Article
Materials Science, Multidisciplinary
Matti Schneider, Marc Josien, Felix Otto
Summary: This study investigates volume-element sampling strategies for stochastic homogenization of particle-reinforced composites and highlights the impact of improper treatment of particles intersecting the boundary of computational cells on computed effective properties accuracy. Computational experiments on microstructures with different inclusions show that periodized ensembles exhibit a superior convergence rate for systematic error compared to snapshot ensembles, with standard deviation decay following the central limit theorem's expectation. The findings provide guidelines for designing representative volume elements and working with digital volume images of material microstructures.
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
(2022)
Article
Materials Science, Multidisciplinary
Baptiste Durand, Arthur Lebee, Pierre Seppecher, Karam Sab
Summary: This paper presents a pantographic material with significant strain-gradient effects, which is easy to fabricate and has excellent performance. By using an appropriate homogenization scheme and scale selection, it is possible to control the strains and displacements in compliant junctions.
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
(2022)
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
Engineering, Mechanical
Marco Lo Cascio, Alberto Milazzo, Ivano Benedetti
Summary: In this work, a hybrid formulation combining the Virtual Element Method (VEM) and the Boundary Element Method (BEM) was proposed for effective computational analysis of multi region domains representing heterogeneous materials. The method simultaneously employs the advantages of VEM and BEM, ensuring high accuracy and efficiency in analyzing multiphase materials.
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2021)
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
Engineering, Multidisciplinary
Lee Alacoque, Ryan T. Watkins, Ali Y. Tamijani
Summary: A topology optimization framework is developed to synthesize high-strength spatially periodic metamaterials with unique thermoelastic properties, and stress and manufacturing uncertainty methods are used to achieve large reductions in stress while maintaining strength and thermal expansion properties.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Engineering, Mechanical
Wenxuan Xia, Erkan Oterkus, Selda Oterkus
Summary: This work presents an ordinary state-based peridynamic homogenization method to obtain effective material properties of periodic micro-structured materials, with the unique advantage of governing equation in integro-differential form. With the rapid advancement in additive manufacturing technology, micro-structured materials with defects have attracted significant attention, and this study provides a new approach to obtain their effective properties.
THEORETICAL AND APPLIED FRACTURE MECHANICS
(2021)
Article
Engineering, Multidisciplinary
Jiabao Li, Qing Wang, Xinfei Li, Lei Ju, Yiheng Zhang
Summary: In this paper, a homogenization method based on peridynamics is proposed, which overcomes the limitation of Poisson's ratio and can be applied to periodic materials with defects.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2022)
Article
Engineering, Multidisciplinary
Zhiqiang Yang, Ming Li, Yi Sun, Shanqiao Huang, Qiang Ma, Junzhi Cui
Summary: In this paper, a high-efficiency second-order reduced homogenization method is established to solve the inelastic problem of periodic heterogeneous structures in cylindrical coordinate. The local solutions at microscale are given using various multiscale auxiliary functions, and the nonlinear high-order homogenization solutions are obtained at macroscale using a modified asymptotic expansion method. The significant novelties of this work include the effective reduced model for solving nonlinear multiscale problems in cylindrical coordinates with less computational cost and the establishment of a new second-order nonlinear multiscale algorithm for simulating the heterogeneous cylindrical structure. The validity and accuracy of the proposed algorithms are verified through three typical numerical examples.
APPLIED MATHEMATICAL MODELLING
(2023)
Article
Mathematics, Applied
S. Aiyappan, K. Pettersson
Summary: This paper addresses the homogenization of a mixed boundary value problem for the Laplace operator in a domain with locally periodic oscillating boundary. The results show that the homogenization holds in terms of weak L-2 convergence of solutions and flows, assuming natural hypotheses on the regularity of the domain. The strong L-2 convergence of average preserving extensions of solutions and flows is also considered.
APPLIED MATHEMATICS AND OPTIMIZATION
(2022)
Article
Mechanics
Wei Huang, Rui Xu, Jie Yang, Qun Huang, Heng Hu
Summary: This paper introduces a multiscale data-driven framework for FRP composites, which collects material databases and simulates structural behavior through a data-driven approach, leading to significant cost savings and promising applications.
COMPOSITE STRUCTURES
(2021)
Article
Mechanics
Jiyang He, Benjamin Favier, Michel Rieutord, Stephane Le Dizes
Summary: This study examines the internal shear layers generated by the longitudinal libration of the inner core in a rotating spherical shell. By using asymptotic and numerical analysis, the researchers provide insights into the behavior of these shear layers and compare the asymptotic predictions with direct numerical results. The study demonstrates that, with decreasing Ekman numbers, the agreement between the asymptotic predictions and numerical results improves.
