12,008 research outputs found
A general constitutive model for dense, fine particle suspensions validated in many geometries
Fine particle suspensions (such as cornstarch mixed with water) exhibit
dramatic changes in viscosity when sheared, producing fascinating behaviors
that captivate children and rheologists alike. Recent examination of these
mixtures in simple flow geometries suggests inter-granular repulsion is central
to this effect --- for mixtures at rest or shearing slowly, repulsion prevents
frictional contacts from forming between particles, whereas, when sheared more
forcefully, granular stresses overcome the repulsion allowing particles to
interact frictionally and form microscopic structures that resist flow.
Previous constitutive studies of these mixtures have focused on particular
cases, typically limited to two-dimensional, steady, simple shearing flows. In
this work, we introduce a predictive and general, three-dimensional continuum
model for this material, using mixture theory to couple the fluid and particle
phases. Playing a central role in the model, we introduce a micro-structural
state variable, whose evolution is deduced from small-scale physical arguments
and checked with existing data. Our space- and time-dependent model is
implemented numerically in a variety of unsteady, non-uniform flow
configurations where it is shown to accurately capture a variety of key
behaviors: (i) the continuous shear thickening (CST) and discontinuous shear
thickening (DST) behavior observed in steady flows, (ii) the time-dependent
propagation of `shear jamming fronts', (iii) the time-dependent propagation of
`impact activated jamming fronts', and (iv) the non-Newtonian, `running on
oobleck' effect wherein fast locomotors stay afloat while slow ones sink
The Dynamics of Liquid Drops and their Interaction with Solids of Varying Wettabilites
Microdrop impact and spreading phenomena are explored as an interface
formation process using a recently developed computational framework. The
accuracy of the results obtained from this framework for the simulation of high
deformation free-surface flows is confirmed by a comparison with previous
numerical studies for the large amplitude oscillations of free liquid drops.
Our code's ability to produce high resolution benchmark calculations for
dynamic wetting flows is then demonstrated by simulating microdrop impact and
spreading on surfaces of greatly differing wettability. The simulations allow
one to see features of the process which go beyond the resolution available to
experimental analysis. Strong interfacial effects which are observed at the
microfluidic scale are then harnessed by designing surfaces of varying
wettability that allow new methods of flow control to be developed
Validity of the Cauchy-Born rule applied to discrete cellular-scale models of biological tissues
The development of new models of biological tissues that consider cells in a discrete manner is becoming increasingly popular as an alternative to PDE-based continuum methods, although formal relationships between the discrete and continuum frameworks remain to be established. For crystal mechanics, the discrete-to-continuum bridge is often made by assuming that local atom displacements can be mapped homogeneously from the mesoscale deformation gradient, an assumption known as the Cauchy-Born rule (CBR). Although the CBR does not hold exactly for non-crystalline materials, it may still be used as a first order approximation for analytic calculations of effective stresses or strain energies. In this work, our goal is to investigate numerically the applicability of the CBR to 2-D cellular-scale models by assessing the mechanical behaviour of model biological tissues, including crystalline (honeycomb) and non-crystalline reference states. The numerical procedure consists in precribing an affine deformation on the boundary cells and computing the position of internal cells. The position of internal cells is then compared with the prediction of the CBR and an average deviation is calculated in the strain domain. For centre-based models, we show that the CBR holds exactly when the deformation gradient is relatively small and the reference stress-free configuration is defined by a honeycomb lattice. We show further that the CBR may be used approximately when the reference state is perturbed from the honeycomb configuration. By contrast, for vertex-based models, a similar analysis reveals that the CBR does not provide a good representation of the tissue mechanics, even when the reference configuration is defined by a honeycomb lattice. The paper concludes with a discussion of the implications of these results for concurrent discrete/continuous modelling, adaptation of atom-to-continuum (AtC) techniques to biological tissues and model classification
Continuum modelling and simulation of granular flows through their many phases
We propose and numerically implement a constitutive framework for granular
media that allows the material to traverse through its many common phases
during the flow process. When dense, the material is treated as a pressure
sensitive elasto-viscoplastic solid obeying a yield criterion and a plastic
flow rule given by the inertial rheology of granular materials. When
the free volume exceeds a critical level, the material is deemed to separate
and is treated as disconnected, stress-free media. A Material Point Method
(MPM) procedure is written for the simulation of this model and many
demonstrations are provided in different geometries. By using the MPM
framework, extremely large strains and nonlinear deformations, which are common
in granular flows, are representable. The method is verified numerically and
its physical predictions are validated against known results
Application of the continuum shell finite element SHB8PS to sheet forming simulation using an extended large strain anisotropic elasticâplastic formulation
http://link.springer.com/article/10.1007%2Fs00419-012-0620-xThis paper proposes an extension of the SHB8PS solidâshell finite element to large strain anisotropic elasto-plasticity, with application to several non-linear benchmark tests including sheet metal forming simulations. This hexahedral linear element has an arbitrary number of integration points distributed along a single line, defining the "thickness" direction; and to control the hourglass modes inherent to this reduced integration, a physical stabilization technique is used. In addition, the assumed strain method is adopted for the elimination of locking. The implementation of the element in Abaqus/Standard via the UEL user subroutine has been assessed through a variety of benchmark problems involving geometric non-linearities, anisotropic plasticity, large deformation and contact. Initially designed for the efficient simulation of elasticâplastic thin structures, the SHB8PS exhibits interesting potentialities for sheet metal forming applications â both in terms of efficiency and accuracy. The element shows good performance on the selected tests, including springback and earing predictions for Numisheet benchmark problems
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