Analysis of the embedded cell method in 1D for the numerical homogenization of metal-ceramic composite materials
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Wolf-Patrick Düll
,
Bastian Hilder
Abstract
In this paper, we analyze the embedding cell method, an algorithm which has been developed for the numerical homogenization of metal-ceramic composite materials. We show the convergence of the iteration scheme of this algorithm and the coincidence of the material properties predicted by the limit with the effective material properties provided by the analytical homogenization theory in two situations, namely for a one-dimensional linear elasticity model and a simple one-dimensional plasticity model.
Funding source: Deutsche Forschungsgemeinschaft
Award Identifier / Grant number: EXC 310/2
Funding statement: The research is partially supported by the Cluster of Excellence “SimTech” at the University of Stuttgart.
Acknowledgements
The authors are grateful for discussions with Siegfried Schmauder and Alexander Mielke.
References
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Articles in the same Issue
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Articles in the same Issue
- Frontmatter
- Deferred weighted 𝒜-statistical convergence based upon the (p,q)-Lagrange polynomials and its applications to approximation theorems
- Some variational principles associated with ODEs of maximal symmetry. Part 1: Equations in canonical form
- On the solutions and conservation laws of a two-dimensional Korteweg de Vries model: Multiple exp-function method
- Existence of solutions for nonlinear Schrödinger systems with periodic data perturbations
- Higher-order conditions for strict local Pareto minima for problems with partial order introduced by a polyhedral cone
- On some nonlinear hyperbolic p(x,t)-Laplacian equations
- Analysis of the embedded cell method in 1D for the numerical homogenization of metal-ceramic composite materials
- Approximately linear recurrences
- Existence and uniqueness of a problem in thermo-elasto-plasticity with phase transitions in TRIP steels under mixed boundary conditions
- Deficit distributions at ruin in a regime-switching Sparre Andersen model
- On some non-Gaussian wave packets
