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DOE OSTI2025

Strongly nonlinear wave propagation in elasto-plastic metamaterials: Low-order dynamic modeling

Nonlinear elastic metamaterials are known to support a variety of dynamic phenomena that enhance our capacity to manipulate elastic waves. Since these properties stem from complex, subwavelength geometry, full-scale dynamic simulations are often prohibitively expensive at scales of interest. Prior studies have therefore utilized low-order effective medium models, such as discrete mass-spring lattices, to capture essential properties in the long-wavelength limit. While models of this type have been successfully implemented for a wide variety of nonlinear elastic systems, they have predominantly considered dynamics depending only on the instantaneous kinematics of the lattice, neglecting history-dependent effects, such as wear and plasticity. Here, to address this limitation, the present study develops a lattice-based modeling framework for nonlinear elastic metamaterials undergoing plastic deformation. Due to the history- and rate-dependent nature of plasticity, the framework generally yields a system of differential-algebraic equations whose computational cost is significantly greater than an elastic system of comparable size. We demonstrate the method using several models inspired by classical lattice dynamics and continuum plasticity theory and explore means to obtain empirical plasticity models for general geometries, thereby gaining insight into the influence of microstructural plasticity on effective material performance, which can be used to improve the design of nonlinear mechanical metamaterials.

Dynamic simulation↗

DOE OSTI2022

Atomistic deformation mechanism of silicon under laser-driven shock compression

Abstract Silicon (Si) is one of the most abundant elements on Earth, and it is the most widely used semiconductor. Despite extensive study, some properties of Si, such as its behaviour under dynamic compression, remain elusive. A detailed understanding of Si deformation is crucial for various fields, ranging from planetary science to materials design. Simulations suggest that in Si the shear stress generated during shock compression is released via a high-pressure phase transition, challenging the classical picture of relaxation via defect-mediated plasticity. However, direct evidence supporting either deformation mechanism remains elusive. Here, we use sub-picosecond, highly-monochromatic x-ray diffraction to study (100)-oriented single-crystal Si under laser-driven shock compression. We provide the first unambiguous, time-resolved picture of Si deformation at ultra-high strain rates, demonstrating the predicted shear release via phase transition. Our results resolve the longstanding controversy on silicon deformation and provide direct proof of strain rate-dependent deformation mechanisms in a non-metallic system.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Microstructure characterization and elastic-plastic self-consistent simulation studies of anisotropic deformation of β -tin

Uniaxial compression tests of 99.9% pure polycrystalline $β$-tin (Sn) were conducted at various strain rates (10 -3 /s, 10 -1 /s and 1/s) and temperatures (294 K and 193 K) to understand the effects of these variables on the stress–strain response, microstructure evolution, and stress relaxation behavior. Multiple Sn specimens were subjected to complex compressive loading/unloading/reloading paths at different strain rates. Specimens initially compressed at higher strain rates showed strain rate-dependent texture evolution and more pronounced relaxation upon reloading, as compared to those pre-strained at lower rates at room temperature (RT). Compression tests conducted at low temperature (193 K) revealed increased strength, similar to the enhanced strength observed when the strain rate was increased at RT. Neutron diffraction was employed to characterize the initial and final bulk textures of the RT specimens. Electron backscatter diffraction was utilized to examine the crystallographic grain orientation and morphology, thereby identifying the signatures of dislocation-mediated deformation, grain refinement, recrystallization, and twinning behaviors. Elastic-plastic self-consistent simulations were performed to investigate the deformation modes responsible for the strain rate-dependent macroscopic stress–strain response and texture evolution. Effects of crystallographic orientation on stress relaxation behavior was also examined. In conclusion, the model predictions are in reasonable agreement with experimental observations.

36 MATERIALS SCIENCE↗

DOE OSTI2025

2024 Second Half Semi Annual Report: Modeling plasticity-mediated flow in metals with pressurized cavities

The objective is to better predict the bulk-scale mechanical behavior of porous metals that have over pressurized cavities (e.g., irradiated metals with helium bubbles) by quantifying the complex coupling among cavity aspects (e.g., size distribution, inhomogeneous overpressure values, spatial arrangement) and metal properties (e.g., rate-dependency, crystallographic lattice). This requires up-scaling local mechanical fields from the single crystal scale and will be accomplished using a homogenization approach that combines full-field numerical simulations, analytical formalisms, and physics-informed machine learning to produce symbolically-defined constitutive equations (e.g., gauge functions). These equations will satisfy the objective because they enable computationally efficient predictions that approach the accuracy of computationally expensive full-field numerical simulations, abide by theoretical requirements (e.g., conservation of energy, work conjugacy), and retain the transparency of analytical models.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Facet-Dependent Doping and Dopant-Dependent Faceting in Si-Doped GaAsSb Nanowires

