Search NASA⌕ Search

SEARCH · Search NASA

Results for “Finite deformation theory”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Approach and rotation of reconnecting topological defect lines in liquid crystal

Topological defects are a universal concept across many disciplines, such as crystallography, liquid-crystalline physics, low-temperature physics, cosmology, and even biology. In nematic liquid crystals, topological defects called disclinations have been widely studied. For their three-dimensional (3D) dynamics, however, only recently have theoretical approaches dealing with fully 3D configurations been reported. Further, recent experiments have observed 3D disclination line reconnections, a phenomenon characteristic of defect line dynamics, but detailed discussions were limited to the case of approximately parallel defects. In this paper, we focus on the case of two disclination lines that approach at finite angles and lie in separate planes, a more fundamentally 3D reconnection configuration. Observing and analyzing such reconnection events, we find the square-root law of the distance between disclinations and the decrease of the interdisclination angle over time. We compare the experimental results with theory and find qualitative agreement on the scaling of distance and angle with time, but quantitative disagreement on distance and angle relative mobilities. To probe this disagreement, we derive the equations of motion for systems with reduced twist constant and also carry out simulations for this case. These, together with the experimental results, suggest that deformations of disclinations may be responsible for the disagreement.

36 MATERIALS SCIENCE↗
DOE OSTI2022

What is the iε for the S-matrix?

Can the S-matrix be complexified in a way consistent with causality? Since the 1960's, the affirmative answer to this question has been well-understood for 2→2 scattering of the lightest particle in theories with a mass gap at low momentum transfer, where the S-matrix is analytic everywhere except at normal-threshold branch cuts. We ask whether an analogous picture extends to realistic theories, such as the Standard Model, that include massless fields, UV/IR divergences, and unstable particles. Especially in the presence of light states running in the loops, the traditional iε prescription for approaching physical regions might break down, because causality requirements for the individual Feynman diagrams can be mutually incompatible. We demonstrate that such analyticity problems are not in contradiction with unitarity. Instead, they should be thought of as finite-width effects that disappear in the idealized 2→2 scattering amplitudes with no unstable particles, but might persist at higher multiplicity. To fix these issues, we propose an iε -like prescription for deforming branch cuts in the space of Mandelstam invariants without modifying the analytic properties. This procedure results in a complex strip around the real part of the kinematic space, where the S-matrix remains causal. In addition to giving a pedagogical introduction to the analytic properties of the perturbative S-matrix from a modern point of view, we illustrate all the points on explicit examples, both symbolically and numerically. Furthermore, to help with the investigation of related questions, we introduce a number of tools, including holomorphic cutting rules, new approaches to dispersion relations, as well as formulae for local behavior of Feynman integrals near branch points.

Anomalous thresholds↗
DOE OSTI2022

Transient MOC with frequency transform and DSA on unstructured mesh

We present an implementation of the transient method of characteristics (MOC) with isotropic time derivatives, accelerated by diffusion synthetic acceleration (DSA). The fully implicit frequency transform method is used to solve the transient problem with analytic precursor integration. The code works on meshes composed of almost any of the commonly used non-curvilinear finite element types, and can handle the deformation of geometry in time-dependent transport calculations. We present results of a continuous Fourier analysis for the transient multigroup DSA problem, and representative benchmarking results are presented for the C5G7-TD benchmark in 2D showing reasonable performance and agreement compared to other codes. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

State densities of heavy nuclei in the static-path plus random-phase approximation

We report that nuclear state densities are important inputs to statistical models of compound-nucleus reactions. State densities are often calculated with self-consistent mean-field approximations that do not include important correlations and must be augmented with empirical collective enhancement factors. Here, we benchmark the static-path plus random-phase approximation (SPA + RPA) to the state density in a chain of samarium isotopes 148–155 Sm against exact results (up to statistical errors) obtained with the shell-model Monte Carlo (SMMC) method. The SPA + RPA method incorporates all static fluctuations beyond the mean field together with small-amplitude quantal fluctuations around each static fluctuation. Using a pairing plus quadrupole interaction, we show that the SPA + RPA state densities agree well with the exact SMMC densities for both the even- and odd-mass isotopes. For the even-mass isotopes, we also compare our results with mean-field state densities calculated with the finite-temperature Hartree-Fock-Bogoliubov (HFB) approximation. We find that the SPA + RPA repairs the deficiencies of the mean-field approximation associated with broken rotational symmetry in deformed nuclei and with the violation of particle-number conservation in the pairing condensate. In particular, in deformed nuclei the SPA + RPA reproduces the rotational enhancement of the state density relative to the mean-field state density.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Dynamic behavior of chemically tunable mechano-responsive hydrogels

