Contours for Planar Cracks Growing in Three Dimensions: Influence of Kinetic Energy

2015 ◽  
Vol 82 (11) ◽  
Author(s):  
L. M. Brock
Keyword(s):  
Kinetic Energy ◽  
Crack Edge ◽  
Three Dimensions ◽  
Crack Plane ◽  
Infinite Plane ◽  
Brittle Crack ◽  
Elastic Solids ◽  
Point Forces ◽  
State Growth ◽  
Subcritical Speed

Dynamic steady-state growth in 3D of a semi-infinite plane brittle crack in isotropic elastic solids is considered. Loads cause growth by translating on the crack surfaces at constant, subcritical speed. An analytical solution is obtained and subjected to a criterion for brittle crack growth based on dynamic energy release rate, with kinetic energy included. The result is a nonlinear differential equation for the crack contour, i.e., the curve formed by the crack edge in the crack plane. The equation is studied for the case of compression loading by translating point forces. At large distances from the forces, the crack edge asymptotically approaches the rectilinear and kinetic energy effects can be negligible. A bulge forms around the forces, however, the effect of kinetic energy on its size can be pronounced.

scholarly journals Longitudinal change in left ventricular 4D flow kinetic energy after myocardial infarction

2021 ◽  
Vol 22 (Supplement_1) ◽  
Author(s):  
H Ben-Arzi ◽  
A Das ◽  
C Kelly ◽  
RJ Van Der Geest ◽  
A Chowdhary ◽  
...  
Keyword(s):  
Myocardial Infarction ◽  
Kinetic Energy ◽  
Left Ventricular ◽  
Three Dimensions ◽  
Longitudinal Change ◽  
P Value ◽  
4D Flow ◽  
Longitudinal Changes ◽  
Funding Sources ◽  
End Diastolic Volume

Abstract Funding Acknowledgements Type of funding sources: Foundation. Main funding source(s): British Heart Foundation HRUK Background. Four-dimensional flow (4D flow) cardiovascular magnetic resonance (CMR) imaging provides quantification of intra-cavity left ventricular (LV) flow kinetic energy (KE) parameters in three dimensions. Myocardial infarction (MI) is known to cause acute alterations in intra-cardiac blood flow but assessments of longitudinal changes are lacking. Purpose. Assess longitudinal changes in LV flow post ST-elevation myocardial infarction (STEMI). Method. Twenty acutely reperfused STEMI patients (13 men, 7 women, mean age 54 ± 9 years) underwent 3T CMR acutely (within 5-7 days) and 3 months post-MI.  CMR protocol included functional imaging, late gadolinium enhancement and 4D flow. Using Q-MASS, LV KE parameters were derived and indexed to LV end-diastolic volume (LVKEiEDV). Based on acute ejection fraction (EF), patients were grouped as follows: preserved (pEF) EF >50%, reduced (rEF) EF <50% including mild (rEF= 40-49%), moderate to severe (EF <40%) impairment.  Results. Out of 20 patients, 13 had rEF acutely (7 mild rEF, 6 moderate to severe rEF). Acute LVKEiEDV parameters varied significantly between pEF and rEF (Table). At 3 months, pEF and mild rEF patients showed a significant (P < 0.05) reduction in average, systolic and peak-A wave LVKEiEDV. Mild rEF patients also had significant (P < 0.05) reduction in minimal and peak-E wave LVKEiEDV. However in patients with moderate to severe rEF in the acute scan, there were no significant change by 3 months (Figure). Conclusion. Following MI, 4D flow LVKE derived biomarkers significantly decreased over time in pEF and mild rEF groups but not in moderate to severe rEF group. 4D flow assessment might provide incremental prognostic value beyond EF assessment alone. Table pEF (n = 7) rEF (n = 13) V1 V2 P-value V1 V2 P-value EF(%) 56 ± 5 55 ± 4 0.40 41 ± 7 47 ± 9 0.01 Infarct Size(%) 31 ± 20 15 ± 9 0.04 18 ± 13† 16 ± 11 0.41 LV KEiEDV parameters Average(µJ/ml) 9 ± 2 7 ± 2 0.02 10 ± 3† 8 ± 3 0.01 Minimal(µJ/ml) 1 ± 0.6 1 ± 0.5 0.46 1.3 ± 0.5 1 ± 0.6 0.03 Systolic(µJ/ml) 10 ± 4 7 ± 2 <0.01 12 ± 4† 7 ± 3 <0.01 Diastolic(µJ/ml) 8 ± 3 7 ± 2 0.13 9 ± 3 8 ± 3 0.09 Peak-E wave(µJ/ml) 22 ± 9 23 ± 8 0.44 20 ± 7 18 ± 10 0.23 Peak-A wave(µJ/ml) 18 ± 10 11 ± 4 0.04 17 ± 9 14 ± 7 0.02 †P < 0.05 V1 comparison between pEF and rEF Abstract Figure

