Failure Surfaces for Finitely Strained Two-Phase Periodic Solids Under General In-Plane Loading

2005 ◽  
Vol 73 (3) ◽  
pp. 505-515 ◽  
Author(s):  
N. Triantafyllidis ◽  
M. D. Nestorović ◽  
M. W. Schraad
Keyword(s):  
Variable Stiffness ◽  
Bloch Wave ◽  
Two Phase ◽  
Buckling Mode ◽  
Unit Cells ◽  
First Occurrence ◽  
Order Of Magnitude ◽  
Ultimate Failure ◽  
Periodic Microstructures ◽  
Strain Space

For ductile solids with periodic microstructures (e.g., honeycombs, fiber-reinforced composites, cellular solids) which are loaded primarily in compression, their ultimate failure is related to the onset of a buckling mode. Consequently, for periodic solids of infinite extent, one can define as the onset of failure the first occurrence of a bifurcation in the fundamental solution, for which all cells deform identically. By following all possible loading paths in strain or stress space, one can construct onset-of-failure surfaces for finitely strained, rate-independent solids with arbitrary microstructures. The calculations required are based on a Bloch wave analysis on the deformed unit cell. The presentation of the general theory is followed by the description of a numerical algorithm which reduces the size of stability matrices by an order of magnitude, thus improving the computational efficiency for the case of continuum unit cells. The theory is subsequently applied to porous and particle-reinforced hyperelastic solids with circular inclusions of variable stiffness. The corresponding failure surfaces in strain-space, the wavelength of the instabilities, and their dependence on micro-geometry and macroscopic loading conditions are presented and discussed.

scholarly journals THU0207 SUSTAINABILITY OF RESPONSE TO UPADACITINIB AS MONOTHERAPY OR IN COMBINATION AMONG PATIENTS WITH RHEUMATOID ARTHRITIS AND PRIOR INADEQUATE RESPONSE TO CONVENTIONAL SYNTHETIC DMARDS

2020 ◽  
Vol 79 (Suppl 1) ◽  
pp. 327.1-328
Author(s):  
A. Kavanaugh ◽  
M. H. Buch ◽  
B. Combe ◽  
L. Bessette ◽  
I. H. Song ◽  
...  
Keyword(s):  
Rheumatoid Arthritis ◽  
Disease Activity ◽  
Inadequate Response ◽  
Research Support ◽  
Two Phase ◽  
First Occurrence ◽  
Activity Measures ◽  
Disease Activity Measures

