Article
Mechanics
Minami Fujioka, Masatoshi Shimoda, Musaddiq Al Ali
Summary: The study proposes a shape optimization method for designing the shapes of microstructures, which can effectively minimize the compliance of macrostructures under constraint conditions. The theoretical derivation of shape gradient function allows for determining the boundary shapes of unit cells. The research highlights the importance of weight reduction in improving performance and resource conservation.
COMPOSITE STRUCTURES
(2021)
Article
Computer Science, Interdisciplinary Applications
Pedro G. Coelho, Bruno C. Barroca, Fabio M. Conde, Jose M. Guedes
Summary: Strength-oriented optimization of porous periodic microstructures has a significant impact on the design of load-bearing lightweight structures to avoid mechanical failure. The study shows that minimizing the peak von-Mises stress through shape or topology design changes can effectively reduce stresses in different load scenarios, demonstrating the importance of material design freedom in achieving lower peak stresses.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2021)
Article
Computer Science, Interdisciplinary Applications
Alex Ferrer, Sebastian Miguel Giusti
Summary: This study aims to solve the inverse homogenization problem using the topological derivative concept, obtaining optimal topologies through a relaxed formulation and penalizing intermediate values for better solutions. The authors' original methodology combines the topological derivative concept with classical optimization algorithms, proposing a new research framework.
ENGINEERING COMPUTATIONS
(2022)
Article
Operations Research & Management Science
Marc Dambrine, Salah Zerrouq
Summary: This paper combines shape optimization and homogenization techniques to search for the optimal design of microstructures in elastic scaffolds. The development of materials with specific properties is of practical interest in medical applications or for the development of lightweight structures in aeronautics. The authors propose a robust approach based on the shape derivative to find a design that is insensitive to domain variations and demonstrate its applicability and feasibility through numerical experiments.
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
(2023)
Article
Computer Science, Interdisciplinary Applications
Samuel Amstutz
Summary: This paper provides a self-contained introduction to the mathematical aspects of the topological derivative, with full justifications given on simple model problems using a modern approach. Closed expressions of topological derivatives are obtained and commented, covering several cases in a unified and didactic presentation. Some elements of proof are novel.
ENGINEERING COMPUTATIONS
(2022)
Article
Multidisciplinary Sciences
Shucong Li, Bolei Deng, Alison Grinthal, Alyssha Schneider-Yamamura, Jinliang Kang, Reese S. Martens, Cathy T. Zhang, Jian Li, Siqin Yu, Katia Bertoldi, Joanna Aizenberg
Summary: The text discusses the impact of cellular topology on properties, introduces a reversible strategy for topological transformations using liquid treatment, and demonstrates the potential applications of this approach.
Article
Engineering, Multidisciplinary
Helmut Harbrecht, Michael Multerer, Remo von Rickenbach
Summary: This article presents an optimal design approach for the microstructure in scaffolds by combining shape optimization and homogenization. By calculating the effective tensor and using the shape gradient to update the microstructure, the desired effective tensor can be achieved. Extensive numerical studies demonstrate the applicability and feasibility of the approach.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Mechanics
Kyeong-Soo Yun, Sung-Kie Youn
Summary: This paper presents a topology optimization method for microstructures of viscoelastic composites, utilizing numerical methods and adjoint sensitivity analysis to find the optimal microstructures and minimize the difference between prescribed and effective relaxation moduli. Several numerical examples demonstrate the effectiveness of the proposed approach in optimizing viscoelastic composites based on volume fraction, relaxation time, and stiffness.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2022)
Article
Mechanics
V. Calisti, A. Lebee, A. A. Novotny, J. Sokolowski
Summary: In this paper, new microstructures with significant strain-gradient effects are generated for the first time through topological optimization of two-dimensional periodic media. The optimized shape functionals depend on the first and second-order homogenized tensors obtained from a two-scale asymptotic expansion homogenization scheme. The optimization method used here relies on the recently derived topological derivative of the second-order homogenized tensor, which measures the strain-gradient sensitivity with respect to a small circular inclusion at the microscopic level with different material properties.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2023)
Article
Engineering, Multidisciplinary
Kai Long, Xiaoyu Yang, Nouman Saeed, Zhuo Chen, Yi Min Xie
Summary: This study proposes a methodology to achieve the maximum modulus in elastic composites. By using a topology optimization algorithm and numerical homogenization technique, microstructures close to theoretical upper bounds are found. The research also reveals that the optimized mechanical properties of the composite materials are close to theoretical limits.
CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES
(2021)
Article
Engineering, Multidisciplinary
Kazem Alidoost, Felipe Fernandez, Philippe H. Geubelle, Daniel A. Tortorelli
Summary: In this study, a method was developed to approximate the energy release rate field associated with small edge or surface cracks, which is computationally attractive compared to conventional methods. A shape optimization scheme for fracture-resistant structures was developed using this energy release rate approximation. The optimization scheme is gradient-based and defines the domain and its boundary implicitly using level-set functions.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Engineering, Multidisciplinary
Xiaoya Zhai, Weiming Wang, Falai Chen, Jun Wu
Summary: This paper introduces the concept of differentiable microstructures and proposes a novel topology optimization method that can generate a series of microstructures with continuous variations in geometry and mechanical properties.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Materials Science, Multidisciplinary
Pai Liu, Yi Yan, Xiaopeng Zhang, Yangjun Luo, Zhan Kang
Summary: This paper introduces a novel gradient-free framework for the design of periodic microstructures, which exhibits strong global searching capabilities and does not require sensitivity information. The method effectively addresses the problem of multiple local minima in microstructural design optimization.
MATERIALS & DESIGN
(2021)
Article
Engineering, Multidisciplinary
Chungang Zhuang, Zhenhua Xiong, Han Ding
Summary: This article presents a Bezier extraction based isogeometric approach for multi-objective topology optimization of periodic microstructures. The method computes the equivalent elastic properties of the representative volume element using numerical homogenization with periodic boundary conditions on the control points, and proposes a distance-based density distribution for the initialization of designing the RVE, which leads to more robust results. Several numerical examples demonstrate the effectiveness of the approach in obtaining various isotropic and anisotropic RVEs and composite structures, while discussing different influences on the optimal design of the RVE and macrostructure.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2021)
Article
Mechanics
Tarkes Dora Pallicity, Thomas Boehlke
Summary: This paper investigates the viscoelastic homogenization problem in processing of composites and compares the full-field solutions with mean-field solutions using finite element simulations. Different elastic bounds-based homogenization methods are coupled with an incremental variational approach for validation. The study explores the effect of various factors on the macroscopic response of composites, providing insights into the homogenization techniques for different microstructures.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2021)
Article
Computer Science, Interdisciplinary Applications
Pedro R. S. Antunes, Cristian Barbarosie, Anca-Maria Toader
JOURNAL OF COMPUTATIONAL PHYSICS
(2017)
Article
Mechanics
Cristian Barbarosie, Sergio Lopes
COMPTES RENDUS MECANIQUE
(2011)
Article
Materials Science, Multidisciplinary
Cristian Barbarosie, Anca-Maria Toader
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES
(2012)
Article
Mathematics, Interdisciplinary Applications
Cristian Barbarosie, Anca-Maria Toader
NETWORKS AND HETEROGENEOUS MEDIA
(2014)
Article
Mathematics, Applied
Sergio Oliveira, Anca-Maria Toader, Paulo Vieira
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2012)
Article
Mathematics, Applied
Cristian Barbarosie
QUARTERLY OF APPLIED MATHEMATICS
(2011)
Article
Automation & Control Systems
Anca-Maria Toader
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
(2011)
Article
Mathematics, Applied
Cristian Barbaroste, Anca-Maria Toader, Sergio Lopes
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
(2020)
Article
Engineering, Multidisciplinary
Cristian Barbarosie, Daniel A. Tortorelli, Seth Watts
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2017)
Proceedings Paper
Engineering, Biomedical
Cristian Barbarosie, Anca-Maria Toader
M2D2015: PROCEEDINGS OF THE 6TH INTERNATIONAL CONFERENCE ON MECHANICS AND MATERIALS IN DESIGN
(2015)
