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DOE OSTI2022

Analyses of internal structures and defects in materials using physics-informed neural networks

Characterizing internal structures and defects in materials is a challenging task, often requiring solutions to inverse problems with unknown topology, geometry, material properties, and nonlinear deformation. Here, we present a general framework based on physics-informed neural networks for identifying unknown geometric and material parameters. By using a mesh-free method, we parameterize the geometry of the material using a differentiable and trainable method that can identify multiple structural features. We validate this approach for materials with internal voids/inclusions using constitutive models that encompass the spectrum of linear elasticity, hyperelasticity, and plasticity. We predict the size, shape, and location of the internal void/inclusion as well as the elastic modulus of the inclusion. Our general framework can be applied to other inverse problems in different applications that involve unknown material properties and highly deformable geometries, targeting material characterization, quality assurance, and structural design.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Effects of Strain Rate and Temperature on the Mechanical Properties of Simulated Silica Ionogels

Ionogels are hybrid materials formed by impregnating the pore space of a solid matrix with a conducting ionic liquid. By combining the properties of both component materials, ionogels can act as self-supporting electrolytes in Li batteries. In this study, molecular dynamics simulations are used to investigate the dependence of mechanical properties of silica ionogels on solid fraction, temperature, and pore width. Comparisons are made with corresponding aerogels. We find that the solid matrix fraction increases the moduli and strength of the ionogel. This varies nonlinearly with temperature and strain rate, according to the contribution of the viscous ionic liquid to resisting deformation. Additionally, owing to the temperature and strain sensitivity of the ionic liquid viscosity, the mechanical properties approach a linear mixing law at high temperature and low strain rates. The median pore width of the solid matrix plays a complex role, with its influence varying qualitatively with deformation mode. Narrower pores increase the relevant elastic modulus under shear and uniaxial compression but reduce the modulus obtained under uniaxial tension. Conversely, shear and tensile strength are increased by narrowing the pore width. All of these pore size effects become more pronounced as the silica fraction increases. Pore size effects, similar to the effects of temperature and strain rate, are linked to the ease of fluid redistribution within the pore space during deformation-induced changes in the geometry of the pores.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Modeling the Nonlinear Rheology of Polymer Additive Manufacturing

This report summarizes molecular and continuum simulation studies focused on developing physics - based predictive models for the evolution of polymer molecular order during the nonlinear processing flows of additive manufacturing. Our molecular simulations of polymer elongation flows identified novel mechanisms of fluid dissipation for various polymer architectures that might be harnessed to enhance material processability. In order to predict the complex thermal and flow history of polymer realistic additive manufacturing processes, we have developed and deployed a high - performance mesh - free hydrodynamics module in Sandia's LAMMPS software. This module called RHEO – short for Reproducing Hydrodynamics and Elastic Objects – hybridizes an updated - Lagrange reproducing - kernel method for complex fluids with a bonded particle method (BPM) to capture solidification and solid objects in multiphase flows. In combination, our two methods allow rapid, multiscale characterization of the hydrodynamics and molecular evolution of polymers in realistic processing geometries.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Egg yolk as a model for gelation: From rheometry to flow physics

Egg yolks are an excellent model for studying sol-gel transitions, particularly the power law viscoelasticity that defines the critical point of gelation. However, prior studies lack comprehensive datasets and fail to visualize flow behavior linked to temperature and time-dependent linear and nonlinear rheology. Here, we present a detailed dataset characterizing egg yolk viscoelasticity across temperature, time, and forcing amplitude using oscillatory shear, step strain, step stress, and constant high strain rate. Novel protorheology visualizations link rheological properties with observable flow behavior. Our findings highlight the nuanced determination of the critical gel point, emphasizing observation timescale dependencies. We compare methods to identify critical temperatures for gelation, including power law viscoelasticity, moduli crossover, diverging zero-shear viscosity, and emerging equilibrium elastic modulus, while visualizing flow consequences near these transitions. Egg yolk is an accessible, realistic, and nontoxic material relevant to the physicist and the chef alike, making it ideal for understanding the rheology of critical gels. By integrating protorheology photos and videos with rigorous rheometric data, we deepen the understanding of critical gels, with broader impacts for studying other materials with sol-gel transitions.

