1,221 research outputs found
Critical scaling in linear response of frictionless granular packings near jamming
We study the origin of the scaling behavior in frictionless granular media
above the jamming transition by analyzing their linear response. The response
to local forcing is non-self-averaging and fluctuates over a length scale that
diverges at the jamming transition. The response to global forcing becomes
increasingly non-affine near the jamming transition. This is due to the
proximity of floppy modes, the influence of which we characterize by the local
linear response. We show that the local response also governs the anomalous
scaling of elastic constants and contact number.Comment: 4 pages, 3 figures. v2: Added new results; removed part of
discussion; changed Fig.
Dynamics of vitrimers: defects as a highway to stress relaxation
We propose a coarse-grained model to investigate stress relaxation in
star-polymer networks induced by dynamic bond exchange processes. We show how
the swapping mechanism, once activated, allows the network to reconfigure,
exploring distinct topological configurations, all of them characterised by
complete extent of reaction. Our results reveal the important role played by
topological defects in mediating the exchange reaction and speeding up stress
relaxation. The model provides a representation of the dynamics in vitrimers, a
new class of polymers characterized by bond swap mechanisms which preserve the
total number of bonds, as well as in other bond-exchange materials.Comment: 5 pages, 5 figures, with 6 pages SI appende
A Hybrid Design Optimization Method using Enriched Craig-Bampton Approach
A hybrid design optimization method is presented which combines a number of techniques such as Component Mode Synthesis (CMS), Design of Computer Experiments and Neural Networks for surrogate modeling with Genetic Algorithms and Sequential Quadratic Programming for optimization. In the method, the FE analysis is decomposed and reduced by a well-known CMS technique called the Craig-Bampton method. Since the optimization method requires CMS calculations of the updated model at each of its iterations due to the changes in the design variables, one can either reuse the reduction basis of the initial components or compute new reduction basis for the condensation of the system matrices. The first option usually leads to inaccurate results and the last one increases the omputation time. In the method, instead of using one of these options, the Enriched Craig-Bampton method, proposed by Masson et al., is employed for efficient optimization. New basis for the modified components are generated by extending the corresponding initial reduction basis with a set of static residual vectors which are calculated using prior knowledge of the initial component designs. Thus, time consuming complete component analyzes are prevented. A theoretical test problem is used for the demonstration of the method
Stability of jammed packings I: the rigidity length scale
In 2005, Wyart et al. (Europhys. Lett., 72 (2005) 486) showed that the low
frequency vibrational properties of jammed amorphous sphere packings can be
understood in terms of a length scale, called l*, that diverges as the system
becomes marginally unstable. Despite the tremendous success of this theory, it
has been difficult to connect the counting argument that defines l* to other
length scales that diverge near the jamming transition. We present an alternate
derivation of l* based on the onset of rigidity. This phenomenological approach
reveals the physical mechanism underlying the length scale and is relevant to a
range of systems for which the original argument breaks down. It also allows us
to present the first direct numerical measurement of l*.Comment: 8 pages, 5 figure
Jammed frictionless discs: connecting local and global response
By calculating the linear response of packings of soft frictionless discs to
quasistatic external perturbations, we investigate the critical scaling
behavior of their elastic properties and non-affine deformations as a function
of the distance to jamming. Averaged over an ensemble of similar packings,
these systems are well described by elasticity, while in single packings we
determine a diverging length scale up to which the response of the
system is dominated by the local packing disorder. This length scale, which we
observe directly, diverges as , where is the difference
between contact number and its isostatic value, and appears to scale
identically to the length scale which had been introduced earlier in the
interpretation of the spectrum of vibrational modes. It governs the crossover
from isostatic behavior at the small scale to continuum behavior at the large
scale; indeed we identify this length scale with the coarse graining length
needed to obtain a smooth stress field. We characterize the non-affine
displacements of the particles using the \emph{displacement angle
distribution}, a local measure for the amount of relative sliding, and analyze
the connection between local relative displacements and the elastic moduli.Comment: 19 pages, 15 figures, submitted to Phys. Rev.
Harnessing entropy to enhance toughness in reversibly crosslinked polymer networks
Reversible crosslinking is a design paradigm for polymeric materials, wherein
they are microscopically reinforced with chemical species that form transient
crosslinks between the polymer chains. Besides the potential for self-healing,
recent experimental work suggests that freely diffusing reversible crosslinks
in polymer networks, such as gels, can enhance the toughness of the material
without substantial change in elasticity. This presents the opportunity for
making highly elastic materials that can be strained to a large extent before
rupturing. Here, we employ Gaussian chain theory, molecular simulation, and
polymer self-consistent field theory for networks to construct an equilibrium
picture for how reversible crosslinks can toughen a polymer network without
affecting its linear elasticity. Maximisation of polymer entropy drives the
reversible crosslinks to bind preferentially near the permanent crosslinks in
the network, leading to local molecular reinforcement without significant
alteration of the network topology. In equilibrium conditions, permanent
crosslinks share effectively the load with neighbouring reversible crosslinks,
forming multi-functional crosslink points. The network is thereby globally
toughened, while the linear elasticity is left largely unaltered. Practical
guidelines are proposed to optimise this design in experiment, along with a
discussion of key kinetic and timescale considerations
Geometry and the onset of rigidity in a disordered network
Disordered spring networks that are undercoordinated may abruptly rigidify
when sufficient strain is applied. Since the deformation in response to applied
strain does not change the generic quantifiers of network architecture - the
number of nodes and the number of bonds between them - this rigidity transition
must have a geometric origin. Naive, degree-of-freedom based mechanical
analyses such as the Maxwell-Calladine count or the pebble game algorithm
overlook such geometric rigidity transitions and offer no means of predicting
or characterizing them. We apply tools that were developed for the topological
analysis of zero modes and states of self-stress on regular lattices to
two-dimensional random spring networks, and demonstrate that the onset of
rigidity, at a finite simple shear strain , coincides with the
appearance of a single state of self stress, accompanied by a single floppy
mode. The process conserves the topologically invariant difference between the
number of zero modes and the number of states of self stress, but imparts a
finite shear modulus to the spring network. Beyond the critical shear, we
confirm previously reported critical scaling of the modulus. In the
sub-critical regime, a singular value decomposition of the network's
compatibility matrix foreshadows the onset of rigidity by way of a continuously
vanishing singular value corresponding to nascent state of self stress.Comment: 6 pages, 6 figue
An optimization method for dynamics of structures with repetitive component patterns
The occurrence of dynamic problems during the operation of machinery may have devastating effects on a product. Therefore, design optimization of these products becomes essential in order to meet safety criteria. In this research, a hybrid design optimization method is proposed where attention is focused on structures having repeating patterns in their geometries. In the proposed method, the analysis is decomposed but the optimization problem itself is treated as a whole. The model of an entire structure is obtained without modeling all the repetitive components using the merits of the Component Mode Synthesis method. Backpropagation Neural Networks are used for surrogate modeling. The optimization is performed using two techniques: Genetic Algorithms (GAs) and Sequential Quadratic Programming (SQP). GAs are utilized to increase the chance of finding the location of the global optimum and since this optimum may not be exact, SQP is employed afterwards to improve the solution. A theoretical test problem is used to demonstrate the method
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