Here, we correlate the spatial distributions of Si, Sb, and rotational twins in Si-doped GaAs 1-x Sb x nanowires. GaAs 1-x Sb x nanowires were grown epitaxially on Si(111) substrates by tuning process conditions to achieve repeated nucleation of rotational twins and growth along the [111]B direction; dilute Sb and Si fluxes were chosen to create a sufficient twin density to achieve high yield while avoiding growth of the wurtzite phase. While the impact of Si and Sb on twin density and nanowire growth rate has been previously reported, the facet-dependent incorporation of these species has not been established. Scanning transmission electron microscopy was used to confirm that Sb incorporates preferentially on the (111)B facets relative to {1 ̅1 ̅0} facets prior to nucleation of a rotational twin. With periodic twinning, this facet dependence leads to alternating regions of enriched and depleted Sb concentration attributed to a growth rate-dependent Sb-As-exchange mechanism. Atom probe tomography measurements establish that while Si doping is not perturbed by twinning on (111)B facets, Si and Sb concentrations are anti-correlated for growth on non-(111)B facets. Density functional theory calculations underpin a thermodynamic model that explains the observed anisotropies in dopant incorporation.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Understanding Oxide–Metal Interactions During Hot Isostatic Pressing to Diffusion Bond Aluminum Alloy 6061 Plates

The interaction between Mg, Si, and Al 2 O 3 during hot isostatic pressing diffusion bonding of aluminum alloy 6061 (AA6061) plates was investigated through thermodynamic calculations and experimental microstructural characterization. Thermodynamic calculations as functions of temperature, pressure, and composition revealed that the interaction among Mg, Si, and Al 2 O 3 yields Mg 2 Si and either MgO + Al or MgAl 2 O 4 + Al, facilitating the reduction of Al 2 O 3 and allowing Al/Al metallic bonds to form. Total pressure variation had a negligible influence on the oxygen partial pressure, and consequently, the reaction product formation. Oxygen partial pressure variation as a function of temperature and initial amount of Al 2 O 3 determined the formation of either MgO or MgAl 2 O 4 . Experimental Hot Isostatic Pressure (HIP) bonding at 723 K and 833 K under a constant pressure of 1017 atm documented the cooling rate-dependent formation of β–Mg 2 Si precipitates. High-resolution transmission electron microscopy imaging and selected area electron diffraction patterns verified the formation of β–Mg 2 Si and MgO at the interface but did not detect MgAl 2 O 4 . In conclusion, findings from this study clarify the role of thermochemical interactions in oxide disruption and bonding mechanisms during HIP diffusion bonding of AA6061 and provide guidance for optimizing joining processes for monolithic nuclear fuel assemblies.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

Implications of point defect accumulation on UO 2 thermal conductivity and fission gas release under accelerated fuel irradiation

Evaluation of thermal properties is a crucial factor for nuclear fuel performance. During reactor operation, the accumulation of fission products and irradiation-induced lattice defects are responsible for degradation in thermal conductivity. Consequently, it affects fuel temperature and fission gas release (FGR) among other Multiphysics processes important for economics and safety analysis. We analyze the implications of point defects (PD) accumulation described using a rate theory (RT) Model on lattice thermal conductivity of UO 2 . Here, we demonstrate that fission rate-dependent point defect concentrations have the largest impact on in-pile thermal conductivity in the periphery of light water reactor fuels below a temperature threshold governed by the migration barrier of defects. Our analysis provides a mechanistic description of this phenomena which current fuel performance codes treat empirically. The reduction of thermal conductivity in the low -temperature rim region acts as additional thermal resistance and leads to a temperature notably larger than suggested by Lucuta thermal conductivity correlation. These effects are anticipated to have notable impacts when fuels are exposed to accelerated radiation. The impact of such point defect-informed treatment of thermal conductivity on fuel performance is evaluated by a detailed analysis of fission gas behavior and its release. We consider several models capturing different stages of fission gas bubble evolution and fission gas release (FGR). Finally, a new fission rate-dependent correction to the Lucuta correlation is proposed. The results show a significant reduction in thermal conductivity at the fuels’ periphery and an increase in fuel centerline temperature specifically at low burnups. Ultimately a modified LC shows a higher FGR compared to the original LC, while the acceleration process results in a reduction in overall FGR.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

Understanding rate-dependent textured growth in zinc electrodeposition via high-throughput in situ x-ray diffraction