Marsh, Maxwell C. [Department of Mechanical Scienc↗

DOE OSTI2023

Soliton formation and topology manipulation of coupled spins via ultrafast re-magnetization

The major goal of the project was to explore the properties of magnetic order driven far out of equilibrium by optical excitations. These include fundamental questions related to the interplay of magnetic, structural and electronic degrees of freedom in materials that are optically excited. These problems break down in short term quenching of the magnetization as a results of the energy of the optical pulse studying how the energy of the optical pulse and the angular momentum of the magnetization flow between the different degrees of freedom. This is followed by the longer time re-emergence of the magnetism as the system cools. Within this goal we explored the formation of solitons, both with and without non-trivial topology, via rapid re-magnetization processes after optical-driven ultrafast demagnetization. Guided by theory, we predict that turbulence and modulational instabilities will drive the formation of solitons, including dispersive shock waves, magnon droplets, and skyrmions. In the case of topological defect formation, i.e. skyrmion generation, related processes have long been predicted based on general principles of symmetry-breaking phase transitions; the density of topological defects in a long-range-ordered phase can be controlled by varying the quench rate through the second-order phase transition, i.e. the Kibble-Zurek (KZ) mechanism. We, more broadly, had the goal to study a range of other emergent magnetic behaviors after optical excitation. While great attention has been given to ultrafast demagnetization, less is known of the subsequent spin dynamics and coupling to the lattice. What is increasingly appreciated is that ultrafast demagnetization leads to spin currents that can carry angular momentum from the rapidly demagnetized sample. These spin currents appear in many ways but fundamentally controls demagnetization, drives interactions between regions of the material, and control the spin resulting structure. They can be probed many ways including THz emission which, in turn, gives insight into the demagnetization processes. Simultaneously if there is magneto-elastic coupling ultrafast demagnetization can drive structural excitations that are not expected from thermal energy added to the lattice. We explored a range of complex phenomena that arise from photo-excitation of magnetic systems with the coupling of electronic, magnetic and structural degrees of freedom. We have made a number of fundamental discoveries that are reflected in our publications list with additional work still being prepared for publication. Highlights of this work include (i) ultra-efficient, nonlinear THz surface acoustics (ii) spin-current-mediated rapid magnon localization and coalescence, (iii) spin-wave soliton formation in ferromagnetic FePt nanoparticles, (iv) dynamic phonon coupling in elemental antiferromagnetic Cr, (v) THz emission from Co/Pt bilayers and FeRh/Pt bilayers, (vi) theoretical investigation of spin hydrodynamics, solitons and shock waves, and (vii) ultrafast perturbation of magnetic domains by optical pumping.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Stress-induced phase transitions in nanoscale CuInP 2 S 6

Using the Landau-Devonshire approach and available experimental results, we constructed multiwell thermodynamic potential of the layered ferroelectric CuInP 2 S 6 (CIPS). The analysis of temperature dependences of the dielectric permittivity and lattice constants for different applied pressures unexpectedly reveals the critically important role of a nonlinear electrostriction in this material. With the nonlinear electrostriction included we calculated the temperature and pressure phase diagrams and spontaneous polarization of a bulk CIPS, within the assumed range of applicable temperatures and applied pressures. Using the developed thermodynamic potential, we revealed the strain-induced phase transitions in thin epitaxial СIPS films, as well as the stress-induced phase transitions in СIPS nanoparticles, the shape of which varies from prolate needles to oblate disks. Furthermore, w also revealed the strong influence of a mismatch strain, elastic stress, and shape anisotropy on the phase diagrams and polar properties of a nanoscale CIPS, and derived analytical expressions allowing for elastic control of the nanoscale CIPS polar properties. Hence obtained results can be of particular interest for the strain engineering of nanoscale layered ferroelectrics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Effective data sampling strategies and boundary condition constraints of physics-informed neural networks for identifying material properties in solid mechanics

