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

Vermaak, Natasha; Michailidis, Georgios; Parry, Guillaume; Estevez, Rafaël; Allaire, Grégoire; Bréchet, Y.

doi:10.1007/s00158-014-1074-2

Cited by 75 publications

(35 citation statements)

References 37 publications

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“…Particularly the two-step filtering process allowing to identify material interfaces and separate length scales of base structure and interface may be useful for problems involving interface modeling. An example is to include graded properties at the interface transition zone for multi-phase structures, thus suggesting an alternative, SIMP-based method to the level-set based approach suggested by Vermaak et al (2014). The width and steepness of the interface may be modeled by modifying smoothing and projection parameters, or different interpolation schemes may be explored.…”

Section: Discussionmentioning

confidence: 99%

“…van Dijk et al (2013). Based on the level-set method, Vermaak et al (2014) present a method for including material interface properties in the optimization of multi-phase elastic and thermoelastic structures. Rather than modeling a sharp interface between two different materials, a transition zone is introduced to allow for graded properties.…”

Section: Introductionmentioning

confidence: 99%

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Topology optimization of coated structures and material interface problems

Clausen

Aage

Sigmund

2015

Computer Methods in Applied Mechanics and Engineering

153

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This paper presents a novel method for including coated structures and prescribed material interface properties into the minimum compliance topology optimization problem. Several elements of the method are applicable to a broader range of interface problems. The approach extends the standard SIMP method by including the normalized norm of the spatial gradient of the design field into the material interpolation function, enforcing coating material at interfaces by attributing particular properties. The length scales of the base structure and the coating are separated by introducing a two-step filtering/projection approach. The modeled coating thickness is derived analytically, and the coating is shown to be accurately controlled and applied in a highly uniform manner over the structure. An alternative interpretation of the model is to perform single-material design for additive manufacturing. Infill is assumed to be constituted of an isotropic porous microstructure satisfying the Hashin-Shtrikman bounds and is modeled using the homogenized material properties. A range of numerical results illustrate the effectiveness of the approach.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Topology optimization of coated structures and material interface problems

Clausen

Aage

Sigmund

2015

Computer Methods in Applied Mechanics and Engineering

153

View full text Add to dashboard Cite

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“…From the perspective of material distribution description, design of structure with graded surface is much more challenging than design of pure uniform or graded structure. Similar to the present work, several research studies have attempted to consider topology optimization of multiphase structure and material with graded interface zone in the level‐set framework. However, to the best of authors' knowledge, there exist no works on topology optimization of structure with graded surface in all topology optimization framework.…”

Section: Introductionmentioning

confidence: 97%

A projection‐based method for topology optimization of structures with graded surfaces

Luo

Liu

2019

Numerical Meth Engineering

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Summary Graded surfaces widely exist in natural structures and inspire engineers to apply functionally graded (FG) materials to cover structural surfaces for performance improvement, protection, or other special functionalities. However, how to design such structures with FG surfaces by topology optimization is a quite challenging problem due to the difficulty for determining material properties of structural surfaces with prescribed variation rule. This paper presents a novel projection‐based method for topology optimization of this class of FG structures. Firstly, a projection process is proposed for ensuring the material properties of the surfaces vary with a prescribed function. A criterion of determining the values of parameters in projection process is given by a strict theoretical derivation, and then, a new interpolation function is established, which is capable of simultaneously obtaining clear substrate topologies and realizable FG surfaces. Though such structures are actually multimaterial gradient structures, only the design variables of single‐material topology optimization problem are needed. In the current research, the classical compliance minimization problem with a mass constraint is considered and the robust formulation is used to control the length scale of substrates. Several 2D and 3D numerical examples illustrate the validity and applicability of the proposed method.

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“…a Initial distribution of two materials (material "a" and material "b") along the sliding surface. b Example evolution of contact pressure and surface topography for a bi-material surface after 0, 50, and 250 sliding cycles This facilitates the possibility to apply modern topology optimization techniques with the goal of improving the wear performance of tribological systems (Bendsøe and Sigmund (2003), Allaire (2007a), Eschenauer and Olhoff (2001), Vermaak et al (2014)). The formulation proposed herein is also compatible with other elliptic models, which could be used for example, to explore multi-physics wear optimization.…”

Section: Introductionmentioning

confidence: 99%

Introducing a level-set based shape and topology optimization method for the wear of composite materials with geometric constraints

Feppon

Michailidis

Sidebottom

et al. 2016

Struct Multidisc Optim

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The wear of materials continues to be a limiting factor in the lifetime and performance of mechanical systems with sliding surfaces. As the demand for low wear materials grows so does the need for models and methods to systematically optimize tribological systems. Elastic foundation models offer a simplified framework to study the wear of multimaterial composites subject to abrasive sliding. Previously, the evolving wear profile has been shown to converge to a steady-state that is characterized by a time-independent elliptic equation. In this article, the steady-state formulation is generalized and integrated with shape optimization to improve the wear performance of bi-material composites. Both macroscopic structures and periodic material microstructures are considered. Several common tribological objectives for systems undergoing wear are identified and mathematically formalized with shape derivatives. These include (i) achieving a planar wear surface from multimaterial composites and (ii) minimizing the run-in volume of material lost before steady-state F. Feppon wear is achieved. A level-set based topology optimization algorithm that incorporates a novel constraint on the levelset function is presented. In particular, a new scheme is developed to update material interfaces; the scheme (i) conveniently enforces volume constraints at each iteration, (ii) controls the complexity of design features using perimeter penalization, and (iii) nucleates holes or inclusions with the topological gradient. The broad applicability of the proposed formulation for problems beyond wear is discussed, especially for problems where convenient control of the complexity of geometric features is desired.

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

Abstract: International audienc

Cited by 75 publications

References 37 publications

Topology optimization of coated structures and material interface problems

Topology optimization of coated structures and material interface problems

A projection‐based method for topology optimization of structures with graded surfaces

Introducing a level-set based shape and topology optimization method for the wear of composite materials with geometric constraints

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