Zn-ion batteries with aqueous electrolytes are promising for large-scale energy storage as they are low-cost, environment-friendly and safe. The commercialization of Zn-ion batteries is hindered by several challenges such as the formation of detrimental Zn dendrites. High current density is previously thought to stimulate the dendritic growth of metals such as Li in electrodeposition. However, our study finds that for metallic Zn negative electrode in Zn-ion batteries, high-current deposition results in a dense and flat Zn layer with a (002) texture, which extends the cycling life. Low-current deposition, on the other hand, leads to a porous and dendritic morphology and a short cycling life. Using a synchrotron-based high-throughput in situ X-ray diffraction method we recently developed, Zn deposition under different conditions is systematically investigated, and a texture formation mechanism is proposed. Based on these findings, we suggest guidelines for designing cycling protocols that enable long-lasting Zn-ion batteries.

36 MATERIALS SCIENCE↗

DOE OSTI2025

A rheological model for loose sands with insights from DEM

A rheological model for loose granular media is developed to capture both solid-like and fluid-like responses during shearing. The proposed model is built by following the mathematical structure of an extended Kelvin–Voigt model, where an elastic spring and plastic slider act in parallel to a viscous damper. This arrangement requires the partition of the total stress into rate-independent and rate-dependent stress components. To model the solid-like behavior, a simple frictional plasticity model is adopted without modifications, thus contributing to the rate-independent stress. Instead, the fluid-like or rate-dependent stress is further decomposed into deviatoric and volumetric parts, by proposing a new formulation based on a combination of the μ(I) relation, originally developed under pressure-controlled shear, with a pressure-shear rate relation derived under volume-controlled shear. The proposed formulation allows the model to capture both the increase in the friction coefficient and the enhanced dilation at high shear rates. High-fidelity simulation data, obtained from discrete element method and multiscale modelling, are used to evaluate the performance of the proposed constitutive model. The model provides accurate results under both drained and undrained simple shear paths across a wide range of shear rates. Furthermore, it successfully reproduces at much lower computational cost the flowslide mobility computed through multiscale simulations, which is primarily regulated by the shear rate dependence of the material properties during the dynamic runout stage.

Elasticity↗

DOE OSTI2023

A constitutive framework for rocks undergoing solid dissolution

Here, we formulate a time-dependent damage theory for rocks subjected to mechanical deformation and solid dissolution. The constitutive description is inspired by the transition state theory, which states that the rate of dissolution is a function of the reactive surface area measured through the crack density in the volume. We use a gradient-enhanced damage framework in which damage depends on the deformation of the material as well as on the amount of solid mass dissolved over time. The gradient-enhanced formulation is characterized by a three-field variational formulation with the solid displacement, nonlocal equivalent strain, and nonlocal rate of solid dissolution as the basic state variables. Traditionally, time-independent damage theories have only allowed damage to increase with increasing external load. In the proposed framework, the degree of damage may increase due to solid dissolution even when the external load is held fixed. In this way, solid dissolution is viewed as a process that is responsible for bringing about rate-dependent effects such as creep and stress-relaxation, which are two common features of geomaterial behavior.

42 ENGINEERING↗

DOE OSTI2023

A statistical mechanics framework for polymer chain scission, based on the concepts of distorted bond potential and asymptotic matching

To design increasingly tough, resilient, and fatigue-resistant elastomers and hydrogels, the relationship between controllable network parameters at the molecular level (bond type, non-uniform chain length, entanglement density, etc.) to macroscopic quantities that govern damage and failure must be established. Many of the most successful constitutive models for elastomers have been rooted in statistical mechanical treatments of polymer chains. Typically, such constitutive models have used variants of the freely jointed chain model with rigid links. However, since the free energy state of a polymer chain is dominated by enthalpic bond distortion effects as the chain approaches its rupture point, bond extensibility ought to be accounted for if the model is intended to capture chain rupture. To that end, a new bond potential is supplemented to the freely jointed chain model (as derived in the u FJC framework of Buche and Silberstein (2021) and Buche et al. (2022)), which we have extended to yield a tractable, closed-form model of single chain behavior that should be amenable to continuum-level constitutive model development. Inspired by the asymptotically matched u FJC model response in both the low/intermediate chain force and high chain force regimes, a simple, quasi-polynomial bond potential energy function is derived. This bond potential exhibits harmonic behavior near the equilibrium state and anharmonic behavior for large bond stretches tending to a characteristic energy plateau (akin to the Lennard-Jones and Morse bond potentials). Using this bond potential, approximate yet highly-accurate analytical functions for bond stretch and chain force dependent upon chain stretch are established. Then, using this polymer chain model, a stochastic thermal fluctuation-driven chain rupture framework is developed. This framework is based upon a force-modified tilted bond potential that accounts for distortional bond potential energy, allowing for the derivation and subsequent calculation of the dissipated chain scission energy. Here, the cases of rate-dependent and rate-independent scission are accounted for throughout the rupture framework. The impact of Kuhn segment number on chain rupture behavior is also investigated. The model is fit to single chain mechanical response data collected from atomic force microscopy tensile tests for validation and to glean deeper insight into the molecular physics taking place. Due to their analytical nature, this polymer chain model and the associated rupture framework can in the future be implemented in finite element models accounting for fracture and fatigue in polydisperse elastomer networks.