Background:The primary treatment goal for patients (pts) with rheumatoid arthritis (RA) is a state of sustained clinical remission (REM) or low disease activity (LDA).1,2Objectives:To assess the long-term sustainability of responses to upadacitinib (UPA), a JAK inhibitor, with or without background csDMARD(s) in pts with RA.Methods:Data are from two phase 3 randomized, controlled trials of UPA in RA pts with roughly similar baseline disease characteristics: SELECT-NEXT enrolled pts with an inadequate response (IR) to csDMARD(s) on background stable csDMARD(s) receiving UPA 15 mg or 30 mg once daily or placebo for 12 weeks (wks); SELECT-MONOTHERAPY enrolled methotrexate (MTX)-IR pts receiving UPA 15 mg or 30 mg monotherapy or blinded MTX for 14 wks. After 12/14 wks, pts could enter a blinded long-term extension and receive UPA 15 mg or 30 mg for up to 5 years. This post hoc analysis evaluated clinical REM (CDAI ≤2.8; SDAI ≤3.3), LDA (CDAI≤10; SDAI≤11), and DAS28(CRP) <2.6/≤3.2 at first occurrence before Wk 84; additionally, these measures were evaluated at 3, 6, and 12 months after the first occurrence for the total number of pts randomized to UPA 15 mg. Sustainability of response was evaluated by Kaplan-Meier only for those pts who achieved REM/LDA and was defined as time to the earliest date of losing response at two consecutive visits or discontinuation of study drug. The predictive ability of time to clinical REM/LDA was assessed using Harrell’s concordance (c)-index (for reference, an index ~ 0.5, indicates no ability to predict; an index of 1 or -1 would be a perfect prediction). The last follow up dates were 22 March, 2018 (SELECT-NEXT) and 25 May, 2019 (SELECT-MONOTHERAPY), when all pts had reached the Wk 84 visit.Results:Through Wk 84, the percent of treated pts achieving CDAI REM/LDA was 43%/79% for those receiving UPA 15 mg with background csDMARD(s) (SELECT-NEXT) and 37%/76% for those receiving UPA 15 mg without background csDMARD(s) (SELECT-MONOTHERAPY). 35%/25% of pts randomized to UPA 15 mg with background csDMARD(s) and 27%/23% of pts randomized to UPA 15 mg without background csDMARD(s) achieved sustained CDAI REM through 6/12 months after the first occurrence. 64%/56% of pts randomized to UPA 15 mg with background csDMARD(s) and 61%/56% of pts randomized to UPA 15 mg without background csDMARD(s) achieved sustained CDAI LDA through 6/12 months after the first occurrence (Figure 1). Time to initial clinical REM/LDA did not appear to be associated with sustained disease control. The c-indices (95%CI) for CDAI REM in the UPA 15 mg with background csDMARD(s) and UPA 15 mg without background csDMARD(s) groups were 0.541 (0.47, 0.62) and 0.568 (0.49, 0.65) and that of LDA were 0.521 (0.46, 0.58) and 0.498 (0.43, 0.56), respectively. Through last follow-up visit, 55% of pts receiving UPA 15 mg with background csDMARD(s) and 62% of pts receiving UPA 15 mg without background csDMARD(s) remained in CDAI REM while 72% and 70% of pts remained in CDAI LDA, respectively (Figure 2). Similar results were observed across other disease activity measures (SDAI REM/LDA and DAS28(CRP) <2.6/≤3.2).Conclusion:More than a quarter and more than a half of pts with RA and prior IR to csDMARD(s) receiving UPA with or without background csDMARD therapy achieved sustained clinical REM and LDA, respectively, across disease activity measures. Sustainability of responses appeared comparable among pts receiving UPA with or without background csDMARDs through up to 84 wks.References:[1]EULAR: Smolen JS, et al. Ann Rheum Dis 2017;76:960–977.[2]ACR: Singh et al. Arthritis & Rheumatology Vol. 68, No. 1, January 2016, pp 1–26.Disclosure of Interests: :Arthur Kavanaugh Grant/research support from: Abbott, Amgen, AstraZeneca, BMS, Celgene Corporation, Centocor-Janssen, Pfizer, Roche, UCB – grant/research support, Maya H Buch Grant/research support from: Pfizer, Roche, and UCB, Consultant of: Pfizer; AbbVie; Eli Lilly; Gilead Sciences, Inc.; Merck-Serono; Sandoz; and Sanofi, Bernard Combe Grant/research support from: Novartis, Pfizer, Roche-Chugai, Consultant of: AbbVie; Gilead Sciences, Inc.; Janssen; Eli Lilly and Company; Pfizer; Roche-Chugai; Sanofi, Speakers bureau: Bristol-Myers Squibb; Gilead Sciences, Inc.; Eli Lilly and Company; Merck Sharp & Dohme; Pfizer; Roche-Chugai; UCB, Louis Bessette Grant/research support from: AbbVie, Amgen, Bristol-Myers Squibb, Celgene, Eli Lilly, Janssen, Merck, Novartis, Pfizer, Roche, Sanofi, UCB Pharma, Consultant of: AbbVie, Amgen, Bristol-Myers Squibb, Celgene, Eli Lilly, Janssen, Merck, Novartis, Pfizer, Roche, Sanofi, UCB Pharma, Speakers bureau: AbbVie, Amgen, Bristol-Myers Squibb, Celgene, Eli Lilly, Janssen, Merck, Novartis, Pfizer, Sanofi, In-Ho Song Shareholder of: AbbVie Inc., Employee of: AbbVie Inc., Yanna Song Shareholder of: AbbVie Inc., Employee of: AbbVie Inc., Jessica Suboticki Shareholder of: AbbVie Inc., Employee of: AbbVie Inc., Peter Nash Grant/research support from: AbbVie, Bristol-Myers Squibb, Celgene, Eli Lilly and Company, Gilead, Janssen, MSD, Novartis, Pfizer Inc, Roche, Sanofi, UCB, Consultant of: AbbVie, Bristol-Myers Squibb, Celgene, Eli Lilly, Gilead, Janssen, MSD, Novartis, Pfizer Inc, Roche, Sanofi, UCB, Speakers bureau: AbbVie, Bristol-Myers Squibb, Celgene, Eli Lilly, Gilead, Janssen, MSD, Novartis, Pfizer Inc, Roche, Sanofi, UCB

