3,579 research outputs found
Viscoplasticity and large-scale chain relaxation in glassy-polymeric strain hardening
A simple theory for glassy polymeric mechanical response which accounts for
large scale chain relaxation is presented. It captures the crossover from
perfect-plastic response to strong strain hardening as the degree of
polymerization increases, without invoking entanglements. By relating
hardening to interactions on the scale of monomers and chain segments, we
correctly predict its magnitude. Strain activated relaxation arising from the
need to maintain constant chain contour length reduces the dependence of
the characteristic relaxation time by a factor during
active deformation at strain rate . This prediction is consistent
with results from recent experiments and simulations, and we suggest how it may
be further tested experimentally.Comment: The theoretical treatment of the mechanical response has been
significantly revised, and the arguments for coherent relaxation during
active deformation made more transparen
Static and sliding contact of rough surfaces: effect of asperity-scale properties and long-range elastic interactions
Friction in static and sliding contact of rough surfaces is important in
numerous physical phenomena. We seek to understand macroscopically observed
static and sliding contact behavior as the collective response of a large
number of microscopic asperities. We develop an efficient numerical framework
that can be used to investigate how the macroscopic response of multiple
frictional contacts depends on long-range elastic interactions, different
constitutive assumptions about the deforming contacts and their local shear
resistance, and surface roughness. We approximate the contact between two rough
surfaces as that between a regular array of discrete deformable elements
attached to a elastic block and a rigid rough surface. The deformable elements
are viscoelastic or elasto/viscoplastic with a range of relaxation times, and
the elastic interaction between contacts is long-range. We find that the model
reproduces main macroscopic features of evolution of contact and friction for a
range of constitutive models of the elements, suggesting that macroscopic
frictional response is robust with respect to the microscopic behavior.
Viscoelasticity/viscoplasticity contributes to the increase of friction with
contact time and leads to a subtle history dependence. Interestingly,
long-range elastic interactions only change the results quantitatively compared
to the meanfield response. We find that sustained increase in the static
friction coefficient during long hold times suggests viscoelastic response of
the underlying material with multiple relaxation time scales. We also find that
the experimentally observed proportionality of the direct effect in velocity
jump experiments to the logarithm of the velocity jump points to a complex
material-dependent shear resistance at the microscale.Comment: 33 pages, 17 figure
An Eulerian projection method for quasi-static elastoplasticity
A well-established numerical approach to solve the Navier--Stokes equations
for incompressible fluids is Chorin's projection method, whereby the fluid
velocity is explicitly updated, and then an elliptic problem for the pressure
is solved, which is used to orthogonally project the velocity field to maintain
the incompressibility constraint. In this paper, we develop a mathematical
correspondence between Newtonian fluids in the incompressible limit and
hypo-elastoplastic solids in the slow, quasi-static limit. Using this
correspondence, we formulate a new fixed-grid, Eulerian numerical method for
simulating quasi-static hypo-elastoplastic solids, whereby the stress is
explicitly updated, and then an elliptic problem for the velocity is solved,
which is used to orthogonally project the stress to maintain the
quasi-staticity constraint. We develop a finite-difference implementation of
the method and apply it to an elasto-viscoplastic model of a bulk metallic
glass based on the shear transformation zone theory. We show that in a
two-dimensional plane strain simple shear simulation, the method is in
quantitative agreement with an explicit method. Like the fluid projection
method, it is efficient and numerically robust, making it practical for a wide
variety of applications. We also demonstrate that the method can be extended to
simulate objects with evolving boundaries. We highlight a number of
correspondences between incompressible fluid mechanics and quasi-static
elastoplasticity, creating possibilities for translating other numerical
methods between the two classes of physical problems.Comment: 49 pages, 20 figure
Dynamics of Viscoplastic Deformation in Amorphous Solids
We propose a dynamical theory of low-temperature shear deformation in
amorphous solids. Our analysis is based on molecular-dynamics simulations of a
two-dimensional, two-component noncrystalline system. These numerical
simulations reveal behavior typical of metallic glasses and other viscoplastic
materials, specifically, reversible elastic deformation at small applied
stresses, irreversible plastic deformation at larger stresses, a stress
threshold above which unbounded plastic flow occurs, and a strong dependence of
the state of the system on the history of past deformations. Microscopic
observations suggest that a dynamically complete description of the macroscopic
state of this deforming body requires specifying, in addition to stress and
strain, certain average features of a population of two-state shear
transformation zones. Our introduction of these new state variables into the
constitutive equations for this system is an extension of earlier models of
creep in metallic glasses. In the treatment presented here, we specialize to
temperatures far below the glass transition, and postulate that irreversible
motions are governed by local entropic fluctuations in the volumes of the
transformation zones. In most respects, our theory is in good quantitative
agreement with the rich variety of phenomena seen in the simulations.Comment: 16 pages, 9 figure
Wall Adhesion and Constitutive Modelling of Strong Colloidal Gels
Wall adhesion effects during batch sedimentation of strongly flocculated
colloidal gels are commonly assumed to be negligible. In this study in-situ
measurements of colloidal gel rheology and solids volume fraction distribution
suggest the contrary, where significant wall adhesion effects are observed in a
110mm diameter settling column. We develop and validate a mathematical model
for the equilibrium stress state in the presence of wall adhesion under both
viscoplastic and viscoelastic constitutive models. These formulations highlight
fundamental issues regarding the constitutive modeling of colloidal gels,
specifically the relative utility and validity of viscoplastic and viscoelastic
rheological models under arbitrary tensorial loadings. The developed model is
validated against experimental data, which points toward a novel method to
estimate the shear and compressive yield strength of strongly flocculated
colloidal gels from a series of equilibrium solids volume fraction profiles
over various column widths.Comment: 37 pages, 12 figures, submitted to Journal of Rheolog
The nonlinear time-dependent response of isotactic polypropylene
Tensile creep tests, tensile relaxation tests and a tensile test with a
constant rate of strain are performed on injection-molded isotactic
polypropylene at room temperature in the vicinity of the yield point. A
constitutive model is derived for the time-dependent behavior of
semi-crystalline polymers. A polymer is treated as an equivalent network of
chains bridged by permanent junctions. The network is modelled as an ensemble
of passive meso-regions (with affine nodes) and active meso-domains (where
junctions slip with respect to their positions in the bulk medium with various
rates). The distribution of activation energies for sliding in active
meso-regions is described by a random energy model. Adjustable parameters in
the stress--strain relations are found by fitting experimental data. It is
demonstrated that the concentration of active meso-domains monotonically grows
with strain, whereas the average potential energy for sliding of junctions and
the standard deviation of activation energies suffer substantial drops at the
yield point. With reference to the concept of dual population of crystalline
lamellae, these changes in material parameters are attributed to transition
from breakage of subsidiary (thin) lamellae in the sub-yield region to
fragmentation of primary (thick) lamellae in the post-yield region of
deformation.Comment: 29 pages, 12 figure
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