Additive manufacturing introduced substructure and computational determination of metamaterials parameters by means of t
- PDF / 914,428 Bytes
- 17 Pages / 595.276 x 790.866 pts Page_size
- 116 Downloads / 204 Views
O R I G I NA L A RT I C L E
Bilen Emek Abali
· Emilio Barchiesi
Additive manufacturing introduced substructure and computational determination of metamaterials parameters by means of the asymptotic homogenization Dedicated to Prof. Holm Altenbach on the occasion of his 65th birthday
Received: 26 September 2020 / Accepted: 13 October 2020 © The Author(s) 2020
Abstract Metamaterials exhibit materials response deviation from conventional elasticity. This phenomenon is captured by the generalized elasticity as a result of extending the theory at the expense of introducing additional parameters. These parameters are linked to internal length scales. Describing on a macroscopic level, a material possessing a substructure at a microscopic length scale calls for introducing additional constitutive parameters. Therefore, in principle, an asymptotic homogenization is feasible to determine these parameters given an accurate knowledge on the substructure. Especially in additive manufacturing, known under the infill ratio, topology optimization introduces a substructure leading to higher-order terms in mechanical response. Hence, weight reduction creates a metamaterial with an accurately known substructure. Herein, we develop a computational scheme using both scales for numerically identifying metamaterials parameters. As a specific example, we apply it on a honeycomb substructure and discuss the infill ratio. Such a computational approach is applicable to a wide class substructures and makes use of open-source codes; we make it publicly available for a transparent scientific exchange. Keywords Metamaterials · Homogenization · Generalized mechanics · Finite element method (FEM)
1 Introduction Mechanics of metamaterials is gaining an increased interest owing to additive manufacturing technologies allowing us to craft sophisticated structures with different length scales. For weight reduction, material is saved by introducing a substructure. Substructure-related change in materials response is already known [1– 3], studied under different assumptions [4–9], and verified experimentally [10–13]. Substructure-related change leads to metamaterials, and this phenomenon is explained by theoretical arguments by assuming conventional elasticity in the smaller length scale (microscale) leading to generalized elasticity in the larger length scale (macroscale) [14–18]. Communicated by Andreas Öchsner. B. E. Abali (B) Institute of Mechanics, MS 2, Technische Universität Berlin, Einsteinufer 5, 10587 Berlin, Germany E-mail: [email protected] B. E. Abali Division of Applied Mechanics, Department of Materials Science and Engineering, Uppsala University, Box 534, 751 21 Uppsala, Sweden E. Barchiesi International Research Center on Mathematics and Mechanics of Complex Systems, Università degli Studi dell’Aquila, Via Giovanni Gronchi 18 - Zona industriale di Pile, 67100 L’Aquila, Italy
B. E. Abali, E. Barchiesi
For constructing theories, different length scales are often incorporated in science. For example, consider the microscale bein
Data Loading...