scholarly journals An experimental and theoretical investigation of diffusion in a two-phase alloy

1948 ◽  
Vol 192 (1031) ◽  
pp. 575-592 ◽  
Keyword(s):  
Free Energy ◽  
Single Phase ◽  
Phase State ◽  
Theoretical Treatment ◽  
Research Association ◽  
Essential Difference ◽  
Two Phase ◽  
Two Factors ◽  
Order Of Magnitude ◽  
The Difference

The present paper describes an investigation of diffusion in the solid state. Previous experimental work has been confined to the case in which the free energy of a mixture is a minimum for the single-phase state, and diffusion decreases local differences of concentration. This may be called ‘diffusion downhill’. However, it is possible for the free energy to be a minimum for the two-phase state; diffusion may then increase differences of concentration; and so may be called ‘diffusion uphill’. Becker (1937) has proposed a simple theoretical treatment of these two types of diffusion in a binary alloy. The present paper describes an experimental test of this theory, using the unusual properties of the alloy Cu 4 FeNi 3 . This alloy is single phase above 800° C and two-phase at lower temperatures, both the phases being face-centred cubic; the essential difference between the two phases is their content of copper. On dissociating from one phase into two the alloy develops a series of intermediate structures showing striking X-ray patterns which are very sensitive to changes of structure. It was found possible to utilize these results for a quantitative study of diffusion ‘uphill’ and ‘downhill’ in the alloy. The experimental results, which can be expressed very simply, are in fair agreement with conclusions drawn from Becker’s theory. It was found that Fick’s equation, dc / dt = D d2c / dx2 , can, within the limits of error, be applied in all cases, with the modification that c denotes the difference of the measured copper concentration from its equilibrium value. The theory postulates that D is the product of two factors, of which one is D 0f the coefficient of diffusion that would be measured if the alloy were an ideal solid solution. The theory is able to calculate D/D 0 , if only in first approximation, and the experiments confirm this calculation. It was found that in most cases the speed of diffusion—‘uphill’ or ‘downhill’—has the order of magnitude of D 0 . * Now with British Electrical Research Association.

Failure Mechanisms of Particulate Two-Phase Composites

1998 ◽  
Vol 529 ◽  
Author(s):  
T. Antretter ◽  
E D. Fischer
Keyword(s):  
Residual Stresses ◽  
Crack Growth ◽  
Opening Angle ◽  
Geometrical Parameters ◽  
Two Phase ◽  
Absolute Size ◽  
The Matrix ◽  
Unit Cells ◽  
Angle Criterion ◽  
Probability Of Fracture

AbstractIn many composites consisting of hard and brittle inclusions embedded in a ductile matrix failure can be attributed to particle cleavage followed by ductile crack growth in the matrix. Both mechanisms are significantly sensitive towards the presence of residual stresses.On the one hand particle failure depends on the stress distribution inside the inclusion, which, in turn, is a function of various geometrical parameters such as the aspect ratio and the position relative to adjacent particles as well as the external load. On the other hand it has been observed that the absolute size of each particle plays a role as well and will, therefore, be taken into account in this work by means of the Weibull theory. Unit cells containing a number of quasi-randomly oriented elliptical inclusions serve as the basis for the finite element calculations. The numerical results are then correlated to the geometrical parameters defining the inclusions. The probability of fracture has been evaluated for a large number of inclusions and plotted versus the particle size. The parameters of the fitting curves to the resulting data points depend on the choice of the Weibull parameters.A crack tip opening angle criterion (CTOA) is used to describe crack growth in the matrix emanating from a broken particle. It turns out that the crack resistance of the matrix largely depends on the distance from an adjacent particle. Residual stresses due to quenching of the material tend to reduce the risk of particle cleavage but promote crack propagation in the matrix.

