1,000 research outputs found
Computational Multiscale Methods
Many physical processes in material sciences or geophysics are characterized by inherently complex interactions across a large range of non-separable scales in space and time. The resolution of all features on all scales in a computer simulation easily exceeds today's computing resources by multiple orders of magnitude. The observation and prediction of physical phenomena from multiscale models, hence, requires insightful numerical multiscale techniques to adaptively select relevant scales and effectively represent unresolved scales. This workshop enhanced the development of such methods and the mathematics behind them so that the reliable and efficient numerical simulation of some challenging multiscale problems eventually becomes feasible in high performance computing environments
Localization Analysis of an Energy-Based Fourth-Order Gradient Plasticity Model
The purpose of this paper is to provide analytical and numerical solutions of
the formation and evolution of the localized plastic zone in a uniaxially
loaded bar with variable cross-sectional area. An energy-based variational
approach is employed and the governing equations with appropriate physical
boundary conditions, jump conditions, and regularity conditions at evolving
elasto-plastic interface are derived for a fourth-order explicit gradient
plasticity model with linear isotropic softening. Four examples that differ by
regularity of the yield stress and stress distributions are presented. Results
for the load level, size of the plastic zone, distribution of plastic strain
and its spatial derivatives, plastic elongation, and energy balance are
constructed and compared to another, previously discussed non-variational
gradient formulation.Comment: 41 pages, 24 figures; moderate revision after the first round of
review, Appendix A re-written completel
The role of the patch test in 2D atomistic-to-continuum coupling methods
For a general class of atomistic-to-continuum coupling methods, coupling
multi-body interatomic potentials with a P1-finite element discretisation of
Cauchy--Born nonlinear elasticity, this paper adresses the question whether
patch test consistency (or, absence of ghost forces) implies a first-order
error estimate.
In two dimensions it is shown that this is indeed true under the following
additional technical assumptions: (i) an energy consistency condition, (ii)
locality of the interface correction, (iii) volumetric scaling of the interface
correction, and (iv) connectedness of the atomistic region. The extent to which
these assumptions are necessary is discussed in detail.Comment: Version 2: correction of some minor mistakes, added discussion of
multiple connected atomistic region, minor improvements of styl
Stationary States and Asymptotic Behaviour of Aggregation Models with Nonlinear Local Repulsion
We consider a continuum aggregation model with nonlinear local repulsion
given by a degenerate power-law diffusion with general exponent. The steady
states and their properties in one dimension are studied both analytically and
numerically, suggesting that the quadratic diffusion is a critical case. The
focus is on finite-size, monotone and compactly supported equilibria. We also
investigate numerically the long time asymptotics of the model by simulations
of the evolution equation. Issues such as metastability and local/ global
stability are studied in connection to the gradient flow formulation of the
model
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