mergers, besides its many effects on the structures of nuclei as well as the dynamics and observables of their collisions. Siemens (1970s) observed that $E_{\textrm{sym}}(\rho )$ scales as $(\rho /\rho _0)^{2/3}$ near the saturation density $\rho _0$ of nuclear matter, since both the kinetic part and the potential contribution (quadratic in momentum) exhibit this dependence. The scaling holds if: (1) the nucleon isoscalar potential is quadratic in momentum, and (2) the isovector interaction is weakly density-dependent. After examining many empirical evidences and understanding theoretical findings in the literature, we conclude that: (1) Siemens’ $\rho ^{2/3}$ scaling is robust and serves as a valuable benchmark for both nuclear theories and experiments up to $2\rho _0$ but breaks down at higher densities, (2) Experimental and theoretical findings about $E_{\textrm{sym}}(\rho )$ up to $2\rho _0$ are broadly consistent, but uncertainties remain large for its curvature $K_{\textrm{sym}}(\rho )$ and higher-order parameters, (3) Above $2\rho _0$ , uncertainties grow due to poorly constrained spin-isospin-dependent tensor and three-body forces as well as the resulting nucleon short-range correlations. Looking forward, combining signals from both observations of neutron stars and terrestrial heavy-ion reaction experiments is the most promising path to finally constraining the high-density $E_{\textrm{sym}}(\rho )$ and the EOS of supradense neutron-rich matter. Multiple examples of community efforts to further constrain the high-density $E_{\textrm{sym}}(\rho )$ using both real and mocked data of present and future high-precision observations of neutron stars, as well as heavy-ion collisions involving high-energy rare isotopes, are briefly reviewed.
Statement of the problem or situation that is being addressed. Although thermal and cold neutron scattering is widely used and is critical for success in many areas of materials science and engineering, relatively low neutron fluxes severely limit applications of not only laboratory neutrons generators, but also large national neutron facilities. State-of-the-art thermal and cold neutron sources are large expensive national facilities, which serve diverse community of scientific and industrial users. The constant need to improve the instruments performance, stems from the fact that neutron methods are gaining in popularity, and becoming more and more powerful, while new neutron sources are not being constructed to keep pace with the developments and needs of the scientific community. Small research reactors at universities and National Labs, and laboratory-based neutron generators, are necessary not only for education and training, but also when samples cannot be transported to other facilities. However, the standard neutron techniques, which were developed for high-flux facilities, require much higher efficiencies to be used effectively with the low fluxes of small sources. Thus, the efficient use of neutron sources, such as with our proposed analyzer, is important for the progress and broader use of these neutron techniques. General statement of how this problem is being addressed. We propose to design and demonstrate novel diffractive optical device, which will enable very efficient residual stress neutron diffractometers. The proposed device will be a multi-foil analyzer, where each foil is constructed of focusing bent single crystals of Si. Such device will enable polychromatic residual stress neutron diffraction. At large national facilities, such as at Oak Ridge National Laboratory, these analyzers would enable very fast measurements for determining residual stress tensors, raster large samples or screen multiple samples. Commercial Applications and Other Benefits The outcome of this project would be the demonstration of commercial devices, novel neutron optical components, which could be utilized to improve the performance of existing instruments or build novel neutron scattering instruments at DOE neutron facilities and commercial laboratory neutron sources. These new devices will widen the scope of research conducted using neutrons and enable measurements not feasible at present. Summary for Members of Congress Thermal and cold neutron beams are a powerful materials science probe, which provide unique information about the structure of matter. The proposed innovations expand the reach of neutron-based investigations to new materials and industries by enabling new instrumentation capabilities, thereby greatly enhancing and expanding the role of small, laboratory-based neutron instrumentation, and improving education and training of neutron users.
A major drawback of Boussinesq-type subgrid-scale stress models used in large-eddy simulations is the inherent assumption of alignment between large-scale strain rates and filtered subgrid-stresses. A priori analyses using direct numerical simulation (DNS) data have shown that this assumption is invalid locally as subgrid-scale stresses are poorly correlated with the large-scale strain rates [J. Bardina, J. Ferziger, and W. Reynolds, Improved subgrid-scale models for large-eddy simulation, in Proceedings of the 13th Fluid and Plasmadynamics Conference, AIAA (1980); C. Meneveau and K. Katz, Scale-invariance and turbulence models for large-eddy simulation, Ann. Rev. Fluid Mech. 32, 1 (2000)]. In the present work, a new, non-Boussinesq subgrid-scale model is presented where the model coefficients are computed dynamically. Some previous non-Boussinesq models have observed issues in providing adequate dissipation of turbulent kinetic energy [e.g., Bardina et al., Proceedings of the 13th Fluid and Plasmadynamics Conference (1980); R. A. Clark, J. Ferziger, and W.C. Reynolds. Evaluation of subgrid-scale models using an accurately simulated turbulent flow, J. Fluid Mech. 91, 1 (1979); S. Stolz and N. A. Adams, An approximate deconvolution procedure for large-eddy simulation, Phys. Fluids 11, 1699 (1999)]; however, the present model is shown to provide sufficient dissipation using dynamic coefficients. Modeled subgrid-scale Reynolds stresses satisfy the consistency requirements of the governing equations for large-eddy simulation (LES), vanish in laminar flow and at solid boundaries, and have the correct asymptotic behavior in the near-wall region of a turbulent boundary layer. The new model, referred to as the dynamic tensor-coefficient Smagorinsky model (DTCSM), has been tested in simulations of canonical flows: decaying and forced homogeneous isotropic turbulence, and wall-modeled turbulent channel flow at high Reynolds numbers. The results show favorable agreement with DNS data. It has been shown that DTCSM offers similar predictive capabilities as the dynamic Smagorinsky model for canonical flows. In order to assess the performance of DTCSM in more complex flows, wall-modeled simulations of high Reynolds number flow over a Gaussian bump (Boeing speed bump) exhibiting smooth-body flow separation are performed. Predictions of surface pressure and skin friction, compared against DNS and experimental data, show improved accuracy from DTCSM in comparison to existing static coefficient (Vreman) and dynamic Smagorinsky model. The computational cost of performing LES with this model is up to 15% higher than the dynamic Smagorinsky model.