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Modeling the
mechanical properties of hybrid composites
Natural
composites such as nacre possess extraordinary toughness compared to
their component materials. This is often attributed to the hierarchical
structure, where features at many length scales are expected to play a
role in the macroscopic deformation of the material. A hierarchical
statistical model is introduced to study these effects.
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Molecular
scale: Modified worm-like chain
The individual polymer molecules are modeled using the entropic spring
energy described by a modified worm-like chain model (Rief et al., PRL
1998). For numerical simulations, parameters fit to titin were used. A
kinetic Monte Carlo technique was used to integrate the unfolding
probabilities and construct the load-extension behavior of the single
polymer.
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Microscale:
A kinetic fiber bundle model
A simulation of ensembles of polymer chains was performed using 1000
non-interacting polymer chains. The chains were loaded in parallel and
shared the load. These calculations were done as an extension
controlled experiment. The initial lengths were chosen randomly, from a
uniform distribution distribution. There are two notable features of
this model. First, the yield strength increases at increasing strain.
Second, the effective spring constant decreases during loading of the
fiber bundle.
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Mesoscale: Spring-block lattice
In order to understand the spatial distribution of damage, a lattice
model consisting of a staggered array of blocks connected by shear
springs is studied. The mineral platelets are assumed to be infinitely
stiff. The modulus is found to be equivalent to a shear-lag model of
composites (e.g. Gao et al. PNAS 2003). We allow the springs to be
progressively damaged. The damage is initially distributed throughout
the sample, but ultimately localizes into a band. However, this plastic
instability is found to be suppressed in simulations using the
microscopic hardening law.
The statistics of failure sizes were also studied, finding that event
sizes follow a power-law distribution, and that there is no
characteristic size scale besides the system size.
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References
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1. M. H.
Jhon, D. C.
Chrzan, Journal of the Mechanical Behavior of Biomedical materials,
submitted
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