Material identification is critical for understanding the relationship between mechanical properties and the associated mechanical functions. However, material identification is a challenging task, especially when the characteristic of the material is highly nonlinear in nature, as is common in biological tissue. In this work, we identify unknown material properties in continuum solid mechanics via physics-informed neural networks (PINNs). To improve the accuracy and efficiency of PINNs, we develop efficient strategies to nonuniformly sample observational data. We also investigate different approaches to enforce Dirichlet-type boundary conditions (BCs) as soft or hard constraints. Finally, we apply the proposed methods to a diverse set of time-dependent and time-independent solid mechanic examples that span linear elastic and hyperelastic material space. The estimated material parameters achieve relative errors of less than 1%. As such, this work is relevant to diverse applications, including optimizing structural integrity and developing novel materials.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

The effect of shear strain and shear localization on fault healing

The seismic cycle of repeated earthquake failure requires that faults regain frictional strength during the interseismic phase, when the fault is locked or undergoing quasi-static creep. Fault healing plays a central role in determining earthquake stress drop, recurrence interval, elastic radiation frequency and other source parameters. In particular, the longer a fault remains quasi-stationary, the stronger it becomes and the larger the potential stress drop can be for the next event. Here, we address the role of shear strain and strain localization on fault healing and healing rate. We performed slide-hold-slide friction experiments on quartz gouge in the double-direct shear configuration for shear strain up to 25 and hold times from 10 to 1000 s. The results show that both healing and healing rate increase nonlinearly with increasing shear strain. Frictional healing scales with volumetric strain within the laboratory fault zone. Using the volumetric strain upon reshear as a proxy for strain localization, we demonstrate that the capacity of a fault to heal is directly proportional to shear bandwidth and degree of strain localization. The more the deformation is localized, the higher are the healing and healing rate, and thus, the fault strength. Our data provide a framework for understanding variations in fault strength over the seismic cycle and the role of brecciation and strain localization on spatiotemporal variations in fault strength.

58 GEOSCIENCES↗

DOE OSTI2022

The role of surface forces in environment-enhanced cracking of brittle solids

Fracture initiation and propagation in brittle materials is promoted in surface-reactive (sorptive) environments, a phenomenon known as subcritical crack growth (SCG). Laboratory measured crack-propagation velocity vs. stress intensity factor relationships typically exhibit highly nonlinear, multi-stage characteristics that are sensitive to environmental factors such as adsorbate concentration and temperature. For practical purposes, empirical relationships (e.g., a power law) have been used to describe this complex phenomenon. However, how the overall SCG behavior emerges from the underlying fundamental processes near the crack tip, such as the interaction of the crack surfaces separated by only a few nanometers and mass transport within the nano-confined space, is still not well understood. This paper develops a mechanistic, surface-force-based fracture theory (SFFT) which integrates surface force models, fluid transport models, and linear elastic fracture mechanics to quantitatively explain the multi-stage characteristics of SCG in brittle solids. A numerical model is developed based on SFFT and solved through an implicit partitioned scheme for efficiency and modularity. The results are validated by Wiederhorn's data on crack propagation in soda-lime glasses at a wide range of relative humidity levels. We show that, for the first time, the entire range of an SCG curve can be captured by a single physics-based model. The predicted SCG curves reveal that the development of repulsive disjoining pressure behind the crack tip can be responsible for the reduced apparent fracture toughness in a sorptive environment. In conclusion, the shape of the SCG curve, and its changes with respect to the environment, is found to critically depend on the assumed transport models.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Elasticity-controlled jamming criticality in soft composite solids

