Stress Singularities in Swelling Soft Solids

Goriely, Alain; Weickenmeier, Johannes; Kuhl, Ellen

doi:10.1103/physrevlett.117.138001

Cited by 28 publications

(27 citation statements)

References 23 publications

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“…The outer crust of a neutron star may actually contain ultradrip nuclei. For instance, the HFB-21 mass model predicts the presence of 124 Sr with S n = 0.83 MeV; the isotope at the neutron-drip line is 121 Sr with S n = −0.33 MeV [16].…”

Section: Nonaccreted Neutron Starsmentioning

confidence: 99%

“…Still, the accuracy of any given functional can be tested against experimental nuclear data, as well as results from microscopic calculations following different many-body approaches. The most accurate exist-ing functionals are able to fit essentially all measured nuclear masses and charge radii with a root-mean square deviation of about 0.5 − 0.6 MeV/c 2 and 0.03 fm respectively, while reproducing at the same time properties of homogeneous infinite nuclear matter (equation of state, pairing gaps, effective masses) obtained from ab initio calculations [81,124]. In the nuclear energy density functional theory, the ground-state energy is obtained by solving the self-consistent Hartree-Fock-Bogoliubov (HFB) equations describing independent quasiparticles in an average field induced by the underlying particles (see, e.g.…”

Section: Nonaccreted Neutron Starsmentioning

confidence: 99%

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Phases of Dense Matter in Compact Stars

Blaschke

Chamel

2018

The Physics and Astrophysics of Neutron Stars

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Formed in the aftermath of gravitational core-collapse supernova explosions, neutron stars are unique cosmic laboratories for probing the properties of matter under extreme conditions that cannot be reproduced in terrestrial laboratories. The interior of a neutron star, endowed with the highest magnetic fields known and with densities spanning about ten orders of magnitude from the surface to the centre, is predicted to exhibit various phases of dense strongly interacting matter, whose physics is reviewed in this chapter. The outer layers of a neutron star consist of a solid nuclear crust, permeated by a neutron ocean in its densest region, possibly on top of a nuclear "pasta" mantle. The properties of these layers and of the homogeneous isospin asymmetric nuclear matter beneath constituting the outer core may still be constrained by terrestrial experiments. The inner core of highly degenerate, strongly interacting matter poses a few puzzles and questions which are reviewed here together with perspectives for their resolution. Consequences of the dense-matter phases for observables such the neutron-star mass-radius relationship and the prospects to uncover their structure with modern observational programmes are touched upon.

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Section: Nonaccreted Neutron Starsmentioning

confidence: 99%

Section: Nonaccreted Neutron Starsmentioning

confidence: 99%

Phases of Dense Matter in Compact Stars

Blaschke

Chamel

2018

The Physics and Astrophysics of Neutron Stars

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“…Current biomechanical predictive criteria for TBI are based on measurements of skull motion such as linear and rotational acceleration [1,2]. Although the relationship between skull motion and injury has been extensively tested [2][3][4][5][6][7], mechanisms relating the two have not been conclusively established [8], due to the complexity of the deformation of the brain [9][10][11] which behaves as a nonlinear viscoelastic medium. In situ measurements of the rapid transient motion of the whole brain during a traumatic event may establish a more accurate biomechanical description of injury.Shear vibration experiments on small brain samples have shown that the stress-strain relationship behaves nonlinearly for amplitudes as low as 1% [12,13], which is well below the strain threshold for injury [7,14,15].…”