36 MATERIALS SCIENCE↗

DOE OSTI2026

A physically based mechanical model for Mullins effect in thermoplastic polyurethanes

Despite decades of research, connecting the chemical and physical structure of thermoplastic polyurethanes to their mechanical properties remains highly challenging. Of particular note are their large-deformation and rate-dependent behaviors, which vary greatly with molecular chemistry, including the type and relative content of soft and hard segments. In this work, we develop a physically motivated mechanical theory for predicting the behavior of thermoplastic polyurethanes. The theory incorporates a representation of microstructural evolution during mechanical deformation, which captures the signatures of stress softening over cyclic loading (commonly referred to as the Mullins effect). There are only eight physically motivated fitting parameters, including a direct dependence on the hard segment fraction. The model predicts that increasing the hard segment fraction leads to higher stiffness and greater energy dissipation, in quantitative agreement with published experimental data. Furthermore, we provide a comprehensive analysis of the model and validate its predictions across several independent datasets focused on mechanical characterization. Direct comparisons to experimental data demonstrate its predictive capability on the effect of loading rate, cyclic deformations, and applied tension or compression. Altogether, this work establishes a predictive framework that connects polymer chemistry and microstructure to emergent mechanical behaviors.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Modeling plasticity-mediated void growth at the single crystal scale: A physics-informed machine learning approach

Modeling the evolution of voids during plastic flow as well as their effects on plastic dissipation is critical for both component manufacturing and lifetime estimation purposes. To this end, we propose a rate-dependent constitutive model to homogenize the effects of semi-randomly distributed voids on single crystal plasticity whilst capturing void interaction and plastic anisotropy. Here, this present work focuses on the case of face centered cubic crystals to introduce an anisotropic gauge function applicable within the crystal plasticity formalism. The approach combines analytical methods to describe the micromechanics of the system in combination with symbolic regression to capture analytically intractable mechanisms from data. The hybrid framework uses a physics-informed genetic programming-based symbolic regression algorithm to solve a multiform optimization problem simultaneously producing a new gauge function and a new strain rate equation. This is also a multi-objective optimization problem with many competing objectives. A new search and selection step is introduced to the genetic algorithm that promotes convergence toward a global solution that better satisfies all the objectives. Overall, the symbolic equations produced leverage data-driven methods to achieve greater accuracy than comparable alternatives on an analytically intractable problem while maintaining model transparency.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Recrystallization driven softening and heating rate dependencies of FeCrAl nuclear fuel cladding during accident transients

A refined understanding of FeCrAl cladding behavior during rapid transients is critical for its potential deployment in light-water reactors. Current assessments focus on transient burst testing metrics such as balloon geometry, burst temperature, and hoop stress, often used as proxies for simpler conventional tensile properties. However, directly correlating isothermal tensile and creep data with accident transient scenarios remains a challenge, although it is essential for high fidelity model development. Recent modeling based on tensile tests up to 800 °C, conducted with both immediate loading and a 10-minute soak, showed that immediate loading better predicts experimental burst temperatures, indicating a thermal softening effect. Building upon this observation, the current study connects transient performance, microstructural evolution, and high-temperature tensile properties by leveraging results from C26M claddings burst tests performed at heating rates of 1–50 °C/s and hoop stresses from 25 to 100 MPa. At 25 MPa, rupture temperatures varied by only 6 °C, but at 100 MPa, the difference reached 116 °C, with faster heating yielding higher burst temperatures. Microstructural analysis identified recrystallization as the primary cause of heating rate-dependent softening, eliminating prior cold-working. In-situ thermomechanical data linked ballooning onset to localized instabilities, similar to ultimate tensile strength behavior in conventional tensile tests. High heating rates correlated with immediate loading tensile data, while lower rates matched soaked data. Furthermore, by linking burst performance to microstructural evolution and tensile properties, this work provides a foundation for more accurate modeling of FeCrAl claddings and potentially other Fe-based materials under accident conditions.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2023

Effects of particle size, shape and loading rate on the normal compaction of an advanced granular ceramic

