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A phase field approach for structural topology optimization with application to additive manufacturing is analyzed. The main novelty is the penalization of overhangs (regions of the design that require underlying support structures during…

Optimization and Control · Mathematics 2023-03-14 Harald Garcke , Kei Fong Lam , Robert Nürnberg , Andrea Signori

Additive manufacturing (AM) could be a novel method of fabricating composite and porous materials having various effective performances based on mechanisms of their internal geometries. Materials fabricated by AM could rapidly be used in…

Materials Science · Physics 2015-08-26 Akihiro Takezawa , Makoto Kobashi , Mitsuru Kitamura

Although stress-constrained topology optimization has been extensively studied in structural design, the development of optimization frameworks to enable the creation of metamaterials with optimal mechanical performance is still an open…

Computational Engineering, Finance, and Science · Computer Science 2026-02-24 Yanda Chen , Sebastian Rodriguez , Beatriz Moya , Francisco Chinesta

There is a growing mechanics literature concerning the macroscopic properties of mechanism-based mechanical metamaterials. This amounts mathematically to a homogenization problem involving nonlinear elasticity. A key goal is to identify the…

Analysis of PDEs · Mathematics 2025-11-10 Xuenan Li , Robert V. Kohn

Materials design can be cast as an optimization problem with the goal of achieving desired properties, by varying material composition, microstructure morphology, and processing conditions. Existence of both qualitative and quantitative…

Computational Physics · Physics 2019-07-08 Akshay Iyer , Yichi Zhang , Aditya Prasad , Siyu Tao , Yixing Wang , Linda Schadler , L Catherine Brinson , Wei Chen

Metamaterials can enable peculiar static and dynamic behavior (such as negative effective mass density, dynamical stiffness, and Poisson's ratio) due to their geometry rather than their chemical composition. The geometry of these…

Soft Condensed Matter · Physics 2022-01-03 Audrey A. Watkins , Austin Eichelberg , Osama R. Bilal

Porous structures such as trabecular bone are widely seen in nature. These structures exhibit superior mechanical properties whilst being lightweight. In this paper, we present a method to generate bone-like porous structures as lightweight…

Graphics · Computer Science 2018-05-01 Jun Wu , Niels Aage , Ruediger Westermann , Ole Sigmund

The idea that a material can exhibit negative compressibility is highly consequential for research and applications. As new forms for this effect are discovered, it is important to examine the range of possible mechanisms and ways to design…

Applied Physics · Physics 2024-10-11 Zachary G. Nicolaou , Feng Jiang , Adilson E. Motter

Multi-objective parametric optimization problem is presented for overwrapped composite pressure vessels under internal pressure for storage and heating water. It is solved using the developed iterative optimization algorithm. Optimal values…

Optimization and Control · Mathematics 2024-10-08 Lyudmyla Rozova , Bilal Meemary , Salim Chaki , Mylène Deléglise-Lagardère , Dmytro Vasiukov

For non-topological quantum materials, introducing defects can significantly alter their properties by modifying symmetry and generating a nonzero analytical index, thus transforming the material into a topological one. We present a method…

Mesoscale and Nanoscale Physics · Physics 2025-07-03 Yuval Abulafia , Amit Goft , Nadav Orion , Eric Akkermans

In this paper, we propose PATO-a producibility-aware topology optimization (TO) framework to help efficiently explore the design space of components fabricated using metal additive manufacturing (AM), while ensuring manufacturability with…

Computational Engineering, Finance, and Science · Computer Science 2021-12-10 Naresh S. Iyer , Amir M. Mirzendehdel , Sathyanarayanan Raghavan , Yang Jiao , Erva Ulu , Morad Behandish , Saigopal Nelaturi , Dean M. Robinson

A topology optimization formulation including a model of the layer-by-layer additive manufacturing (AM) process is considered. Defined as a multi-objective minimization problem, the formulation accounts for the performance and cost of both…

Numerical Analysis · Mathematics 2022-06-29 G. A. Haveroth , C-J. Thore , M. R. Correa , R. F. Ausas , S. Jakobsson , J. A. Cuminato , A. Klarbring

The mechanical environment of a substrate plays a key role in influencing the behavior of adherent biological cells. Traditional tunable substrates have limitations as their mechanical properties cannot be dynamically altered in-situ during…

Soft Condensed Matter · Physics 2025-11-12 Manu Sebastian , Sreenath Balakrishnan , Safvan Palathingal

Auxetic materials become thicker rather than thinner when stretched, exhibiting an unusual negative Poisson's ratio well suited for designing shape transforming metamaterials. Current auxetic designs, however, are often monostable and…

Soft Condensed Matter · Physics 2016-12-20 Ahmad Rafsanjani , Damiano Pasini

The adjoint method allows efficient calculation of the gradient with respect to the design variables of a topology optimization problem. This method is almost exclusively used in combination with traditional Finite-Element-Analysis, whereas…

Computational Engineering, Finance, and Science · Computer Science 2022-06-20 Indre Jödicke , Richard J. Leute , Till Junge , Lars Pastewka

Despite their outstanding mechanical properties, with many industrial applications, a rational and systematic design of new and controlled auxetic materials remains poorly developed. Here a unified framework is established to describe…

Soft Condensed Matter · Physics 2021-06-28 Daniel Acuna , Francisco Gutiérrez , Rodrigo Silva , Humberto Palza , Alvaro S. Nunez , Gustavo Düring

Novel two-dimensional (2D) emergent fermions and negative Poisson's ratio in 2D materials are fascinating subjects of research. Here, based on first-principles calculations and theoretical analysis, we predict that the hexacoordinated…

Mesoscale and Nanoscale Physics · Physics 2018-10-24 Shan-Shan Wang , Ying Liu , Zhi-Ming Yu , Xian-Lei Sheng , Liyan Zhu , Shan Guan , Shengyuan A. Yang

Additive manufacturing has become one of the forefront technologies in fabrication, enabling new products impossible to manufacture before. Although many materials exist for additive manufacturing, they typically suffer from performance…

We describe three perspectives on higher quantization, using the example of magnetic Poisson structures which embody recent discussions of nonassociativity in quantum mechanics with magnetic monopoles and string theory with non-geometric…

High Energy Physics - Theory · Physics 2021-07-28 Richard J. Szabo

We find a closed-form expression for the Poisson's coefficient of curved-crease variants of the ``Miura ori'' origami tessellation. This is done by explicitly constructing a continuous one-parameter family of isometric piecewise-smooth…

Soft Condensed Matter · Physics 2023-10-13 Asma Karami , Adam Reddy , Hussein Nassar