mentioning

confidence: 99%

Shear Shock Waves Observed in the Brain

2017

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The internal deformation of the brain is far more complex than the rigid motion of the skull. An ultrasound imaging technique that we have developed has a combination of penetration, frame-rate, and motion detection accuracy required to directly observe, for the first time, the formation and evolution of shear shock waves in the brain. Experiments at low impacts on the traumatic brain injury scale demonstrate that they are spontaneously generated and propagate within the porcine brain. Compared to the initially smooth impact, the acceleration at the shock front is amplified up to a factor of 8.5. This highly localized increase in acceleration suggests that shear shock waves are a fundamental mechanism for traumatic injuries in soft tissue.PACS numbers: Valid PACS appear here Traumatic brain injuries (TBI's) are a major source of death and disability worldwide. Falls and motor vehicle related accidents are the largest contributors. Current biomechanical predictive criteria for TBI are based on measurements of skull motion such as linear and rotational acceleration [1,2]. Although the relationship between skull motion and injury has been extensively tested [2][3][4][5][6][7], mechanisms relating the two have not been conclusively established [8], due to the complexity of the deformation of the brain [9][10][11] which behaves as a nonlinear viscoelastic medium. In situ measurements of the rapid transient motion of the whole brain during a traumatic event may establish a more accurate biomechanical description of injury.Shear vibration experiments on small brain samples have shown that the stress-strain relationship behaves nonlinearly for amplitudes as low as 1% [12,13], which is well below the strain threshold for injury [7,14,15]. Therefore, even mild injuries typically occur within the nonlinear elastic regime. Furthermore, the brain's shear wave speed (c t ∼2 m/s) is three orders of magnitude smaller than the compressional wave speed (c p ∼1500 m/s) therefore the deformation from an impact is almost entirely in shear mode.Outside of ultrasound, current methods that measure brain motion cannot capture this nonlinear behavior of shear waves due to limitations in either, frame rate, penetration, or motion detection accuracy. For instance, magnetic resonance elastography (MRE) has been used to investigate shear wave propagation in the brain, typically at frame rates on the order of tens of images/second. Furthermore the temporal sampling of MRE is fundamentally limited to a few ms by the finite integration time over the spin relaxation [16,17]. The harmonics generated by nonlinear shear wave propagation exceed these sampling capabilities. Optical methods have larger frame rates and they can measure motion in optically trans- * david.espindola@unc.edu † gfp@unc.edu parent materials [18][19][20]. However, they are limited to shallow penetration depths in soft tissue (∼ 2 mm) [21]. The only experimental corroboration of nonlinear shear waves and its characteristic harmonic signature was made over a decade ago in a homo...

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“…To date, the precise criteria related to the optimal timing of treatment, the optimal location and size of the skull opening, and the long-term functional outcome remain unclear. From a mechanical perspective, a decompressive craniectomy is a compromise between maximizing the management of the intracranial pressure and minimizing the deformations induced by the bulging brain [17]. Recent studies have characterized bulge kinematics based on computerized tomography images before and after a decompressive craniectomy using non-linear image registration [19]; yet, little is know about the stress, stretch, and strain inside the brain.…”

mentioning

confidence: 99%

Bulging Brains

Weickenmeier

Saéz

Butler

et al. 2016

J Elast

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Brain swelling is a serious condition associated with an accumulation of fluid inside the brain that can be caused by trauma, stroke, infection, or tumors. It increases the pressure inside the skull and reduces blood and oxygen supply. To relieve the intracranial pressure, neurosurgeons remove part of the skull and allow the swollen brain to bulge outward, a procedure known as decompressive craniectomy. Decompressive craniectomy has been preformed for more than a century; yet, its effects on the swollen brain remain poorly understood. Here we characterize the deformation, strain, and stretch in bulging brains using the nonlinear field theories of mechanics. Our study shows that even small swelling volumes of 28 to 56 ml induce maximum principal strains in excess of 30%. For radially outward-pointing axons, we observe maximal normal stretches of 1.3 deep inside the bulge and maximal tangential stretches of 1.3 around the craniectomy edge. While the stretch magnitude varies with opening site and swelling region, our study suggests that the locations of maximum stretch are universally shared amongst all bulging brains. Our model has the potential to inform neurosurgeons and rationalize the shape and position of the skull opening, with the ultimate goal to reduce brain damage and improve the structural and functional outcomes of decompressive craniectomy in trauma patients.

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Stress Singularities in Swelling Soft Solids

Cited by 28 publications

References 23 publications

Phases of Dense Matter in Compact Stars

Phases of Dense Matter in Compact Stars

Shear Shock Waves Observed in the Brain

Bulging Brains

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