Multiscale Topology Optimization With Gaussian Process Regression Models

2021 ◽  
Author(s):  
Joel C. Najmon ◽  
Homero Valladares ◽  
Andres Tovar
Keyword(s):  
Topology Optimization ◽  
Gaussian Process ◽  
Regression Models ◽  
Computational Cost ◽  
Gaussian Process Regression ◽  
Analytical Sensitivity ◽  
Inverse Homogenization ◽  
Discrete Location ◽  
Unit Cells ◽  
Periodic Microstructures

Abstract Multiscale topology optimization (MSTO) is a numerical design approach to optimally distribute material within coupled design domains at multiple length scales. Due to the substantial computational cost of performing topology optimization at multiple scales, MSTO methods often feature subroutines such as homogenization of parameterized unit cells and inverse homogenization of periodic microstructures. Parameterized unit cells are of great practical use, but limit the design to a pre-selected cell shape. On the other hand, inverse homogenization provide a physical representation of an optimal periodic microstructure at every discrete location, but do not necessarily embody a manufacturable structure. To address these limitations, this paper introduces a Gaussian process regression model-assisted MSTO method that features the optimal distribution of material at the macroscale and topology optimization of a manufacturable microscale structure. In the proposed approach, a macroscale optimization problem is solved using a gradient-based optimizer The design variables are defined as the homogenized stiffness tensors of the microscale topologies. As such, analytical sensitivity is not possible so the sensitivity coefficients are approximated using finite differences after each microscale topology is optimized. The computational cost of optimizing each microstructure is dramatically reduced by using Gaussian process regression models to approximate the homogenized stiffness tensor. The capability of the proposed MSTO method is demonstrated with two three-dimensional numerical examples. The correlation of the Gaussian process regression models are presented along with the final multiscale topologies for the two examples: a cantilever beam and a 3-point bending beam.

scholarly journals Are cosmological gas accretion streams multiphase and turbulent?

2018 ◽  
Vol 610 ◽  
pp. A75 ◽  
Author(s):  
Nicolas Cornuault ◽  
Matthew D. Lehnert ◽  
François Boulanger ◽  
Pierre Guillard
Keyword(s):  
Galaxy Formation ◽  
Direct Interaction ◽  
Mass Range ◽  
Initial Kinetic Energy ◽  
Two Phase ◽  
Dynamical Time ◽  
Order Of Magnitude ◽  
Post Shock ◽  
Gas Accretion ◽  
Halo Gas

Simulations of cosmological filamentary accretion reveal flows (“streams”) of warm gas, T ~ 104 K, which bring gas into galaxies efficiently. We present a phenomenological scenario in which gas in such flows, if it is shocked as it enters the halo as we assume and depending on the post-shock temperature, stream radius, its relative overdensity, and other factors, becomes biphasic and turbulent. We consider a collimated stream of warm gas that flows into a halo from an overdense filament of the cosmic web. The post-shock streaming gas expands because it has a higher pressure than the ambient halo gas and fragments as it cools. The fragmented stream forms a two phase medium: a warm cloudy phase embedded in hot post-shock gas. We argue that the hot phase sustains the accretion shock. During fragmentation, a fraction of the initial kinetic energy of the infalling gas is converted into turbulence among and within the warm clouds. The thermodynamic evolution of the post-shock gas is largely determined by the relative timescales of several processes. These competing timescales characterize the cooling, expansion of the post-shock gas, amount of turbulence in the clouds, and dynamical time of the halo. We expect the gas to become multiphase when the gas cooling and dynamical times are of the same order of magnitude. In this framework, we show that this mainly occurs in the mass range, Mhalo ~ 1011 to 1013 M⊙, where the bulk of stars have formed in galaxies. Because of the expansion of the stream and turbulence, gas accreting along cosmic web filaments may eventually lose coherence and mix with the ambient halo gas. Through both the phase separation and “disruption” of the stream, the accretion efficiency onto a galaxy in a halo dynamical time is lowered. Decollimating flows make the direct interaction between galaxy feedback and accretion streams more likely, thereby further reducing the overall accretion efficiency. As we discuss in this work, moderating the gas accretion efficiency through these mechanisms may help to alleviate a number of significant challenges in theoretical galaxy formation.

