165 research outputs found
Mechanical Properties of End-crosslinked Entangled Polymer Networks using Sliplink Brownian Dynamics Simulations
The mechanical properties of a polymeric network containing both crosslinks
and sliplinks (entanglements) are studied using a multi-chain Brownian dynamics
simulation. We coarse-grain at the level of chain segments connecting
consecutive nodes (cross- or sliplinks), with particular attention to the
Gaussian statistics of the network. Affine displacement of nodes is not
imposed: their displacement as well as sliding of monomers through sliplinks is
governed by force balances. The simulation results of stress in uniaxial
extension and the full stress tensor in simple shear including the (non-zero)
second normal stress difference are presented for monodisperse chains with up
to 18 entanglements between two crosslinks. The cases of two different force
laws of the subchains (Gaussian chains and chains with finite extensibility)
for two different numbers of monomers in a subchain (no = 50 and no = 100) are
examined. It is shown that the additivity assumption of slip- and crosslink
contribution holds for sufficiently long chains with two or more entanglements,
and that it can be used to construct the strain response of a network of
infinitely long chains. An important consequence is that the contribution of
sliplinks to the small-strain shear modulus is about ⅔ of the
contribution of a crosslink
Nonlinear Elasticity in Biological Gels
Unlike most synthetic materials, biological materials often stiffen as they
are deformed. This nonlinear elastic response, critical for the physiological
function of some tissues, has been documented since at least the 19th century,
but the molecular structure and the design principles responsible for it are
unknown. Current models for this response require geometrically complex ordered
structures unique to each material. In this Article we show that a much simpler
molecular theory accounts for strain stiffening in a wide range of molecularly
distinct biopolymer gels formed from purified cytoskeletal and extracellular
proteins. This theory shows that systems of semi-flexible chains such as
filamentous proteins arranged in an open crosslinked meshwork invariably
stiffen at low strains without the need for a specific architecture or multiple
elements with different intrinsic stiffnesses.Comment: 23 pages, 5 figures, submitted to Natur
Multi-scale modelling of rubber-like materials and soft tissues: an appraisal
We survey, in a partial way, multi-scale approaches for the modelling of rubber-like and soft tissues and compare them with classical macroscopic phenomenological models. Our aim is to show how it is possible to obtain practical mathematical models for the mechanical behaviour of these materials incorporating mesoscopic (network scale) information. Multi-scale approaches are crucial for the theoretical comprehension and prediction of the complex mechanical response of these materials. Moreover, such models are fundamental in the perspective of the design, through manipulation at the micro- and nano-scales, of new polymeric and bioinspired materials with exceptional macroscopic properties
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