1,100,447 research outputs found
Accurate computation of surface stresses and forces with immersed boundary methods
Many immersed boundary methods solve for surface stresses that impose the
velocity boundary conditions on an immersed body. These surface stresses may
contain spurious oscillations that make them ill-suited for representing the
physical surface stresses on the body. Moreover, these inaccurate stresses
often lead to unphysical oscillations in the history of integrated surface
forces such as the coefficient of lift. While the errors in the surface
stresses and forces do not necessarily affect the convergence of the velocity
field, it is desirable, especially in fluid-structure interaction problems, to
obtain smooth and convergent stress distributions on the surface. To this end,
we show that the equation for the surface stresses is an integral equation of
the first kind whose ill-posedness is the source of spurious oscillations in
the stresses. We also demonstrate that for sufficiently smooth delta functions,
the oscillations may be filtered out to obtain physically accurate surface
stresses. The filtering is applied as a post-processing procedure, so that the
convergence of the velocity field is unaffected. We demonstrate the efficacy of
the method by computing stresses and forces that converge to the physical
stresses and forces for several test problems
Stresses in lipid membranes
The stresses in a closed lipid membrane described by the Helfrich
hamiltonian, quadratic in the extrinsic curvature, are identified using
Noether's theorem. Three equations describe the conservation of the stress
tensor: the normal projection is identified as the shape equation describing
equilibrium configurations; the tangential projections are consistency
conditions on the stresses which capture the fluid character of such membranes.
The corresponding torque tensor is also identified. The use of the stress
tensor as a basis for perturbation theory is discussed. The conservation laws
are cast in terms of the forces and torques on closed curves. As an
application, the first integral of the shape equation for axially symmetric
configurations is derived by examining the forces which are balanced along
circles of constant latitude.Comment: 16 pages, introduction rewritten, other minor changes, new references
added, version to appear in Journal of Physics
Residual Stresses in Glasses
The history dependence of the glasses formed from flow-melted steady states
by a sudden cessation of the shear rate is studied in colloidal
suspensions, by molecular dynamics simulations, and mode-coupling theory. In an
ideal glass, stresses relax only partially, leaving behind a finite persistent
residual stress. For intermediate times, relaxation curves scale as a function
of , even though no flow is present. The macroscopic stress
evolution is connected to a length scale of residual liquefaction displayed by
microscopic mean-squared displacements. The theory describes this history
dependence of glasses sharing the same thermodynamic state variables, but
differing static properties.Comment: submitted to Physical Revie
Interplay of internal stresses, electric stresses and surface diffusion in polymer films
We investigate two destabilization mechanisms for elastic polymer films and
put them into a general framework: first, instabilities due to in-plane stress
and second due to an externally applied electric field normal to the film's
free surface. As shown recently, polymer films are often stressed due to
out-of-equilibrium fabrication processes as e.g. spin coating. Via an
Asaro-Tiller-Grinfeld mechanism as known from solids, the system can decrease
its energy by undulating its surface by surface diffusion of polymers and
thereby relaxing stresses. On the other hand, application of an electric field
is widely used experimentally to structure thin films: when the electric
Maxwell surface stress overcomes surface tension and elastic restoring forces,
the system undulates with a wavelength determined by the film thickness. We
develop a theory taking into account both mechanisms simultaneously and discuss
their interplay and the effects of the boundary conditions both at the
substrate and the free surface.Comment: 14 pages, 7 figures, 1 tabl
Three-Dimensional Quantification of Cellular Traction Forces and Mechanosensing of Thin Substrata by Fourier Traction Force Microscopy
We introduce a novel three-dimensional (3D) traction force microscopy (TFM)
method motivated by the recent discovery that cells adhering on plane surfaces
exert both in-plane and out-of-plane traction stresses. We measure the 3D
deformation of the substratum on a thin layer near its surface, and input this
information into an exact analytical solution of the elastic equilibrium
equation. These operations are performed in the Fourier domain with high
computational efficiency, allowing to obtain the 3D traction stresses from raw
microscopy images virtually in real time. We also characterize the error of
previous two-dimensional (2D) TFM methods that neglect the out-of-plane
component of the traction stresses. This analysis reveals that, under certain
combinations of experimental parameters (\ie cell size, substratums' thickness
and Poisson's ratio), the accuracy of 2D TFM methods is minimally affected by
neglecting the out-of-plane component of the traction stresses. Finally, we
consider the cell's mechanosensing of substratum thickness by 3D traction
stresses, finding that, when cells adhere on thin substrata, their out-of-plane
traction stresses can reach four times deeper into the substratum than their
in-plane traction stresses. It is also found that the substratum stiffness
sensed by applying out-of-plane traction stresses may be up to 10 times larger
than the stiffness sensed by applying in-plane traction stresses
3D Residual Stress Field in Arteries: Novel Inverse Method Based on Optical Full-field Measurements
Arterial tissue consists of multiple structurally important constituents that
have individual material properties and associated stress-free configurations
that evolve over time. This gives rise to residual stresses contributing to the
homoeostatic state of stress in vivo as well as adaptations to perturbed loads,
disease or injury. The existence of residual stresses in an intact but
load-free excised arterial segment suggests compressive and tensile stresses,
respectively, in the inner and outer walls. Accordingly, an artery ring springs
open into a sector after a radial cut. The measurement of the opening angle is
commonly used to deduce the residual stresses, which are the stresses required
to close back the ring. The opening angle method provides an average estimate
of circumferential residual stresses but it gives no information on local
distributions through the thickness and along the axial direction. To address
this lack, a new method is proposed in this article to derive maps of residual
stresses using an approach based on the contour method. A piece of freshly
excised tissue is carefully cut into the specimen, and the local distribution
of residual strains and stresses is determined from whole-body digital image
correlation measurements using an inverse approach based on a finite element
model
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The effect of weld residual stresses and their re-distribution with crack growth during fatigue under constant amplitude loading
In this work the evolution of the residual stresses in a MIG-welded 2024-T3 aluminium alloy M(T) specimen during in situ fatigue crack growth at constant load amplitude has been measured with neutron diffraction. The plastic relaxation and plasticity-induced residual stresses associated with the fatigue loading were found to be small compared with the stresses arising due to elastic re-distribution of the initial residual stress field. The elastic re-distribution was modelled with a finite element simulation and a good correlation between the experimentally-determined and the modelled stresses was found. A significant mean stress effect on the fatigue crack growth rate was seen and this was also accurately predicted using the measured initial residual stresses
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