Compaction behavior of granular materials is influenced by strain rate, particle size, and shape. In this report, boron carbide powders with different particle sizes under uni-axial strain conditions are studied using quasi-static compression, dynamic Kolsky bar experiments and normal plate impact. A rounded powder is compacted to investigate the effect of particle shape. The normal plate impact technique is an excellent tool in characterization of powder compaction behavior up to strain rates of ~10 5 s -1 . From our experiments, granular boron carbide shows a highly compressible behavior with significant volume compaction. Constitutive responses are obtained for four powders. Particle fracture is identified as key deformation mechanism. Dynamic loading introduces more particle fragmentation than quasi-static loading. Morphological characterization of particle shapes shows that the deformation from powder compaction alters the particle shape distribution, which is also rate-dependent. Particle size, shape and strain rate effects on the normal stress are discussed accordingly.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Flow-Driven Stretch Fluctuations Govern the Nonlinear Viscoelasticity of Elongating Associative Polymer Networks

We use nonequilibrium molecular dynamics simulations to verify recent tube-model predictions that associative polymer networks exhibit broad stretch fluctuations during elongational flow. Simulations further show that these fluctuating dynamics give rise to the rate-dependent extensional viscosity 𝜂 𝐸 measured in filament stretching experiments on H-bonding networks. Simulations model bivalent associative networks with a reactive bead-spring model for varying association strength and extensional strain rate. We observe that stretch fluctuations are driven by a new form of chain tumbling, where chains continually collapse and elongate as their associations break and reform within the advecting network. This produces a broad, nearly uniform distribution of chain stretch over a wide range of strain rates, manifesting as a rate-independent plateau in the extensional stress. Our results show that the nonlinear viscoelasticity of associative networks is dominated by large fluctuations in molecular response, which cannot be captured by current mean-field models.

biomimetic & bio-inspired materials↗

DOE OSTI2024

On the length scale and rate-dependent mechanical behavior of monolithic (oxy)sulfidic glassy solid-state electrolytes

In the controlled atmosphere of a dedicated glove box, nanoindentation performed with a diamond Berkovich indenter tip has been used to examine the mechanical behavior of three (oxy)sulfide solid-state electrolytes (SSEs), 70Li 2 S·(30–x)P 2 S 5 ·xP 2 O 5 (x = 0, 2, and 5). At a drive frequency of 120 Hz, the elastic modulus is found to be predominantly depth independent over the range of 100 nm to 1 μm and generally insensitive to the varying mol fraction of oxygen (0, 2, and 5%) as well as the imposed strain rates of 0.025, 0.05, and 0.1 1/s. All three SSEs exhibit significant room-temperature creep. Strain burst activity observed during loading (potentially representative of pore collapse or cracking) is attenuated with the addition of oxygen. The hardness is found to be insensitive to the imposed strain rates but varying with depth and oxygen content. Furthermore, the highest oxygen concentration yields the lowest hardness and strongest depth dependence.

36 MATERIALS SCIENCE↗

DOE OSTI2023

On the flow-stress model of Preston, Tonks, and Wallace - Observations, parameter constraints, and implementations (Rev. 1)

A detailed discussion about the PTW flow-stress model has been presented, including theoretical considerations, model calibrations to experimental data, and model implementations in LANL ASC hydro-codes. The main findings are: In order to reproduce the intended behavior of the PTW model at high strain rates, the following conditions on the model parameters need to be valid: y 1 ≥ s 0 and y 2 ≥ β ; When the conditions above are not satisfied, PTW and PTW_Mod1 have slightly different behavior in the phonon-drag regime, and should be treated as different models. PTW exhibits a discontinuity above the critical strain rate. PTW_Mod1 does not show such a discontinuity but implies a different strain-rate dependence at high strain rates. Examples of this behavior include older calibrations for stainless steel and depleted uranium; In the thermal-activation regime, some flexibility was introduced in the original PTW model to allow for different rate-dependent behaviors at intermediate strain rates. Example: copper. However, many material calibrations do not require this extra flexibility, and the complexity and ambiguity of the intended behavior can be partially blamed for the inconsistent model implementations across ASC codes; The limit for the material constant p going to zero is well defined and leads to a simplified flow-stress equation, discontinuity free; Modern calibrations of the PTW parameters are done using Impala. Constraints on the PTW parameters are enforced; Implementation of the PTW model in LANL ASC hydro-codes suffered of several shortcom ings. At the time of writing, FLAG and xRAGE contain consistent and correct implemen tations of the PTW and PTW_Mod1 models. Corresponding changes to Pagosa have been suggested.

36 MATERIALS SCIENCE↗