scholarly journals On some nonlinear inverse problems in elasticity

2011 ◽  
Vol 38 (2) ◽  
pp. 125-154 ◽  
Author(s):  
S. Andrieux ◽  
H.D. Bui
Keyword(s):  
Inverse Problems ◽  
Closed Form ◽  
Variational Equation ◽  
Material Constant ◽  
Displacement Discontinuity ◽  
Crack Plane ◽  
Nonlinear Case ◽  
Elastic Solids ◽  
Linear Inverse Problems ◽  
Statics And Dynamics

In this paper, we make a review of some inverse problems in elasticity, in statics and dynamics, in acoustics, thermoelasticity and viscoelasticity. Crack inverse problems have been solved in closed form, by considering a nonlinear variational equation provided by the reciprocity gap functional. This equation involves the unknown geometry of the crack and the boundary data. It results from the symmetry lost between current fields and adjoint fields which is related to their support. The nonlinear equation is solved step by step by considering linear inverse problems. The normal to the crack plane, then the crack plane and finally the geometry of the crack, defined by the support of the crack displacement discontinuity, are determined explicitly. We also consider the problem of a volumetric defect viewed as the perturbation of a material constant in elastic solids which satisfies the nonlinear Calderon?s equation. The nonlinear problem reduces to two successive ones: a source inverse problem and a Volterra integral equation of the first kind. The first problem provides information on the inclusion geometry. The second one provides the magnitude of the perturbation. The geometry of the defect in the nonlinear case is obtained in closed form and compared to the linearized Calderon?s solution. Both geometries, in linearized and nonlinear cases, are found to be the same.

scholarly journals Tracking capsule activation and crack healing in a microcapsule-based self-healing polymer

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
S. A. McDonald ◽  
S. B. Coban ◽  
N. R. Sottos ◽  
P. J. Withers
Keyword(s):  
Healing Process ◽  
Polymeric Materials ◽  
Time Lapse ◽  
Repair Process ◽  
Three Dimensions ◽  
Crack Plane ◽  
Self Healing ◽  
Crack Healing ◽  
Healing Agent ◽  
First Time

AbstractStructural polymeric materials incorporating a microencapsulated liquid healing agent demonstrate the ability to autonomously heal cracks. Understanding how an advancing crack interacts with the microcapsules is critical to optimizing performance through tailoring the size, distribution and density of these capsules. For the first time, time-lapse synchrotron X-ray phase contrast computed tomography (CT) has been used to observe in three-dimensions (3D) the dynamic process of crack growth, microcapsule rupture and progressive release of solvent into a crack as it propagates and widens, providing unique insights into the activation and repair process. In this epoxy self-healing material, 150 µm diameter microcapsules within 400 µm of the crack plane are found to rupture and contribute to the healing process, their discharge quantified as a function of crack propagation and distance from the crack plane. Significantly, continued release of solvent takes place to repair the crack as it grows and progressively widens.

scholarly journals Three-dimensional magnetic reconnection and its application to solar flares