Here, using theory and simulation, we model the mechanical behavior of gels that encompass loops and dangling chain ends. If the loops remain folded and dangling ends are chemically inert, then these topological features just serve as defects. If, however, the loops unfold to expose the hidden (“cryptic”) binding sites and the ends of the dangling chains are reactive, these moieties can form bonds that improve the gel's mechanical properties. For gels with a lower critical solubility temperature (LCST), we systematically switch on the possible unfolding and binding events. To quantify the resulting effects, we derive equations for the gel's equilibrium and dynamic elastic moduli. We also use a finite element approach to simulate the gel's response to deformation and validate the analytic calculations. Herein, we show that the equilibrium moduli are highly sensitive to the presence of unfolding and binding transitions. The dynamical moduli are sensitive not only to these structural changes, but also to the frequency of deformation. For example, when reactive ends bind to exposed cryptic sites at T = 29 °C and relatively high frequency, the storage shear modulus is 119% greater than the corresponding equilibrium value, while the storage Young's modulus is 109% greater than at equilibrium. These findings provide guidelines for tuning the chemical reactivity of loops and dangling ends and the frequency of deformation to tailor the mechano-responsive behavior of polymer networks.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Veneziano variations: how unique are string amplitudes?

String theory offers an elegant and concrete realization of how to consistently couple states of arbitrarily high spin. But how unique is this construction? In this paper we derive a novel, multi-parameter family of four-point scattering amplitudes exhibiting i) polynomially bounded high-energy behavior and ii) exchange of an infinite tower of high-spin modes, albeit with a finite number of states at each resonance. These amplitudes take an infinite-product form and, depending on parameters, exhibit mass spectra that are either unbounded or bounded, thus corresponding to generalizations of the Veneziano and Coon amplitudes, respectively. For the bounded case, masses converge to an accumulation point, a peculiar feature seen in the Coon amplitude but more recently understood to arise naturally in string theory [1]. Importantly, our amplitudes contain free parameters allowing for the customization of the slope and offset of the spin-dependence in the Regge trajectory. We compute all partial waves for this multi-parameter class of amplitudes and identify unitary regions of parameter space. For the unbounded case, we apply similar methods to derive new deformations of the Veneziano and Virasoro-Shapiro amplitudes.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Global description of $β$ – decay with the axially deformed Skyrme finite-amplitude method: Extension to odd-mass and odd-odd nuclei

Here we use the finite-amplitude method (FAM), an efficient implementation of the quasiparticle random phase approximation, to compute $β$-decay rates with Skyrme energy-density functionals for 3983 nuclei, essentially all the medium-mass and heavy isotopes on the neutron-rich side of stability. We employ an extension of the FAM that treats odd-mass and odd-odd nuclear ground states in the equal filling approximation. Our rates are in reasonable agreement both with experimental data where available and with rates from other global calculations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

A hereditary integral, transient network approach to modeling permanent set and viscoelastic response in polymers

An efficient numerical framework is presented for modeling viscoelasticity and permanent set of polymers. It is based on the hereditary integral form of transient network theory, in which polymer chains belong to distinct networks each with different natural equilibrium states. Chains continually detach from previously formed networks and reattach to new networks in a state of zero stress. The free energy of these networks is given in terms of the deformation gradient relative to the configuration at which the network was born . A decomposition of the kernel for various free energies allows for a recurrence relationship to be established, bypassing the need to integrate over all time history. The technique is established for both highly compressible and nearly incompressible materials through the use of neo-Hookean, Blatz–Ko, Yeoh, and Ogden-Hill material models. Multiple examples are presented showing the ability to handle rate-dependent response and residual strains under complex loading histories.

