75 research outputs found
Analysis and simulations for a phaseâfield fracture model at finite strains based on modified invariants
Phaseâfield models have already been proven to predict complex fracture patterns for brittle fracture at small strains. In this paper we discuss a model for phaseâfield fracture at finite deformations in more detail. Among the identification of crack location and projection of crack growth the numerical stability is one of the main challenges in solid mechanics. Here we present a phaseâfield model at finite strains, which takes into account the anisotropy of damage by applying an anisotropic split of the modified invariants of the right CauchyâGreen strain tensor. We introduce a suitable weak notion of solution that also allows for a spatial and temporal discretization of the model. In this framework we study the existence of solutions and we show that the timeâdiscrete solutions converge in a weak sense to a solution of the timeâcontinuous formulation of the model. Numerical examples in two and three space dimensions illustrate the range of validity of the analytical results
A Model for the Elasticity of Compressed Emulsions
We present a new model to describe the unusual elastic properties of
compressed emulsions. The response of a single droplet under compression is
investigated numerically for different Wigner-Seitz cells. The response is
softer than harmonic, and depends on the coordination number of the droplet.
Using these results, we propose a new effective inter-droplet potential which
is used to determine the elastic response of a monodisperse collection of
disordered droplets as a function of volume fraction. Our results are in
excellent agreement with recent experiments. This suggests that anharmonicity,
together with disorder, are responsible for the quasi-linear increase of
and observed at .Comment: RevTeX with psfig-included figures and a galley macr
Deformation of Small Compressed Droplets
We investigate the elastic properties of small droplets under compression.
The compression of a bubble by two parallel plates is solved exactly and it is
shown that a lowest-order expansion of the solution reduces to a form similar
to that obtained by Morse and Witten. Other systems are studied numerically and
results for configurations involving between 2 and 20 compressing planes are
presented. It is found that the response to compression depends on the number
of planes. The shear modulus is also calculated for common lattices and the
stability crossover between f.c.c.\ and b.c.c.\ is discussed.Comment: RevTeX with psfig-included figures and a galley macr
Study on the temperature dependence of the bulk modulus of polyisoprene by molecular dynamics simulations
The temperature dependence of the bulk modulus of polyisoprene has been studied using molecular dynamics simulations. Virtual polyisoprenes have been submitted to volume contractions above and below the glass transition. Bulk modulus has been observed to be linearly dependent on temperature both above and below the glass transition respectively, and it dropped by a factor of about 2 while temperatures was risen above the glass transition. By monitoring the energy changes during volume contractions, it was observed that the bulk modulus arises mainly from the Van de Waals interactions. Nevertheless, the entropy contribution to the bulk modulus becomes significant above the glass transition. At a first order, the entropy part of the bulk modulus can be considered as independent on the temperature.Projet ANR jeunes chercheurs MELAC JC05_43403
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