73 research outputs found
Laplacian transfer across a rough interface: Numerical resolution in the conformal plane
We use a conformal mapping technique to study the Laplacian transfer across a
rough interface. Natural Dirichlet or Von Neumann boundary condition are simply
read by the conformal map. Mixed boundary condition, albeit being more complex
can be efficiently treated in the conformal plane. We show in particular that
an expansion of the potential on a basis of evanescent waves in the conformal
plane allows to write a well-conditioned 1D linear system. These general
principle are illustrated by numerical results on rough interfaces
Modeling the mechanics of amorphous solids at different length and time scales
We review the recent literature on the simulation of the structure and
deformation of amorphous glasses, including oxide and metallic glasses. We
consider simulations at different length and time scales. At the nanometer
scale, we review studies based on atomistic simulations, with a particular
emphasis on the role of the potential energy landscape and of the temperature.
At the micrometer scale, we present the different mesoscopic models of
amorphous plasticity and show the relation between shear banding and the type
of disorder and correlations (e.g. elastic) included in the models. At the
macroscopic range, we review the different constitutive laws used in finite
element simulations. We end the review by a critical discussion on the
opportunities and challenges offered by multiscale modeling and transfer of
information between scales to study amorphous plasticity.Comment: 58 pages, 14 figure
Quantitative prediction of effective toughness at random heterogeneous interfaces
The propagation of an adhesive crack through an anisotropic heterogeneous
interface is considered. Tuning the local toughness distribution function and
spatial correlation is numerically shown to induce a transition between weak to
strong pinning conditions. While the macroscopic effective toughness is given
by the mean local toughness in case of weak pinning, a systematic toughness
enhancement is observed for strong pinning (the critical point of the depinning
transition). A self-consistent approximation is shown to account very
accurately for this evolution, without any free parameter
Avalanches, precursors and finite size fluctuations in a mesoscopic model of amorphous plasticity
We discuss avalanche and finite size fluctuations in a mesoscopic model to
describe the shear plasticity of amorphous materials. Plastic deformation is
assumed to occur through series of local reorganizations. Yield stress criteria
are random while each plastic slip event induces a quadrupolar long range
elastic stress redistribution. The model is discretized on a regular square
lattice. Shear plasticity can be studied in this context as a depinning dynamic
phase transition. We show evidence for a scale free distribution of avalanches
with a non trivial exponent
significantly different from the mean field result . Finite size
effects allow for a characterization of the scaling invariance of the yield
stress fluctuations observed in small samples. We finally identify a population
of precursors of plastic activity and characterize its spatial distribution
Material independent crack arrest statistics
The propagation of (planar) cracks in a heterogeneous brittle material
characterized by a random field of toughness is considered, taking into account
explicitly the effect of the crack front roughness on the local stress
intensity factor. In the so-called strong-pinning regime, the onset of crack
propagation appears to map onto a second-order phase transition characterized
by universal critical exponents which are independent of the local
characteristics of the medium. Propagation over large distances can be
described by using a simple one-dimensional description, with a correlation
length and an effective macroscopic toughness distribution that scale in a
non-trivial fashion with the crack front length. As an application of the above
concepts, the arrest of indentation cracks is addressed, and the analytical
expression for the statistical distribution of the crack radius at arrest is
derived. The analysis of indentation crack radii on alumina is shown to obey
the predicted algebraic expression for the radius distribution and its
dependence on the indentation load
Cracks in random brittle solids: From fiber bundles to continuum mechanics
Statistical models are essential to get a better understanding of the role of
disorder in brittle disordered solids. Fiber bundle models play a special role
as a paradigm, with a very good balance of simplicity and non-trivial effects.
We introduce here a variant of the fiber bundle model where the load is
transferred among the fibers through a very compliant membrane. This Soft
Membrane fiber bundle mode reduces to the classical Local Load Sharing fiber
bundle model in 1D. Highlighting the continuum limit of the model allows to
compute an equivalent toughness for the fiber bundle and hence discuss
nucleation of a critical defect. The computation of the toughness allows for
drawing a simple connection with crack front propagation (depinning) models.Comment: The European Physical Journal Special Topics Special Topics, 201
From depinning transition to plastic yielding of amorphous media: A soft modes perspective
A mesoscopic model of amorphous plasticity is discussed in the context of
depinning models. After embedding in a d + 1 dimensional space, where the
accumulated plastic strain lives along the additional dimension, the gradual
plastic deformation of amorphous media can be regarded as the motion of an
elastic manifold in a disordered landscape. While the associated depinning
transition leads to scaling properties, the quadrupolar Eshelby interactions at
play in amorphous plasticity induce specific additional features like
shear-banding and weak ergodicity breakdown. The latters are shown to be
controlled by the existence of soft modes of the elastic interaction, the
consequence of which is discussed in the context of depinning
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