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All sources NASA NTRS DOE OSTI

DOE OSTI2026

Hourglass control in staggered-grid hydrodynamics using virtual element stabilization techniques

Numerical simulations using the staggered-grid hydrodynamics (SGH) discretization suffer from hourglass instabilities. In this work, we develop a stabilization method to suppress the hourglass instabilities using techniques from the virtual element method (VEM). The stiffness matrix of the VEM consists of two terms: the consistency matrix which is rank deficient and the stability matrix. Here, we first show that in two dimensions and on general polygons, the stiffness matrix of the SGH is identical to the consistency matrix of the linear VEM for both the diffusion equation and the linear elasticity equation. These analyses explain the origin of the hourglass instabilities of the SGH discretization method, and establish a theoretical foundation for our proposed stabilization method by augmenting the stiffness matrix of the SGH discretization using the VEM stability matrix. Then, we present numerical examples using Lagrangian SGH simulations. The numerical experiments demonstrate that the proposed VEM stabilization method is effective at eliminating hourglass modes in the SGH discretization.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1995

Analysis and Development of Finite Element Methods for the Study of Nonlinear Thermomechanical Behavior of Structural Components

Underintegrated methods are investigated with respect to their stability and convergence properties. The focus was on identifying regions where they work and regions where techniques such as hourglass viscosity and hourglass control can be used. Results obtained show that underintegrated methods typically lead to finite element stiffness with spurious modes in the solution. However, problems exist (scalar elliptic boundary value problems) where underintegrated with hourglass control yield convergent solutions. Also, stress averaging in underintegrated stiffness calculations does not necessarily lead to stable or convergent stress states.

Oden, J. Tinsley↗

NASA NTRS1994

Analysis and control of hourglass instabilities in underintegrated linear and nonlinear elasticity

Methods are described to identify and correct a bad finite element approximation of the governing operator obtained when under-integration is used in numerical code for several model problems: the Poisson problem, the linear elasticity problem, and for problems in the nonlinear theory of elasticity. For each of these problems, the reason for the occurrence of instabilities is given, a way to control or eliminate them is presented, and theorems of existence, uniqueness, and convergence for the given methods are established. Finally, numerical results are included which illustrate the theory.

Jacquotte, Olivier P.↗

NASA NTRS1984

Analysis of hourglass instabilities and control in underintegrated finite element methods

Belytschko et al. (1981, 1984) has developed stabilization methods for the treatment of underintegrated FEM problems; these methods involve the computation of an underintegrated stiffness matrix, which is rank-deficient, and the addition of a stabilization matrix which effectively eliminates the spurious modes. An attempt is presently made to give this a priori stabilization method a mathematical means of support. Attention is also given to an a posteriority stabilization method for hourglass control, in which an approximate solution of the underintegrated system is obtained and then subjected to a special projection in order to eliminate the hourglass modes. A proof is obtained for the convergence of this stabilized underintegrated approximation to the exact solution of a model problem at almost the same rate (as the mesh is refined) as the fully integrated solutions.

Jacquotte, O.-P.↗

DOE OSTI2025

How the Arrangement of Platinum Atoms on Ruthenium Nanoparticles Improves Hydrogen Evolution Activity

The platinum‐ruthenium (PtRu) system is highly active for hydrogen evolution reaction (HER) in alkaline media with both Pt and Ru playing active roles in the water dissociation step that generates adsorbed hydrogen atoms. Precise control of the arrangement of Pt atoms on Ru nanoparticles can maximize the Pt‐Ru sites for water dissociation and Pt‐Pt sites for hydrogen production and can considerably improve HER catalytic performance. By directing the growth and distribution of Pt on Ru hourglass nanoparticles, the arrangement of Pt on Ru is controlled into forming Pt islands, small Pt clusters, and strings of a few Pt atoms. Calculations show that the unique atomic string arrangements of Pt on Ru is the thermodynamically favorable configuration. Additionally, these strings have a favorable combination of Pt‐Ru and Pt‐Pt sites, making the Pt‐string on Ru the most active catalyst with a more than fivefold increase in turnover frequency for alkaline HER compared to the Pt‐island on Ru catalyst. The results show how controlling the Pt atomic arrangement on Ru nanoparticle surfaces for the tuning of Pt‐Pt and Pt‐Ru neighboring sites can direct toward a more efficient HER mechanism and thereby significantly enhancing HER performance.

36 MATERIALS SCIENCE↗

NASA NTRS1973

High temperature, low cycle fatigue of copper-base alloys in argon. Part 3: Zirconium-copper; thermal-mechanical strain cycling, hold-time and notch fatigue results

The low-cycle fatigue characteristics of smooth bar and notched bar specimens (hourglass shape) of zirconium-copper, 1/2 Hard, material (R-2 Series) were evaluated at room temperature in axial strain control. Over the fatigue life range from about 300 to 3000 cycles the ratio of fatigue life for smooth bar to fatigue life for notched bar remained constant at a value of about 6.0. Some additional hold-time data for the R-2 alloy tested in argon at 538 C are reported. An analysis of the relaxation data obtained in these hold-time tests is also reported and it is shown that these data yield a fairly consistent correlation in terms of instantaneous stress rate divided by instantaneous stress. Two thermal-mechanical strain cycling tests were also performed using a cyclic frequency of 4.5 cycles per hour and a temperature cycling interval from 260 to 538 C. The fatigue life values in these tests were noticeably lower than that observed in isothermal tests at 538 C.

Conway, J. B.↗

DOE OSTI2024

Mechanically activated and deactivated ion transport across nanopores with heterogeneous surface charge distributions

To mimic the intricate and adaptive functionalities of biological ion channels, electrohydrodynamic ion transport has been studied extensively, albeit mostly, across uniformly charged nanochannels. Here, we analyze the ion transport under coupled electric field and pressure across heterogeneously charged nanopores with oppositely charged sections on their lateral surface. We only consider such pores with symmetric hourglass-like and cylindrical shapes to focus on the effects of the non-uniform surface charge distribution. Finite-element simulations of a continuum model demonstrate that a pressure applied in either direction of the pore-axis equally suppresses or amplifies the ionic conductance, depending on the electric field polarity, by distorting the quasi-static distribution of ions in the pore. The resulting anomalous mechanical deactivation and activation of ionic current under opposite voltage biases exhibit the functional modularity of our setup, while their intensities are highly tunable, substantially greater than those of analogous behaviors in other nanochannels, and fundamentally correlated to ionic current rectification (ICR) in our pores. A detailed study of ICR subsequently reveals its counterintuitive non-monotonous variations, in the pores, with the magnitude of applied voltage and the pore length, that can help optimize their diode-like behavior. We further illustrate that while the hourglass-shaped nanopores yield the more efficient mechanical suppressors of ion transport, their cylindrical analogs are the superior rectifiers and mechanical amplifiers of ion conduction. Therefore, this article provides a blueprint for the strategic design of nanofluidic circuits to attain a robust, modular, and tunable control of ion transport under external electrical and mechanical stimuli.

Physics↗