Soft composite solids are made of inclusions dispersed within soft matrices. They are ubiquitous in nature and form the basis of many biological tissues. In the field of materials science, synthetic soft composites are promising candidates for building various engineering devices due to their highly programmable features. However, when the volume fraction of the inclusions increases, predicting the mechanical properties of these materials poses a significant challenge for the classical theories of composite mechanics. The difficulty arises from the inherently disordered, multi-scale interactions between the inclusions and the matrix. To address this challenge, we systematically investigated the mechanics of densely filled soft elastomers containing stiff microspheres. We experimentally demonstrate how the strain-stiffening response of the soft composites is governed by the critical scalings in the vicinity of a shear-jamming transition of the included particles. The proposed criticality framework quantitatively connects the overall mechanics of a soft composite with the elasticity of the matrix and the particles, and captures the diverse mechanical responses observed across a wide range of material parameters. The findings uncover a novel design paradigm of composite mechanics that relies on engineering the jamming properties of the embedded inclusions.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Modeling the contributions to acoustic nonlinearity from complex dislocation networks using 3D dislocation dynamics

Nonlinear ultrasonic parameters are highly sensitive to microstructural features that affect macroscale material behavior, providing a nondestructive means to characterize their evolution. Although dislocations are known to be a strong source of acoustic nonlinearity, establishing quantitative links between the acoustic nonlinearity parameter (β), measured via Second Harmonic Generation, and dislocation morphology—such as dislocation length and density—remains an open challenge. This work advances the numerical modeling of dislocation–β relationships using 3D dislocation dynamics (DD) simulations in two approaches: a “static” method computing strain and stress fields from dislocation configurations in the absence of external loading, and a “quasi-static” method to estimate β from the curvature of dislocation lines under applied load. First, the static method is combined with finite element analysis to investigate a recent assertion that heterogeneous initial strain fields can induce higher harmonic generation in a linear elastic medium; the present results do not corroborate this outcome. Then, the quasi-static method is applied to multiple-dislocation scenarios through parametric studies, revealing behaviors not predicted by analytical models, such as the competing interactions of edge and screw dislocations and the significant influence of applied stress on β. Finally, the simulations are used to model SHG experimental results and validate the hypothesis that β can decrease during plastic deformation, despite increasing dislocation density. As the DD code used here is open-source, it provides a practical platform for future investigation into microstructure–β relationships important to the interpretation of SHG results.

Materials science↗

DOE OSTI2020

Hydrokinetic Power Conversion Using Vortex-Induced Oscillation with Cubic Restoring Force

A cubic-spring restoring function with high-deformation stiffening is introduced to passively improve the harnessed marine hydrokinetic power by using flow-induced oscillations/vibrations (FIO/V) of a cylinder. In these FIO/V experiments, a smooth, rigid, single-cylinder on elastic end-supports is tested at Reynolds numbers ranging from 24,000 < Re < 120,000. The parameters of the tested current energy converter (CEC) are cubic stiffness and linear damping. Using the second generation of digital virtual spring-damping (Vck) controller developed by the Marine Renewable Energy Laboratory (MRELab), the cubic modeling of the oscillator stiffness is tested. Experimental results show the influence of the parameter variation on the amplitude, frequency, energy conversion, energy efficiency, and power of the converter. All experiments are conducted in the low turbulence-free surface water (LTFSW) channel of the MRELab of the University of Michigan. The main conclusions are: (1) The nonlinearity in the cubic oscillator is an effective way to extend the vortex-induced vibration (VIV) upper branch, which results in higher harnessing power and efficiency compared to the linear stiffness cylinder converter. (2) Compared to the linear converter, the overall power increase is substantial. The nonlinear power optimum, occurring at the end of the VIV upper branch, is 63% higher than its linear counterpart. (3) The cubic stiffness converter with low harnessing damping achieves consistently good performance in all the VIV regions because of the hardening restoring force, especially at higher flow velocity.

13 HYDRO ENERGY↗

DOE OSTI2021

Recurrent neural network-based multiaxial plasticity model with regularization for physics-informed constraints

We report a recurrent neural network (RNN) based model is developed as a surrogate to predict nonlinear plastic response under multiaxial loading. The RNN-based model is trained and tested on stress versus strain curves generated using a numerical solution based on the classical radial return method. Besides simply learning the basic constitutive relationship, a novel approach is taken to enforce certain physical conditions. Specifically, regularization is employed to maintain non-negative plastic power density throughout the loading history thereby ensuring monotonically increasing plastic work and thermodynamic consistency. Enforcing physics in this manner permits coupling of the data-driven RNN approach with physics-based knowledge and laws. This has the effect of reducing the necessary amount of data and ensuring known physical laws are not violated. Since, once trained, the model need not perform the expensive task of solving nonlinear equations, its efficiency is orders of magnitude greater than its numerical counterpart. The RNN-based model has been trained on varied sets of data and the accuracy on test datasets validated. The developed model is general and robust and has widespread application such as in the simulation of metal forming, large scale plasticity, and part life prediction.

