1,015 research outputs found
Normal stresses, contraction, and stiffening in sheared elastic networks
When elastic solids are sheared, a nonlinear effect named after Poynting
gives rise to normal stresses or changes in volume. We provide a novel relation
between the Poynting effect and the microscopic Gr\"uneisen parameter, which
quantifies how stretching shifts vibrational modes. By applying this relation
to random spring networks, a minimal model for, e.g., biopolymer gels and solid
foams, we find that networks contract or develop tension because they vibrate
faster when stretched. The amplitude of the Poynting effect is sensitive to the
network's linear elastic moduli, which can be tuned via its preparation
protocol and connectivity. Finally, we show that the Poynting effect can be
used to predict the finite strain scale where the material stiffens under
shear.Comment: 5 pages, 5 figure
Force balance in canonical ensembles of static granular packings
We investigate the role of local force balance in the transition from a
microcanonical ensemble of static granular packings, characterized by an
invariant stress, to a canonical ensemble. Packings in two dimensions admit a
reciprocal tiling, and a collective effect of force balance is that the area of
this tiling is also invariant in a microcanonical ensemble. We present
analytical relations between stress, tiling area and tiling area fluctuations,
and show that a canonical ensemble can be characterized by an intensive
thermodynamic parameter conjugate to one or the other. We test the equivalence
of different ensembles through the first canonical simulations of the force
network ensemble, a model system.Comment: 9 pages, 9 figures, submitted to JSTA
Beyond linear elasticity: Jammed solids at finite shear strain and rate
The shear response of soft solids can be modeled with linear elasticity,
provided the forcing is slow and weak. Both of these approximations must break
down when the material loses rigidity, such as in foams and emulsions at their
(un)jamming point -- suggesting that the window of linear elastic response near
jamming is exceedingly narrow. Yet precisely when and how this breakdown occurs
remains unclear. To answer these questions, we perform computer simulations of
stress relaxation and shear startup experiments in athermal soft sphere
packings, the canonical model for jamming. By systematically varying the strain
amplitude, strain rate, distance to jamming, and system size, we identify
characteristic strain and time scales that quantify how and when the window of
linear elasticity closes, and relate these scales to changes in the microscopic
contact network. Our findings indicate that the mechanical response of jammed
solids are generically nonlinear and rate-dependent on experimentally
accessible strain and time scales.Comment: 10 pages, 9 figure
The Convenient Alliance: President Reagan and Pope John Paul II, Cold Warriors
Historians and non-scholars alike have long regarded the work of President Reagan and Pope John Paul II to be a tremendous force in helping to end the Cold War. In 1992, Time Magazine cited the relationship as a “Holy Alliance”, a political partnering of two men who, after surviving separate assassination attempts merely six weeks apart, saw their role in global politics as a divine signal to promote the free world and take down communism internationally. By the time the President and the Pope first met at the Vatican in 1982, the two were privately discussing Cold War politics. They agreed that communism was a threat to human rights and global stability, and that it should be confronted. John Paul II and Reagan were clearly aligned in their abhorrence for communism, but they had differing primary goals; the Pope strived to introduce democracy to his native Poland, and Reagan was occupied with the disintegration of the Soviet Union. Thus, the two world leaders were able to team up not out of necessity, but out of mutual benefit. It was an alliance of convenience, with two governing organizations able to use one another’s global power and influences to promote their own political goals. Indeed, the President and the Pope shared Cold War information, but never intimately planned or initiated policy to jointly bring about democratic reform throughout the globe. My research project concentrates on the Washington-Vatican relationship during the Reagan years and how the partnership helped defeat communism, with particular attention paid to the Pope’s native Poland. I also explore the role the alliance has formed in the years since Reagan left office, presenting ideas that may counter what many people have assumed about the relationship between President Reagan and Pope John Paul II
Contact Changes of Sheared Systems: Scaling, Correlations, and Mechanisms
We probe the onset and effect of contact changes in 2D soft harmonic particle
packings which are sheared quasistatically under controlled strain. First, we
show that in the majority of cases, the first contact changes correspond to the
creation or breaking of contacts on a single particle, with contact breaking
overwhelmingly likely for low pressures and/or small systems, and contact
making and breaking equally likely for large pressures and in the thermodynamic
limit. The statistics of the corresponding strains are near-Poissonian. The
mean characteristic strains exhibit scaling with the number of particles N and
pressure P, and reveal the existence of finite size effects akin to those seen
for linear response quantities. Second, we show that linear response accurately
predicts the strains of the first contact changes, which allows us to study the
scaling of the characteristic strains of making and breaking contacts
separately. Both of these show finite size scaling, and we formulate scaling
arguments that are consistent with the observed behavior. Third, we probe the
effect of the first contact change on the shear modulus G, and show in detail
how the variation of G remains smooth and bounded in the large system size
limit: even though contact changes occur then at vanishingly small strains,
their cumulative effect, even at a fixed value of the strain, are limited, so
that effectively, linear response remains well-defined. Fourth, we explore
multiple contact changes under shear, and find strong and surprising
correlations between alternating making and breaking events. Fifth, we show
that by making a link with extremal statistics, our data is consistent with a
very slow crossover to self averaging with system size, so that the
thermodynamic limit is reached much more slowly than expected based on finite
size scaling of elastic quantities or contact breaking strains
Softening and Yielding of Soft Glassy Materials
Solids deform and fluids flow, but soft glassy materials, such as emulsions,
foams, suspensions, and pastes, exhibit an intricate mix of solid and
liquid-like behavior. While much progress has been made to understand their
elastic (small strain) and flow (infinite strain) properties, such
understanding is lacking for the softening and yielding phenomena that connect
these asymptotic regimes. Here we present a comprehensive framework for
softening and yielding of soft glassy materials, based on extensive numerical
simulations of oscillatory rheological tests, and show that two distinct
scenarios unfold depending on the material's packing density. For dense
systems, there is a single, pressure-independent strain where the elastic
modulus drops and the particle motion becomes diffusive. In contrast, for
weakly jammed systems, a two-step process arises: at an intermediate softening
strain, the elastic and loss moduli both drop down and then reach a new plateau
value, whereas the particle motion becomes diffusive at the distinctly larger
yield strain. We show that softening is associated with an extensive number of
microscopic contact changes leading to a non-analytic rheological signature.
Moreover, the scaling of the softening strain with pressure suggest the
existence of a novel pressure scale above which softening and yielding
coincide, and we verify the existence of this crossover scale numerically. Our
findings thus evidence the existence of two distinct classes of soft glassy
materials -- jamming dominated and dense -- and show how these can be
distinguished by their rheological fingerprint.Comment: 9 pages, 11 figures, to appear in Soft Matte
- …