Finite element method↗
DOE OSTI2021

A continuum meshfree method for sandbox-style numerical modeling of accretionary and doubly vergent wedges

Here, in this study, we introduce and utilize GEOSPH, a Lagrangian particle-based continuum Smoothed Particle Hydrodynamics (SPH) code to simulate the deformation of geologic materials in sandbox-style experiments using an elastoplastic constitutive model. Due to the meshfree nature of SPH, our proposed framework is capable of handling the large deformations characteristic of sandbox-style experiments. SPH is also able to capture strain localization and discontinuities, allowing us to resolve faulting patterns emerging in the sandbox experiments. We successfully validate our SPH implementation against the benchmark experiments of Buiter and co-workers, and then apply SPH to understand the deformational processes occurring in doubly vergent orogens resultant from the S-point experimental setup and from finitely high wedge-like indenter backstops of different inclinations. We find that the topographic slope of the prowedge results from the competing processes of vertical uplift due to the indenter and forward thrusting, while the topographic slope of the retrowedge is a product of repeated shallow slope failure. Our findings show that SPH is a promising numerical method which should be added to the current palette of computational tools used by structural geologists for solving problems relating to tectonics and crustal deformation.

58 GEOSCIENCES↗
DOE OSTI2024

Effects of quasiparticle-vibration coupling on Gamow-Teller strength and 𝛽 decay with the Skyrme proton-neutron finite-amplitude method

We adapt the proton-neutron finite-amplitude method, which in its original form is an efficient implementation of the Skyrme quasiparticle random phase approximation, to include the coupling of quasiparticles to like-particle phonons. The approach allows us to add beyond-quasiparticle random-phase approximation correlations to computations of Gamow-Teller strength and 𝛽-decay rates in deformed nuclei for the first time. We test the approach in several deformed isotopes for which measured strength distributions are available. Furthermore, the additional correlations dramatically improve agreement with the data, and will lead to improved global 𝛽-decay rates.

Beta decay↗
DOE OSTI2021

Crack tip microplasticity mediated by microstructure gradients

Abstract Traditional fracture theories infer damage at cracks (local field) by surveying loading conditions away from cracks (far field). This approach has been successful in predicting ductile fracture, but it normally assumes isotropic and homogeneous materials. However, myriads of manufacturing procedures induce heterogeneous microstructural gradients that can affect the accuracy of traditional fracture models. This work presents a microstructure‐sensitive finite element approach to explore the shielding effects of grain size and crystallographic orientation gradients on crack tip microplasticity and blunting. A dislocation density‐based crystal plasticity model conveys texture evolution, grain size effects, and directional hardening by computing the constraint from dislocation structures. The results demonstrate that the microstructure can act as a buffer between the local and far fields that affects the crack tip microplasticity variability. For nominal opening loading, grain size and texture affect the local ductility and induce a non‐negligible multiaxial plastic deformation. Furthermore, driving forces based on measuring displacements away from the crack tip are less affected by the microstructure, which suggests that traditional experimental methods smear out important crack tip variability.

Castelluccio, Gustavo M.↗
DOE OSTI2022

Microscopic-macroscopic level densities for low excitation energies

Level density ρ(E,Q) is derived within the micro-macroscopic approximation (MMA) for a system of strongly interacting Fermi particles with the energy E and additional integrals of motion Q , in line with several topics of the universal and fruitful activity of A. S. Davydov. Within the extended Thomas Fermi and semiclassical periodic orbit theory beyond the Fermi-gas saddle-point method, we obtain ρ ∝ I ν (S)/S ν , where I ν (S) is the modified Bessel function of the entropy S . For small shell-structure contribution, one finds ν = κ/2 + 1, where κ is the number of additional integrals of motion. This integer number is a dimension of Q, Q = { N, Z , …} for the case of two-component atomic nuclei, where N and Z are the numbers of neutrons and protons, respectively. For much larger shell structure contributions, one obtains ν = κ /2 + 2. The MMA level density ρ reaches the well-known Fermi gas asymptote for large excitation energies and the finite micro-canonical combinatoric limit for low excitation energies. Further, the additional integrals of motion can also be the projection of the angular momentum of a nuclear system for nuclear rotations of deformed nuclei, number of excitons for collective dynamics, and so on. Fitting the MMA total level density ρ( E , Q) for a set of the integrals of motion Q = { N, Z }, to experimental data on a long nuclear isotope chain for low excitation energies, one obtains the results for the inverse level-density parameter K , which differs significantly from those of neutron resonances due to shell, isotopic asymmetry, and pairing effects.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Considering computational speed vs. accuracy: Choosing appropriate mesoscale RVE boundary conditions