42 ENGINEERING↗

DOE OSTI2021

A quantitative assessment of the model form error of friction models across different interface representations for jointed structures

Hysteretic models are widely used to model frictional interactions in joints to recreate experimental behavior. However, it is unclear which models are best suited for fitting or predicting the responses of structures. Here, the present study evaluates 26 friction model/interface representation combinations to quantify the model form error. A Quasi-Static Modal Analysis approach (termed Rayleigh Quotient Nonlinear Modal Analysis) is adopted to calculate the nonlinear system response, and a Multi-Objective Optimization is solved to fit experimental data of the first mode of the Brake-Reuß Beam. Optimized parameters from the first mode are applied to the second and third bending modes to quantify the predictive ability of the models. Formulations for both tracing full hysteresis loops and recreating hysteresis loops from a single loading curve (Masing assumptions) are considered. Smoothly varying models applied to a five patch representation showed the highest flexibility (for fitting mode 1) and good predictive potential (for modes 2 and 3). For a second formulation, which uses 152 frictional elements to represent the interface, the physically motivated spring in series with a Coulomb slip model (elastic dry friction) has high error for fitting mode 1 and performs near the middle for predicting higher modes. For both interface representation, the best fit models are not the most physical, but rather the ones with the most parameters (as expected); however, the more physical models perform somewhat better for predicting the higher modes.

42 ENGINEERING↗

DOE OSTI2025

A Poromechanical Framework for Internal Interactions Induced by Solid Inclusions

The framework of poromechanics is generalized to simulate the multiscale behavior of porous media subjected to internal loadings stemming from the growth of solid inclusions. This generalization is designed to enable the study of anisotropic internal stress generation from solid growth within the pores, while recovering isotropic fluid-induced loading as a particular case. For this purpose, a mathematical strategy to define constitutive tensors in a thermodynamically consistent form is proposed, thus offering new opportunities for determining the poromechanical properties of a porous solid through advanced experimentation or micromechanical models. The framework is specialized by means of established elastic solutions for single pore–matrix interaction, as well as through homogenization schemes considering the interaction among congruent pores. In particular, the second Eshelby solution and the Tanaka–Mori–Benveniste homogenization scheme are used to derive a microporoelastic model. At an elemental scale, the model is tested under mixed control conditions by replicating different scenarios of geomaterial testing. In addition, the model characteristics are outlined with reference to inelastic microscopic loadings replicating chemo-mechanical forcing, such as expansive crystal formation. Through a series of parametric analyses, it is shown that the microstructure of the pores significantly influences the properties of porous media. Most notably, it is shown that the effects of a solid forming within the pores depend in a highly nonlinear fashion on the constitutive characteristics of the inhomogeneities and can therefore not be readily quantified or predicted without models capturing the diverse multiscale interactions among pores, inhomogeneities, and matrix.

chemomechanics↗

DOE OSTI2023

The influence of Al2O3 on the structural properties of MgSiO3 akimotoite

Abstract Akimotoite, a MgSiO3 polymorph present in the lower transition zone within ultramafic portions of subducting slabs and potentially also in the ambient mantle, will partition some amount of Al, raising the question of how this will affect its crystal structure and properties. In this study, a series of samples along the MgSiO3-Al2O3 (akimotoite-corundum) solid solution have been investigated by means of single-crystal X-ray diffraction to examine their crystal chemistry. Results show a strong nonlinear behavior of the a- and c-axes as a function of Al content, which arises from fundamentally different accommodation mechanisms in the akimotoite and corundum structures. Furthermore, two Al2O3-bearing akimotoite samples were investigated at high pressure to determine the different compression mechanisms associated with Al substitution. Al2O3-bearing akimotoite becomes more compressible at least up to 20 mol% Al2O3, due likely to an increase in compressibility as the Al cation is incorporated into the SiO6 octahedron. This observation is in strong contrast to the stiffer corundum end-member having a KT = 250 GPa, which is larger than that of the akimotoite end-member [KT = 205(1) GPa]. These findings have implications for mineral physics models of elastic properties, which have in the past assumed linear mixing behavior between the MgSiO3 akimotoite and Al2O3 corundum end-members to calculate sound wave velocities for Al-bearing akimotoite at high pressure and temperature.