2017 ◽  
Vol 83 (1) ◽  
Author(s):  
Miho Janvier
Keyword(s):  
Kinetic Energy ◽  
Numerical Simulations ◽  
Magnetic Reconnection ◽  
Solar Flares ◽  
Magnetic Energy ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Current Layer ◽  
Solar Observations ◽  
The Universe

Solar flares are powerful radiations occurring in the Sun’s atmosphere. They are powered by magnetic reconnection, a phenomenon that can convert magnetic energy into other forms of energy such as heat and kinetic energy, and which is believed to be ubiquitous in the universe. With the ever increasing spatial and temporal resolutions of solar observations, as well as numerical simulations benefiting from increasing computer power, we can now probe into the nature and the characteristics of magnetic reconnection in three dimensions to better understand the phenomenon’s consequences during eruptive flares in our star’s atmosphere. We review in the following the efforts made on different fronts to approach the problem of magnetic reconnection. In particular, we will see how understanding the magnetic topology in three dimensions helps in locating the most probable regions for reconnection to occur, how the current layer evolves in three dimensions and how reconnection leads to the formation of flux ropes, plasmoids and flaring loops.

Analysis of the Reflection of Point Force-Induced Crack Surface Waves by a Crack Edge

1985 ◽  
Vol 52 (1) ◽  
pp. 57-61 ◽  
Author(s):  
L. M. Brock ◽  
H. P. Rossmanith
Keyword(s):  
Surface Waves ◽  
Crack Surface ◽  
Crack Edge ◽  
Stress Fields ◽  
Surface Reflection ◽  
Reflection Process ◽  
Point Forces ◽  
Analytical Expressions ◽  
Insight Into ◽  
Component Parallel

Dynamic stress fields near cracks follow in part from the reflection of crack surface waves by the crack edges. To gain insight into the reflection process, the problem of stationary normal and tangential point forces applied to one surface of a stationary semi-infinite crack is considered, and analytical expressions for the crack surface reflection-generated particle velocity waves presented. Study of these expressions shows that the dominant reflected wave is singular at its wave front, travels at the Rayleigh speed, and is generated by the reflection of a singular Rayleigh wave. However, the reflection process “moves” the singularity from the velocity component parallel to the particular force to the component normal to it.

scholarly journals A Comprehensive Observational Study of Graupel and Hail Terminal Velocity, Mass Flux, and Kinetic Energy

2018 ◽  
Vol 75 (11) ◽  
pp. 3861-3885 ◽  
Author(s):  
Andrew Heymsfield ◽  
Miklós Szakáll ◽  
Alexander Jost ◽  
Ian Giammanco ◽  
Robert Wright
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Mass Flux ◽  
Three Dimensional ◽  
Acrylonitrile Butadiene Styrene ◽  
Terminal Velocity ◽  
Three Dimensions ◽  
Cross Sectional ◽  
Wide Range ◽  
3D Volume

Abstract This study uses novel approaches to estimate the fall characteristics of hail, covering a size range from about 0.5 to 7 cm, and the drag coefficients of lump and conical graupel. Three-dimensional (3D) volume scans of 60 hailstones of sizes from 2.5 to 6.7 cm were printed in three dimensions using acrylonitrile butadiene styrene (ABS) plastic, and their terminal velocities were measured in the Mainz, Germany, vertical wind tunnel. To simulate lump graupel, 40 of the hailstones were printed with maximum dimensions of about 0.2, 0.3, and 0.5 cm, and their terminal velocities were measured. Conical graupel, whose three dimensions (maximum dimension 0.1–1 cm) were estimated from an analytical representation and printed, and the terminal velocities of seven groups of particles were measured in the tunnel. From these experiments, with printed particle densities from 0.2 to 0.9 g cm−3, together with earlier observations, relationships between the drag coefficient and the Reynolds number and between the Reynolds number and the Best number were derived for a wide range of particle sizes and heights (pressures) in the atmosphere. This information, together with the combined total of more than 2800 hailstones for which the mass and the cross-sectional area were measured, has been used to develop size-dependent relationships for the terminal velocity, the mass flux, and the kinetic energy of realistic hailstones.

Sign in / Sign up

Export Citation Format

Share Document