Modeling a material’s microstructure using continuum theories allows for inspection of the relationship between coarse scale and fine scale behaviors. Computational limits generally require selection of a sub-volume from a bulk sample in order to directly model the microstructure. Boundary conditions are applied to the sub-volume to mimic the excluded bulk material. Appropriate selection of boundary conditions helps effectively determine the appropriate spatial scale required of the sub-volume. Applicable boundary conditions include direct displacement, periodic, and uniform traction. While direct displacement and periodic boundary conditions are commonly used, uniform traction boundary conditions have seen limited use due to rigid body stability issues in simulations of compression or shear deformation. A new application of uniform traction boundary conditions was developed through linear constraint equations, similar to approaches employed by direct displacement and periodic boundary conditions, to quench rigid body motions with minimal interference of the relative deformation of the model. These boundary conditions were tested by compressing several synthetically generated periodic microstructures using the finite element method. Evaluating the effective stiffness along the compression axis, the direct displacement boundary condition produced the stiffest response, whereas the uniform traction boundary condition produced the most compliant. Periodic boundary conditions produced the same response for all volumes analyzed and both the direct displacement and uniform traction boundary conditions trended toward the periodic response as the domain volume increased. Computational performance was also evaluated for each boundary condition using implicit and explicit solvers. Direct displacement boundary conditions presented the lowest computational cost of all of the boundary conditions followed by periodic then uniform traction. The computational expense of periodic and uniform traction boundary conditions limited the viable spatial scale and mesh resolutions able to be simulated. Selection of appropriate boundary conditions for specific uses need to be a balance between allowable computational expense and accuracy of the method. Techniques for evaluating which boundary conditions to use are discussed.

42 ENGINEERING↗
DOE OSTI2024

Multipole responses in fissioning nuclei and their uncertainties

Electromagnetic multipole responses are key inputs to model the structure, decay, and reactions of atomic nuclei. With the introduction of the finite amplitude method (FAM), large-scale calculations of the nuclear linear response in heavy deformed nuclei have become possible. This work provides a detailed study of multipole responses in actinide nuclei with Skyrme energy density functionals. We quantify both systematic and statistical uncertainties induced by the functional parametrization in FAM calculations. We also extend the FAM formalism to perform blocking calculations with the equal filling approximation for odd-mass and odd-odd nuclei, and analyze the impact of blocking configurations on the response. In conclusion, by examining the entire plutonium isotopic chain from the proton to the neutron drip line, we find a large variability of the response with the neutron number and study how it correlates with the deformation of the nuclear ground state.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Modeling of Magnetic Properties of Magnetorheological Elastomers Using JA Hysteresis Model

Magnetorheological elastomers (MREs) are composite materials that consist of magnetically permeable particles in a nonmagnetic polymeric matrix. Under the influence of an external magnetic field, a reversible deformation change occurs in the mechanical properties of these materials. Due to their coupled magnetomechanical response, these materials have been found suitable for a range of applications including tunable vibration absorbers, sensors, and actuators. Notably, improvement of such devices are prerequisites to efficient energy conversion systems, hence the need to understand further the MRE technology. The Jiles-Atherton (JA) theory takes into consideration the magneto-coupling experienced by effective domains in a magnetic material. Algorithm based on the theory yields five model parameters; saturation magnetization (M s ), domain density (a), domain coupling (α), loss coefficient (k), and reversibility (c). Using JA theory, model parameters were calculated and linked to the physical attributes of Fe powder and isotropic MRE. The results show that the calculated Ms for the MRE is reasonably related to that of the Fe powder by a factor of the particle's volume fraction used in the MRE. Further, the calculated k, a, and α provided support for the reduced pinning factor, domain density, and increased domain coupling in the MRE due to the changes in the domain structure between the two materials. From the calculated JA parameters, finite-element modeling (FEM) of the MRE hysteresis loop was performed. The analysis showed that the modeled magnetic properties including coercivity, remanence, and coordinates of the hysteresis loop tip vary with geometric position.

