94 research outputs found
Parallel three-dimensional simulations of quasi-static elastoplastic solids
Hypo-elastoplasticity is a flexible framework for modeling the mechanics of
many hard materials under small elastic deformation and large plastic
deformation. Under typical loading rates, most laboratory tests of these
materials happen in the quasi-static limit, but there are few existing
numerical methods tailor-made for this physical regime. In this work, we extend
to three dimensions a recent projection method for simulating quasi-static
hypo-elastoplastic materials. The method is based on a mathematical
correspondence to the incompressible Navier-Stokes equations, where the
projection method of Chorin (1968) is an established numerical technique. We
develop and utilize a three-dimensional parallel geometric multigrid solver
employed to solve a linear system for the quasi-static projection. Our method
is tested through simulation of three-dimensional shear band nucleation and
growth, a precursor to failure in many materials. As an example system, we
employ a physical model of a bulk metallic glass based on the shear
transformation zone theory, but the method can be applied to any
elastoplasticity model. We consider several examples of three-dimensional shear
banding, and examine shear band formation in physically realistic materials
with heterogeneous initial conditions under both simple shear deformation and
boundary conditions inspired by friction welding.Comment: Final version. Accepted for publication in Computer Physics
Communication
Asymmetric collapse by dissolution or melting in a uniform flow
An advection--diffusion-limited dissolution model of an object being eroded
by a two-dimensional potential flow is presented. By taking advantage of the
conformal invariance of the model, a numerical method is introduced that tracks
the evolution of the object boundary in terms of a time-dependent Laurent
series. Simulations of a variety of dissolving objects are shown, which shrink
and then collapse to a single point in finite time. The simulations reveal a
surprising exact relationship whereby the collapse point is the root of a
non-analytic function given in terms of the flow velocity and the Laurent
series coefficients describing the initial shape. This result is subsequently
derived using residue calculus. The structure of the non-analytic function is
examined for three different test cases, and a practical approach to determine
the collapse point using a generalized Newton--Raphson root-finding algorithm
is outlined. These examples also illustrate the possibility that the model
breaks down in finite time prior to complete collapse, due to a topological
singularity, as the dissolving boundary overlaps itself rather than breaking up
into multiple domains (analogous to droplet pinch-off in fluid mechanics). In
summary, the model raises fundamental mathematical questions about broken
symmetries in finite-time singularities of both continuous and stochastic
dynamical systems.Comment: 20 pages, 11 figure
Differential-activity driven instabilities in biphasic active matter
Active stresses can cause instabilities in contractile gels and living
tissues. Here we describe a generic hydrodynamic theory that treats these
systems as a mixture of two phases of varying activity and different mechanical
properties. We find that differential activity between the phases provides a
mechanism causing a demixing instability. We follow the nonlinear evolution of
the instability and characterize a phase diagram of the resulting patterns. Our
study complements other instability mechanisms in mixtures such as differential
growth, shape, motion or adhesion
Density-equalizing maps for simply-connected open surfaces
In this paper, we are concerned with the problem of creating flattening maps
of simply-connected open surfaces in . Using a natural principle
of density diffusion in physics, we propose an effective algorithm for
computing density-equalizing flattening maps with any prescribed density
distribution. By varying the initial density distribution, a large variety of
mappings with different properties can be achieved. For instance,
area-preserving parameterizations of simply-connected open surfaces can be
easily computed. Experimental results are presented to demonstrate the
effectiveness of our proposed method. Applications to data visualization and
surface remeshing are explored
Eulerian method for multiphase interactions of soft solid bodies in fluids
We introduce an Eulerian approach for problems involving one or more soft
solids immersed in a fluid, which permits mechanical interactions between all
phases. The reference map variable is exploited to simulate finite-deformation
constitutive relations in the solid(s) on the same fixed grid as the fluid
phase, which greatly simplifies the coupling between phases. Our coupling
procedure, a key contribution in the current work, is shown to be
computationally faster and more stable than an earlier approach, and admits the
ability to simulate both fluid--solid and solid--solid interaction between
submerged bodies. The interface treatment is demonstrated with multiple
examples involving a weakly compressible Navier--Stokes fluid interacting with
a neo-Hookean solid, and we verify the method's convergence. The solid contact
method, which exploits distance-measures already existing on the grid, is
demonstrated with two examples. A new, general routine for cross-interface
extrapolation is introduced and used as part of the new interfacial treatment
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
Optimizing intermittent water supply in urban pipe distribution networks
In many urban areas of the developing world, piped water is supplied only
intermittently, as valves direct water to different parts of the water
distribution system at different times. The flow is transient, and may
transition between free-surface and pressurized, resulting in complex dynamical
features with important consequences for water suppliers and users. Here, we
develop a computational model of transition, transient pipe flow in a network,
accounting for a wide variety of realistic boundary conditions. We validate the
model against several published data sets, and demonstrate its use on a real
pipe network. The model is extended to consider several optimization problems
motivated by realistic scenarios. We demonstrate how to infer water flow in a
small pipe network from a single pressure sensor, and show how to control water
inflow to minimize damaging pressure gradients
TriMe++: Multi-threaded triangular meshing in two dimensions
We present TriMe++, a multi-threaded software library designed for generating
two-dimensional meshes for intricate geometric shapes using the Delaunay
triangulation. Multi-threaded parallel computing is implemented throughout the
meshing procedure, making it suitable for fast generation of large-scale
meshes. Three iterative meshing algorithms are implemented: the DistMesh
algorithm, the centroidal Voronoi diagram meshing, and a hybrid of the two. We
compare the performance of the three meshing methods in TriMe++, and show that
the hybrid method retains the advantages of the other two. The software library
achieves significant parallel speedup when generating a large mesh with
points. TriMe++ can handle complicated geometries and generates adaptive meshes
of high quality
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