Towards imperfection insensitive buckling response of shell structures-shells with plate-like post-buckled responses

2016 ◽  
Vol 120 (1224) ◽  
pp. 233-253 ◽  
Author(s):  
S. C. White ◽  
P. M. Weaver
Keyword(s):  
Variable Stiffness ◽  
Axial Stiffness ◽  
Asymptotic Model ◽  
Imperfection Sensitivity ◽  
Asymptotic Results ◽  
Buckling Mode ◽  
Design Variables ◽  
Non Linear ◽  
Buckling Stability ◽  
Post Buckling

ABSTRACTThe imperfection sensitivity of cylindrical panels under compression loading is shown to be not only reduced but effectively eliminated using stiffness tailoring techniques. Shells are designed with variable angle-tow (VAT) laminae, giving their laminates variable-stiffness properties over the surface co-ordinates. By employing an asymptotic model of the non-linear shell behaviour and a genetic algorithm, the post-buckling stability was maximised with respect to the VAT design variables. Results for optimised straight-fibre and VAT shells are presented in comparison with quasi-isotropic designs. In the straight-fibre case, small improvements in the post-buckling stability are shown to be possible but at the expense of the buckling load. In the VAT case, on the other hand, considerable improvements in the post-buckling stability are obtained and drops in axial stiffness and load associated with buckling are reduced to negligible levels. The improvements are shown to be a result of a benign membrane stress distribution prior to buckling and a localisation of the buckling mode. The asymptotic results are compared with non-linear finite-element analyses and are found to be in good agreement. Potential future multi-objective optimisation studies are discussed.

Liquid and Gas Phase Velocity Measurements for Two Phase Flow in a Branching Microchannel Network

2007 ◽  
Author(s):  
Younghoon Kwak ◽  
Deborah Pence ◽  
James Liburdy ◽  
Vinod Narayanan
Keyword(s):  
Liquid Velocity ◽  
Leading Edge ◽  
Velocity Measurements ◽  
Trailing Edge ◽  
Two Phase ◽  
Order Of Magnitude ◽  
Image Pairs ◽  
Superficial Gas Velocity ◽  
Liquid Flows ◽  
Velocity Deficits

This is a work in progress. The objective of the present work is to develop techniques for assessing velocity deficits in branching microchannel networks. Liquid velocity distributions were acquired using μPIV in gas-liquid flows through the initial branch in a fractal-like branching microchannel flow network. Gas interface velocities were determined along the centerline of the channel. The flow rate of air and water were 0.0016 g/min and 20 g/min, respectively. The primary observed flow regime was elongated bubbles. Experimental liquid velocities well matched the 0.20 m/s superficial liquid velocity. Experimental interface velocities were approximately an order of magnitude higher than the superficial gas velocity of 0.01 m/s. Velocity deficits based on measurements are on the order of 0.065 m/s. Using interfacial velocities at the channel centerline, the trailing edge velocity was observed to be 15% percent faster, on average, than the leading edge velocity. This could be attributed to bubbles expanding into the bifurcation. Twenty percent standard deviations in average interface velocities were attributed to insufficient samples as well as projected to be a consequence of changing shape of the interface between consecutive image pairs. Changes in bubble shape may also be responsible for the observed differences between leading and trailing edge velocities.

scholarly journals Absolute linear instability in laminar and turbulent gas–liquid two-layer channel flow