42 ENGINEERING↗
DOE OSTI2024

Interaction-enhanced nesting in spin-fermion and Fermi-Hubbard models

The spin-fermion (SF) model postulates that the dominant coupling between low-energy fermions in near critical metals is mediated by collective spin fluctuations (paramagnons) peaked at the Néel wave vector, Q N , connecting hot spots on opposite sides of the Fermi surface. It has been argued that strong correlations at hot spots lead to a Fermi surface deformation (FSD) featuring flat regions and increased nesting. This conjecture was confirmed in the perturbative self-consistent calculations when the paramagnon propagator dependence on momentum deviation from Q N is given by χ − 1 ∝ | Δ q | . Using diagrammatic Monte Carlo (diagMC) technique we show that such a dependence holds only at temperatures orders of magnitude smaller than any other energy scale in the problem, indicating that a different mechanism may be at play. Instead, we find that a χ − 1 ∝ | Δ q | 2 dependence yields a robust finite- T scenario for achieving FSD. To link phenomenological and microscopic descriptions, we applied the connected determinant diagMC method to the ( t − t ′ ) Hubbard model and found that at large U / t > 5.5 before the formation of electron and hole pockets (i) the FSD defined as a maximum of the spectral function is not very pronounced; instead, it is the lines of zeros of the renormalized dispersion relation that deforms toward nesting, and (ii) the static spin susceptibility is well described by χ − 1 ∝ | Δ q | 2 . Flat FS regions yield a nontrivial scenario for realizing a non-Fermi liquid state. Published by the American Physical Society 2024

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

An adaptive space-time phase field formulation for dynamic fracture of brittle shells based on LR NURBS

Here, we present an adaptive space-time phase field formulation for dynamic fracture of brittle shells. Their deformation is characterized by the Kirchhoff–Love thin shell theory using a curvilinear surface description. All kinematical objects are defined on the shell’s mid-plane. The evolution equation for the phase field is determined by the minimization of an energy functional based on Griffith’s theory of brittle fracture. Membrane and bending contributions to the fracture process are modeled separately and a thickness integration is established for the latter. The coupled system consists of two nonlinear fourth-order PDEs and all quantities are defined on an evolving two-dimensional manifold. Since the weak form requires C 1 -continuity, isogeometric shape functions are used. The mesh is adaptively refined based on the phase field using Locally Refinable (LR) NURBS. Time is discretized based on a generalized-α method using adaptive time-stepping, and the discretized coupled system is solved with a monolithic Newton–Raphson scheme. Finally, the interaction between surface deformation and crack evolution is demonstrated by several numerical examples showing dynamic crack propagation and branching.

42 ENGINEERING↗
DOE OSTI2022

Properties of the neutron star crust: Quantifying and correlating uncertainties with improved nuclear physics

A compressible liquid-drop model (CLDM) is used to correlate uncertainties associated with the properties of the neutron star (NS) crust with theoretical estimates of the uncertainties associated with the equation of state (EOS) of homogeneous neutron and nuclear matter. For the latter, we employ recent calculations based on Hamiltonians constructed using chiral effective-field theory (χEFT). Fits to experimental nuclear masses are employed to constrain the CLDM further, and we find that they disfavor some of the χEFT Hamiltonians. The CLDM allows us to study the complex interplay between bulk, surface, curvature, and Coulomb contributions, and their impact on the NS crust. It also reveals how the curvature energy alters the correlation between the surface energy and the bulk symmetry energy. Here our analysis quantifies how the uncertainties associated with the EOS of homogeneous matter implies significant uncertainties for the composition of the crust, its proton fraction, and the volume fraction occupied by nuclei. We find that the finite-size effects impact the crust composition but have a negligible effect on the net isospin asymmetry of matter. The isospin asymmetry is largely determined by the bulk properties and the isospin dependence of the surface energy. The most significant uncertainties associated with matter properties in the densest regions of the crust, the precise location of the crust-core transition, are found to be strongly correlated with uncertainties associated with the Hamiltonians. By adopting a unified model to describe the crust and the core of NSs, we tighten the correlation between their global properties such as their mass-radius relationship, moment of inertia, crust thickness, and tidal deformability with uncertainties associated with the nuclear Hamiltonians.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