252 research outputs found
Thermodynamics of non-local materials: extra fluxes and internal powers
The most usual formulation of the Laws of Thermodynamics turns out to be
suitable for local or simple materials, while for non-local systems there are
two different ways: either modify this usual formulation by introducing
suitable extra fluxes or express the Laws of Thermodynamics in terms of
internal powers directly, as we propose in this paper. The first choice is
subject to the criticism that the vector fluxes must be introduced a posteriori
in order to obtain the compatibility with the Laws of Thermodynamics. On the
contrary, the formulation in terms of internal powers is more general, because
it is a priori defined on the basis of the constitutive equations. Besides it
allows to highlight, without ambiguity, the contribution of the internal powers
in the variation of the thermodynamic potentials. Finally, in this paper, we
consider some examples of non-local materials and derive the proper expressions
of their internal powers from the power balance laws.Comment: 16 pages, in press on Continuum Mechanics and Thermodynamic
Designing of a Fleet-Leader Program for Carbon Composite Overwrapped Pressure Vessels
Composite Overwrapped Pressure Vessels (COPVs) are often used for storing pressurant gases on board spacecraft when mass saving is a prime requirement. Substantial weight savings can be achieved compared to all metallic pressure vessels. For example, on the space shuttle, replacement of all metallic pressure vessels with Kevlar COPVs resulted in a weight savings of about 30 percent. Mass critical space applications such as the Ares and Orion vehicles are currently being planned to use as many COPVs as possible in place of all-metallic pressure vessels to minimize the overall mass of the vehicle. Due to the fact that overwraps are subjected to sustained loads during long periods of a mission, stress rupture failure is a major concern. It is, therefore, important to ascertain the reliability of these vessels by analysis, since it is practically impossible to show by experimental testing the reliability of flight quality vessels. Also, it is a common practice to set aside flight quality vessels as "fleet leaders" in a test program where these vessels are subjected to slightly accelerated operating conditions so that they lead the actual flight vessels both in time and load. The intention of fleet leaders is to provide advanced warning if there is a serious design flaw in the vessels so that a major disaster in the flight vessels can be averted with advance warning. On the other hand, the accelerating conditions must be not so severe as to be prone to false alarms. The primary focus of the present paper is to provide an analytical basis for designing a viable fleet leader program for carbon COPVs. The analysis is based on a stress rupture behavior model incorporating Weibull statistics and power-law sensitivity of life to fiber stress level
Time evolution of damage under variable ranges of load transfer
We study the time evolution of damage in a fiber bundle model in which the
range of interaction of fibers varies through an adjustable stress transfer
function recently introduced. We find that the lifetime of the material
exhibits a crossover from mean field to short range behavior as in the static
case. Numerical calculations showed that the value at which the transition
takes place depends on the system's disorder. Finally, we have performed a
microscopic analysis of the failure process. Our results confirm that the
growth dynamics of the largest crack is radically different in the two limiting
regimes of load transfer during the first stages of breaking.Comment: 8 pages, 7 figures, revtex4 styl
Distributed optimal control of a nonstandard system of phase field equations
We investigate a distributed optimal control problem for a phase field model
of Cahn-Hilliard type. The model describes two-species phase segregation on an
atomic lattice under the presence of diffusion; it has been recently introduced
by the same authors in arXiv:1103.4585v1 [math.AP] and consists of a system of
two highly nonlinearly coupled PDEs. For this reason, standard arguments of
optimal control theory do not apply directly, although the control constraints
and the cost functional are of standard type. We show that the problem admits a
solution, and we derive the first-order necessary conditions of optimality.Comment: Key words: distributed optimal control, nonlinear phase field
systems, first-order necessary optimality condition
Fracture model with variable range of interaction
We introduce a fiber bundle model where the interaction among fibers is
modeled by an adjustable stress-transfer function which can interpolate between
the two limiting cases of load redistribution, the global and the local load
sharing schemes. By varying the range of interaction several features of the
model are numerically studied and a crossover from mean field to short range
behavior is obtained. The properties of the two regimes and the emergence of
the crossover in between are explored by numerically studying the dependence of
the ultimate strength of the material on the system size, the distribution of
avalanches of breakings, and of the cluster sizes of broken fibers. Finally, we
analyze the moments of the cluster size distributions to accurately determine
the value at which the crossover is observed.Comment: 8 pages, 8 figures. Two columns revtex format. Final version to be
published in Phys. Rev.
Failure due to fatigue in fiber bundles and solids
We consider first a homogeneous fiber bundle model where all the fibers have
got the same stress threshold beyond which all fail simultaneously in absence
of noise. At finite noise, the bundle acquires a fatigue behavior due to the
noise-induced failure probability at any stress. We solve this dynamics of
failure analytically and show that the average failure time of the bundle
decreases exponentially as the stress increases. We also determine the
avalanche size distribution during such failure and find a power law decay. We
compare this fatigue behavior with that obtained phenomenologically for the
nucleation of Griffith cracks. Next we study numerically the fatigue behavior
of random fiber bundles having simple distributions of individual fiber
strengths, at stress less than the bundle's strength (beyond which it fails
instantly). The average failure time is again seen to decrease exponentially as
the stress increases and the avalanche size distribution shows similar power
law decay. These results are also in broad agreement with experimental
observations on fatigue in solids. We believe, these observations regarding the
failure time are useful for quantum breakdown phenomena in disordered systems.Comment: 13 pages, 4 figures, figures added and the text is revise
Self-consistent quantum effects in the quark meson coupling model
We derive the equation of state of nuclear matter including vacuum
polarization effects arising from the nucleons and the sigma mesons in the
quark-meson coupling model which incorporates explicitly quark degrees of
freedom with quark coupled to the scalar and vector mesons. This leads to a
softer equation of state for nuclear matter giving a lower value of
incompressibility than would be reached without quantum effects. The {\it
in-medium} nucleon and sigma meson masses are also calculated in a
self-consistent manner.Comment: 10 pages, latex, 5 figure
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