14,658 research outputs found
Asynchronous Variational Contact Mechanics
An asynchronous, variational method for simulating elastica in complex
contact and impact scenarios is developed. Asynchronous Variational Integrators
(AVIs) are extended to handle contact forces by associating different time
steps to forces instead of to spatial elements. By discretizing a barrier
potential by an infinite sum of nested quadratic potentials, these extended
AVIs are used to resolve contact while obeying momentum- and
energy-conservation laws. A series of two- and three-dimensional examples
illustrate the robustness and good energy behavior of the method
A novel approach to rigid spheroid models in viscous flows using operator splitting methods
Calculating cost-effective solutions to particle dynamics in viscous flows is
an important problem in many areas of industry and nature. We implement a
second-order symmetric splitting method on the governing equations for a rigid
spheroidal particle model with torques, drag and gravity. The method splits the
operators into a vector field that is conservative and one that takes into
account the forces of the fluid. Error analysis and numerical tests are
performed on perturbed and stiff particle-fluid systems. For the perturbed
case, the splitting method greatly improves the solution accuracy, when
compared to a conventional multi-step method, and the global error behaves as
for roughly equal computational cost. For stiff
systems, we show that the splitting method retains stability in regimes where
conventional methods blow up. In addition, we show through numerical
experiments that the global order is reduced from
in the non-stiff regime to in
the stiff regime.Comment: 24 pages, 6 figures (13 if you count sub figs), all figures are in
colou
A Variational Formulation of Dissipative Quasicontinuum Methods
Lattice systems and discrete networks with dissipative interactions are
successfully employed as meso-scale models of heterogeneous solids. As the
application scale generally is much larger than that of the discrete links,
physically relevant simulations are computationally expensive. The
QuasiContinuum (QC) method is a multiscale approach that reduces the
computational cost of direct numerical simulations by fully resolving complex
phenomena only in regions of interest while coarsening elsewhere. In previous
work (Beex et al., J. Mech. Phys. Solids 64, 154-169, 2014), the originally
conservative QC methodology was generalized to a virtual-power-based QC
approach that includes local dissipative mechanisms. In this contribution, the
virtual-power-based QC method is reformulated from a variational point of view,
by employing the energy-based variational framework for rate-independent
processes (Mielke and Roub\'i\v{c}ek, Rate-Independent Systems: Theory and
Application, Springer-Verlag, 2015). By construction it is shown that the QC
method with dissipative interactions can be expressed as a minimization problem
of a properly built energy potential, providing solutions equivalent to those
of the virtual-power-based QC formulation. The theoretical considerations are
demonstrated on three simple examples. For them we verify energy consistency,
quantify relative errors in energies, and discuss errors in internal variables
obtained for different meshes and two summation rules.Comment: 38 pages, 21 figures, 4 tables; moderate revision after review, one
example in Section 5.3 adde
An embedded formulation with conforming
Use of strong discontinuities with satisfaction of compatibilit
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