Topological derivative for multi-scale linear elasticity models applied to the synthesis of microstructures

This paper proposes an algorithm for the synthesis/optimization of microstructures based on an exact formula for the topological derivative of the macroscopic elasticity tensor and a level set domain representation. The macroscopic elasticity tensor is estimated by a standard multi‐scale constitutiv...

Full description

Saved in:
Bibliographic Details
Published in:International journal for numerical methods in engineering 2010-11, Vol.84 (6), p.733-756
Main Authors: Amstutz, S., Giusti, S. M., Novotny, A. A., de Souza Neto, E. A.
Format: Article
Language:English
Subjects:
Algorithms
Derivatives
Elasticity
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
level set domain representation
Mathematical analysis
Mathematical models
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Microstructure
multi-scale modelling
Numerical analysis. Scientific computation
Optimization
Physics
Sciences and techniques of general use
sensitivity analysis
Solid mechanics
Static elasticity (thermoelasticity...)
Structural and continuum mechanics
synthesis of microstructures
topological derivative
Topology
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This paper proposes an algorithm for the synthesis/optimization of microstructures based on an exact formula for the topological derivative of the macroscopic elasticity tensor and a level set domain representation. The macroscopic elasticity tensor is estimated by a standard multi‐scale constitutive theory where the strain and stress tensors are volume averages of their microscopic counterparts over a representative volume element. The algorithm is of simple computational implementation. In particular, it does not require artificial algorithmic parameters or strategies. This is in sharp contrast with existing microstructural optimization procedures and follows as a natural consequence of the use of the topological derivative concept. This concept provides the correct mathematical framework to treat topology changes such as those characterizing microstuctural optimization problems. The effectiveness of the proposed methodology is illustrated in a set of finite element‐based numerical examples.Copyright © 2010 John Wiley & Sons, Ltd.
ISSN:0029-5981
1097-0207
1097-0207
DOI:10.1002/nme.2922