Geochemistry & Geophysics↗

DOE OSTI2024

A non-isothermal breakage-damage model for plastic-bonded granular materials incorporating temperature, pressure, and rate dependencies

Plastic-bonded granular materials (PBM) are widely used in industrial sectors, including building construction, abrasive applications, and defense applications such as plastic-bonded explosives. The mechanical behavior of PBM is highly nonlinear, irreversible, rate dependent, and temperature sensitive governed by various micromechanical attributions such as grain crushing and binder damage. This paper presents a thermodynamically consistent, microstructure-informed constitutive model to capture these characteristic behaviors of PBM. Key features of the model include a breakage internal variable to upscale the grain-scale information to the continuum level and to predict grain size evolution under mechanical loading. In addition, a damage internal state variable is introduced to account for the damage, deterioration, and debonding of the binder matrix upon loading. Temperature is taken as a fundamental external state variable to handle non-isothermal loading paths. The proposed model is able to capture with good accuracy several important aspects of the mechanical properties of PBM, such as pressure-dependent elasticity, pressure-dependent yield strength, brittle-to-ductile transition, temperature dependency, and rate dependency in the post-yielding regime. Furthermore, the model is validated against multiple published datasets obtained from confined and unconfined compression tests, covering various PBM compositions, confining pressures, temperatures, and strain rates.

Breakage↗

DOE OSTI2021

NUMERICAL CALCULATION OF LOSSES OF TRAPPED VORTICES UNDER STRONG RF MEISSNER CURRENT AND DC SUPERHEATING FIELD IN TYPE II SUPERCONDUCTORS

Research on the vortex dynamics and enhancing of superheating field in superconductors has attracted much attention in accelerator physics community to develop next-generation high-performance accelerator cavities. However, the extreme dynamics of curvilinear elastic vortices driven by very strong currents close to the depairing limit or superheating field of a superconductor with a nanostructured surface has not been well understood. We calculated the superheating field Hsh and critical momentum kc characterizing the wavelength of the instability ?m of the Meissner state to flux penetration by solving numerically the Ginzburg?Landau equations. A bulk superconductor, superconductor with the inhomogeneous surface disorder (S-S), and multilayered surface (S-I-S) have been thoroughly investigated in this work. Our result showed that S-S and S-I-S structures can enhance the superheating field well above their clean limit. In this work extensive numerical simulation of the power dissipated by an oscillating vortex segment driven by the surface ac Meissner currents was performed. Our simulations take into account the nonlinear vortex line tension, vortex mass, Bardeen?Stephen viscous vortex drag applicable at low fields, and nonlinear Larkin-Ovchinnikov (LO) viscous drag coefficient ?(v) at high fields and pinning force. We showed that the LO decrease of ?(v) with the vortex velocity v could radically change the field dependence of the surface resistance Ri(H) caused by trapped vortices. At low frequencies Ri(H) exhibits a conventional increase with H. However, as frequency increases, the surface resistance becomes a nonmonotonic function of H which decreases with H at higher fields irrespective of the pinning distribution. Overheating can mask the descending field dependence of Ri(H) as frequency increases. Our numerical simulations also show that the LO effect can cause a vortex bending instability at high field amplitudes and frequencies, giving rise to the formation of dynamic kinks along with the vortex when a vortex is pinned strongly to one end. Nonlinear losses of trapped vortices in thick films under high-amplitude RF fields as functions of frequency, mean free path and pinning characteristics have been calculated.

Pathirana, Walive↗