2013 ◽  
Vol 714 ◽  
pp. 58-94 ◽  
Author(s):  
Lennon Ó Náraigh ◽  
Peter D. M. Spelt ◽  
Stephen J. Shaw
Keyword(s):  
Gas Flow ◽  
Oil And Gas ◽  
Stability Boundary ◽  
Density Ratio ◽  
Bottom Layer ◽  
Linear Instability ◽  
Absolute Instability ◽  
Two Phase ◽  
Order Of Magnitude ◽  
Temporal Modes

AbstractWe study two-phase stratified flow where the bottom layer is a thin laminar liquid and the upper layer is a fully developed gas flow. The gas flow can be laminar or turbulent. To determine the boundary between convective and absolute instability, we use Orr–Sommerfeld stability theory, and a combination of linear modal analysis and ray analysis. For turbulent gas flow, and for the density ratio $r= 1000$, we find large regions of parameter space that produce absolute instability. These parameter regimes involve viscosity ratios of direct relevance to oil and gas flows. If, instead, the gas layer is laminar, absolute instability persists for the density ratio $r= 1000$, although the convective/absolute stability boundary occurs at a viscosity ratio that is an order of magnitude smaller than in the turbulent case. Two further unstable temporal modes exist in both the laminar and the turbulent cases, one of which can exclude absolute instability. We compare our results with an experimentally determined flow-regime map, and discuss the potential application of the present method to nonlinear analyses.

Characterization of Minority-Carrier Hole Transport in Nitride-Based Light-Emitting Diodes with Optical and Electrical Time-Resolved Techniques

2004 ◽  
Vol 831 ◽  
Author(s):  
R. J. Kaplar ◽  
S. R. Kurtz ◽  
D. D. Koleske ◽  
A. A. Allerman ◽  
A. J. Fischer ◽  
...  
Keyword(s):  
Light Emitting Diodes ◽  
Minority Carrier ◽  
Hole Transport ◽  
Optical Measurements ◽  
Hole Density ◽  
Transport Parameters ◽  
Two Phase ◽  
Time Resolved ◽  
Light Emitting ◽  
Order Of Magnitude

ABSTRACTForward-to-reverse bias step-recovery measurements were performed on In.07Ga.93N/GaN and Al.36Ga.64N/Al.46Ga.54N quantum-well (QW) light-emitting diodes grown on sapphire. With the QW sampling the minority-carrier hole density at a single position, distinctive two-phase optical decay curves were observed. Using diffusion equation solutions to self-consistently model both the electrical and optical responses, hole transport parameters τp = 758 ± 44 ns, Lp = 588 ± 45 nm, and μp = 0.18 ± 0.02 cm2/Vs were obtained for GaN. The mobility was thermally activated with an activation energy of 52 meV, suggesting trap-modulated transport. Optical measurements of sub-bandgap peaks exhibited slow responses approaching the bulk lifetime. For Al.46Ga.54N, a longer lifetime of τp = 3.0 μs was observed, and the diffusion length was shorter, Lp ≈ 280 nm. Mobility was an order of magnitude smaller than in GaN, μp ≈ 10−2 cm2/Vs, and was insensitive to temperature, suggesting hole transport through a network of defects.

The specific heat of lithium from 20 to 300 °K: the martensitic transformation

1960 ◽  
Vol 254 (1279) ◽  
pp. 444-454 ◽  
Keyword(s):  
Martensitic Transformation ◽  
Specific Heat ◽  
Atomic Weight ◽  
Phase Region ◽  
Two Phase ◽  
Self Diffusion ◽  
Debye Temperatures ◽  
Order Of Magnitude ◽  
Two Phases ◽  
Heat Of Transformation

Measurements on lithium of atomic weight 6·945 are reported. A thermal study of the martensitic transformation showed a large specific-heat anomaly in the reversion region and a specific heat dependent upon thermal history in the two-phase region. The high-temperature end of the reversion anomaly shows time effects which suggest that the process here is controlled by a spectrum of activation energies of the same order of magnitude as that for self diffusion. With some assumptions the heat of transformation from hexagonal closepacked to body-centered cubic lithium is deduced to be about 14 cal/g atom and the Debye temperatures of the two phases at 60 °K are 390 and 371 °K respectively. The entropy at 298·15 °K is 6·95 ±0·04 cal/°K g atom.

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