Material interface effects on the topology optimization of multi-phase structures using a level set method

Natasha Vermaak (1) , Georgios Michailidis (2) , Guillaume Parry (3) , Raphael Estevez (3) , Grégoire Allaire (4, 2) , Yves Brechet (3)

1 Packard Laboratory
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
3 SIMaP - Science et Ingénierie des Matériaux et Procédés
4 DeFI - Shape reconstruction and identification

A level set method is used as a framework to study the effects of including material interface properties in the optimization of multi-phase elastic and thermoelastic structures. In contrast to previous approaches, the material properties do not have a discontinuous change across the interface that is often represented by a sharp geometric boundary between material regions. Instead, finite material interfaces with monotonic and non-monotonic property variations over a physically motivated interface zone are investigated. Numerical results are provided for several 2D problems including compliance and displacement minimization of structures composed of two and three materials. The results highlight the design performance changes attributed to the presence of the continuously graded material interface properties.

Mots clés: Multi-phase; Thermoelastic; Elasticity; Level set method; Multi-material; Graded interface; Shape optimization; Topology

Domaines: Optimisation et contrôle [math.OC]; Analyse numérique [math.NA]; Matériaux

Natasha Vermaak, Georgios Michailidis, Guillaume Parry, Raphael Estevez, Grégoire Allaire, et al.. Material interface effects on the topology optimization of multi-phase structures using a level set method. Structural and Multidisciplinary Optimization, 2014, 50 (4), pp.623-644. ⟨10.1007/s00158-014-1074-2⟩. ⟨hal-01072223⟩