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Topology optimization of particle‐matrix composites for optimal fracture resistance taking into account interfacial damage
Author(s) -
Da Daicong,
Yvonnet Julien,
Xia Liang,
Li Guangyao
Publication year - 2018
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5818
Subject(s) - topology optimization , classification of discontinuities , materials science , fracture mechanics , fracture (geology) , volume fraction , topology (electrical circuits) , optimization problem , brittleness , nucleation , composite material , mathematical optimization , structural engineering , mathematics , finite element method , mathematical analysis , engineering , physics , combinatorics , thermodynamics
Summary This paper presents a topology optimization framework for optimizing the fracture resistance of two‐phase composites considering interfacial damage interacting with crack propagation through a redistribution of the inclusions phase. A phase field method for fracture capable of describing interactions between bulk brittle fracture and interfacial damage is adopted within a diffuse approximation of discontinuities. This formulation avoids the burden of remeshing problem during crack propagation and is well adapted to topology optimization purpose. Efficient design sensitivity analysis is performed by using the adjoint method, and the optimization problem is solved by an extended bidirectional evolutionary structural optimization method. The sensitivity formulation accounts for the whole fracturing process involving crack nucleation, propagation, and interaction, either from the interfaces and then through the solid phases, or the opposite. The spatial distribution of material phases are optimally designed using the extended bidirectional evolutionary structural optimization method to improve the fractural resistance. We demonstrate through several examples that the fracture resistance of the composite can be significantly increased at constant volume fraction of inclusions by the topology optimization process.