In vivo measurement of shear modulus of the human cornea using optical coherence elastography

Corneal stiffness plays a critical role in shaping the cornea with respect to intraocular pressure and physical interventions. However, it remains difficult to measure the mechanical properties noninvasively. Here, we report the first measurement of shear modulus in human corneas in vivo using optical coherence elastography (OCE) based on surface elastic waves. In a pilot study of 12 healthy subjects aged between 25 and 67, the Rayleigh-wave speed was 7.86 ± 0.75 m/s, corresponding to a shear modulus of 72 ± 14 kPa. Our data reveal two unexpected trends: no correlation was found between the wave speed and IOP between 13–18 mmHg, and shear modulus decreases with age (− 0.32 ± 0.17 m/s per decade). We propose that shear stiffness is governed by the interfibrillar matrix, whereas tensile strength is dominated by collagen fibrils. Rayleigh-wave OCE may prove useful for clinical diagnosis, refractive surgeries, and treatment monitoring.

On Propagation of Rayleigh Type Surface Wave in Five Different Theories of Thermoelasticity

The governing equations for a homogeneous and isotropic thermoelastic medium are formulated in the context of coupled thermoelasticity, Lord and Shulman theory of generalized thermoelasticity with one relaxation time, Green and Lindsay theory of generalized thermoelasticity with two relaxation times, Green and Nagdhi theory of thermoelasticity without energy dissipation and Chandrasekharaiah and Tzou theory of thermoelasticity. These governing equations are solved to obtain general surface wave solutions. The particular solutions in a half-space are obtained with the help of appropriate radiation conditions. The two types of boundaries at athe surface of a half-space are considered namely, the stress free thermally insulated boundary and stress free isothermal boundary. The particular solutions obtained in a half-space satisfy the relevant boundary conditions at the free surface of the half-space and a frequency equation for the Rayleigh wave speed is obtained for both thermally insulated and isothermal cases. The non-dimensional Rayleigh wave speed is computed for aluminium metal to observe the effects of frequency, thermal relaxation time and different theories of thermoelasticity.

Effect of triaxial stress distribution upon roughness of brittle fracture surface

To observe the effect of stress triaxiality upon brittle fracture surface, we performed two types of experiments which differ in stress triaxiality. As a result, crack branch starting speed changes in two specimens and the speed was affected by stress triaxiality. In bending condition, branch starting speed is around 0.86 cr (cr: Rayleigh wave speed), which is higher than that in tensile condition, 0.59 cr. It was realized that in higher stress triaxiality, branching is easy to occur because in bending condition stress triaxiality is said to be lower. On the other hand, mirror-mist transition speed is not affected by stress triaxiality. By fracture surface observation, we proposed that branch occurs when microbranch grew. This proposition was supported by FEM calculation with microbranch model, it was proved that in bending condition microbranch is difficult to grow. Additionally, we proposed a qualitative explanation that microbranch is easy to grow when stress triaxiality is higher because growth of microbranch is affected by T-stress. It is since the phenomena is not on the main crack propagating plane.

Refined boundary conditions on the free surface of an elastic half-space taking into account non-local effects

The dynamic response of a homogeneous half-space, with a traction-free surface, is considered within the framework of non-local elasticity. The focus is on the dominant effect of the boundary layer on overall behaviour. A typical wavelength is assumed to considerably exceed the associated internal lengthscale. The leading-order long-wave approximation is shown to coincide formally with the ‘local’ problem for a half-space with a vertical inhomogeneity localized near the surface. Subsequent asymptotic analysis of the inhomogeneity results in an explicit correction to the classical boundary conditions on the surface. The order of the correction is greater than the order of the better-known correction to the governing differential equations. The refined boundary conditions enable us to evaluate the interior solution outside a narrow boundary layer localized near the surface. As an illustration, the effect of non-local elastic phenomena on the Rayleigh wave speed is investigated.

Elastodynamic image forces on dislocations

The elastodynamic image forces on edge and screw dislocations in the presence of a planar-free surface are derived. The explicit form of the elastodynamic fields of an injected, quiescent screw dislocation are also derived. The resulting image forces are affected by retardation effects: the dislocations experience no image force for a period of time defined by the arrival and reflection at the free surface of the dislocation fields. For the case of injected, stationary dislocations, it is shown that the elastodynamic image force tends asymptotically to the elastotatic prediction. For the case of injected, moving dislocations, it is shown that the elastodynamic image force on both the edge and the screw dislocations is magnified by inertial effects, and becomes increasingly divergent with time; this additional effect, missing in the elastostatic description, is shown to be substantial even for slow moving dislocations. Finally, it is shown that the elastodynamic image force of an edge dislocation moving towards the surface at the Rayleigh wave speed becomes repulsive, rather than attractive; this is suggestive of instabilities at the core of the dislocation, and likely resonances with the free surface.

The transition from subsonic to supersonic cracks

We present the full analytical solution for steady-state in-plane crack motion in a brittle triangular lattice. This allows quick numerical evaluation of solutions for very large systems, facilitating comparisons with continuum fracture theory. Cracks that propagate faster than the Rayleigh wave speed have been thought to be forbidden in the continuum theory, but clearly exist in lattice systems. Using our analytical methods, we examine in detail the motion of atoms around a crack tip as crack speed changes from subsonic to supersonic. Subsonic cracks feature displacement fields consistent with a stress intensity factor. For supersonic cracks, the stress intensity factor disappears. Subsonic cracks are characterized by small-amplitude, high-frequency oscillations in the vertical displacement of an atom along the crack line, while supersonic cracks have large-amplitude, low-frequency oscillations. Thus, while supersonic cracks are no less physical than subsonic cracks, the connection between microscopic and macroscopic behaviour must be made in a different way. This is one reason supersonic cracks in tension had been thought not to exist.

Molecular Dynamics of Crack Propagation in Nickel and Nickel-Aluminum Bimetal Interface

Molecular dynamics simulations were used to study crack propagation in a Nickel single crystal and a Nickel-Aluminum bimetal interface. The embedded atom method interatomic potential was used to investigate the behavior of (001) [100] crack system under mode I loading in the two systems. The propagation mechanisms and fracture behavior and properties of a propagating crack in Ni were compared with propagation, behavior and properties of a surface crack in Ni-Al that initiates and propagates from Ni towards the Ni-Al bimetal interface. Our results for Ni show an initial brittle crack propagation followed by a roughening of the crack surfaces at one-third of the Rayleigh wave speed and are in agreement with previous investigations. In Ni-Al the crack surfaces initially grow brittle. However, two regimes of crack propagation velocities were observed in this case with crack getting decelerated as it nears the interface. Further dynamic analysis of the crack propagation indicated a cease in the crack propagation in Ni due to a brittle to ductile transition. In Ni-Al bimetal interface system, as the crack approaches the interface, a process zone representing local disorder at the crack tip was observed to start growing and interacting with interfacial defects that eventually results in a blunting of the crack tip.