## This content will become publicly available on September 7, 2020

## Multi-scale topology optimization of multi-material structures with controllable geometric complexity — Applications to heat transfer problems

## Abstract

This study presents a topology optimization method to design assemblies of periodic cellular materials with controllable geometric complexity. The framework is based on a novel multi-scale and multi-material design model in which the structure, the layout of the material subdomains, and their micro-structures are optimized concurrently. To allow a tight control over its geometrical complexity, the layout at the macro-scale is described by level-set fields, parameterized by geometric primitives. The micro-scale geometry is represented through a density approach. A nonlinear programming algorithm drives the optimization process using design sensitivities computed by the discrete adjoint method. The proposed design framework is studied with heat transfer problems. Practical design problems, such as a heat sink and a thermal storage unit with phase change are discussed. The macro-scale analysis model relies on a generalized transient diffusion equation. At the micro-scale, homogenization is used to compute equivalent material properties. The numerical examples in this study show that the optimized multi-scale multi-material layouts outperform the corresponding mono-scale structures while maintaining geometric simplicity at the macro-scale level.

- Authors:

- Politecnico di Torino, Turin (Italy). Dept. of Energy
- National Renewable Energy Lab. (NREL), Golden, CO (United States)
- Univ. of Colorado, Boulder, CO (United States). Dept. of Aerospace Engineering Sciences
- Univ. of Birmingham, Birmingham (United Kingdom). Birmingham Center for Energy Storage (BCES), School of Chemical Engineering

- Publication Date:

- Research Org.:
- National Renewable Energy Lab. (NREL), Golden, CO (United States)

- Sponsoring Org.:
- U.S. Department of Defense (DOD), Defense Advanced Research Projects Agency (DARPA)

- OSTI Identifier:
- 1562441

- Report Number(s):
- NREL/JA-5000-73798

Journal ID: ISSN 0045-7825

- Grant/Contract Number:
- AC36-08GO28308

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Computer Methods in Applied Mechanics and Engineering

- Additional Journal Information:
- Journal Volume: 357; Journal Issue: C; Journal ID: ISSN 0045-7825

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING; geometric primitives; level-set; manufacturing; multi-material; multi-scale; topology optimization

### Citation Formats

```
Pizzolato, Alberto, Sharma, Ashesh, Maute, Kurt, Sciacovelli, Adriano, and Verda, Vittorio. Multi-scale topology optimization of multi-material structures with controllable geometric complexity — Applications to heat transfer problems. United States: N. p., 2019.
Web. doi:10.1016/j.cma.2019.07.021.
```

```
Pizzolato, Alberto, Sharma, Ashesh, Maute, Kurt, Sciacovelli, Adriano, & Verda, Vittorio. Multi-scale topology optimization of multi-material structures with controllable geometric complexity — Applications to heat transfer problems. United States. doi:10.1016/j.cma.2019.07.021.
```

```
Pizzolato, Alberto, Sharma, Ashesh, Maute, Kurt, Sciacovelli, Adriano, and Verda, Vittorio. Sat .
"Multi-scale topology optimization of multi-material structures with controllable geometric complexity — Applications to heat transfer problems". United States. doi:10.1016/j.cma.2019.07.021.
```

```
@article{osti_1562441,
```

title = {Multi-scale topology optimization of multi-material structures with controllable geometric complexity — Applications to heat transfer problems},

author = {Pizzolato, Alberto and Sharma, Ashesh and Maute, Kurt and Sciacovelli, Adriano and Verda, Vittorio},

abstractNote = {This study presents a topology optimization method to design assemblies of periodic cellular materials with controllable geometric complexity. The framework is based on a novel multi-scale and multi-material design model in which the structure, the layout of the material subdomains, and their micro-structures are optimized concurrently. To allow a tight control over its geometrical complexity, the layout at the macro-scale is described by level-set fields, parameterized by geometric primitives. The micro-scale geometry is represented through a density approach. A nonlinear programming algorithm drives the optimization process using design sensitivities computed by the discrete adjoint method. The proposed design framework is studied with heat transfer problems. Practical design problems, such as a heat sink and a thermal storage unit with phase change are discussed. The macro-scale analysis model relies on a generalized transient diffusion equation. At the micro-scale, homogenization is used to compute equivalent material properties. The numerical examples in this study show that the optimized multi-scale multi-material layouts outperform the corresponding mono-scale structures while maintaining geometric simplicity at the macro-scale level.},

doi = {10.1016/j.cma.2019.07.021},

journal = {Computer Methods in Applied Mechanics and Engineering},

number = C,

volume = 357,

place = {United States},

year = {2019},

month = {9}

}