JOURNAL OF FLUID MECHANICS
(2022)
Article
Materials Science, Multidisciplinary
A. G. Kolpakov, S. Rakin
Summary: This study presents a procedure for reducing a three-dimensional problem to several two-dimensional problems for plates with a unidirectional system of inhomogeneities, demonstrating the existence of boundary layers that result in wrinkling of the top and bottom surfaces of the plate and influencing its strength and interaction with surrounding media.
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES
(2022)
Article
Mathematics, Applied
Eduard Rohan, Robert Cimrman, Salah Naili
Summary: The study focuses on acoustic wave propagation in a poroelastic medium with periodic structure, examining the influence of permanent seepage flow on wave propagation. By homogenization and wave dispersion analysis, the impact of advection flow and microstructure geometry on wave propagation properties is explored.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Engineering, Multidisciplinary
Andrea Bacigalupo, Maria Laura De Bellis, Giorgio Zavarise
Summary: A micropolar-based asymptotic homogenization approach is proposed for analyzing composite materials with periodic microstructure. The macro descriptors are consistently derived and shown to be directly related to perturbation functions and micropolar two-dimensional deformation modes. An energy equivalence concept is introduced to derive the consistent overall micropolar constitutive tensors.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Mechanics
Rosaria Del Toro, Andrea Bacigalupo, Marco Paggi
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2019)
Article
Mechanics
Andrea Bacigalupo, Luigi Gambarotta, Marco Lepidi, Francesca Vadala
Article
Materials Science, Multidisciplinary
Ferdinando Auricchio, Andrea Bacigalupo, Luigi Gambarotta, Marco Lepidi, Simone Morganti, Francesca Vadala
MATERIALS & DESIGN
(2019)
Article
Mechanics
Andrea Bacigalupo, Maria Laura De Bellis, Giorgio Gnecco
Article
Engineering, Mechanical
Marco Lepidi, Andrea Bacigalupo
NONLINEAR DYNAMICS
(2019)
Article
Engineering, Multidisciplinary
Maria Laura De Bellis, Andrea Bacigalupo, Giorgio Zavarise
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2019)
Article
Operations Research & Management Science
Andrea Bacigalupo, Giorgio Gnecco, Marco Lepidi, Luigi Gambarotta
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
(2020)
Article
Engineering, Mechanical
Andrea Bacigalupo, Luigi Gambarotta
EXTREME MECHANICS LETTERS
(2020)
Article
Engineering, Multidisciplinary
Andrea Bacigalupo, Luigi Gambarotta
Summary: This paper focuses on dynamic homogenization of lattice-like materials with lumped mass at nodes to obtain energetically consistent models for accurate descriptions of the discrete system's acoustic behavior. By utilizing proper mapping and enhanced continualization, equivalent continuum models with non-local terms are derived, achieving energy-consistent differential equations for effective representation of the system's behavior.
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
(2021)
Article
Mechanics
Vito Diana, Andrea Bacigalupo, Luigi Gambarotta
Summary: This paper investigates lattice-like materials with periodic planar tessellation, focusing on their chiral properties and the resulting auxetic and dispersive acoustic behaviors. Through an enhanced continualization scheme, an equivalent non-local continuum model is developed, which shows thermodynamic consistency and matches the actual frequency band structure.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2023)
Article
Engineering, Mechanical
Francesca Fantoni, Andrea Bacigalupo, Giorgio Gnecco, Luigi Gambarotta
Summary: This paper proposes an advanced computational method to achieve an approximately optimal design for a specific class of acoustic metamaterials. By combining multi-objective optimization and dimensionality reduction, the method models metamaterials as beam lattices with resonators coupled through a viscoelastic phase. The dynamics are described by integro-differential equations transformed into the Z-Laplace space to obtain the dispersion relation of Bloch waves. The method combines numerical optimization with machine learning, employing sequential linear programming algorithm and principal component analysis for optimized sensitivity analysis.
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2023)
Article
Mechanics
Andrea Bacigalupo, Vito Diana, Luigi Gambarotta
Summary: A novel energy absorbing material with a layered microstructure is proposed, which consists of repeating plane lattices with hex-achiral topology with alternate chirality. The material exhibits rotation of rigid disks and frictional dissipative mechanisms, allowing for energy dissipation and self-recovering. It is suitable for the design of shock absorbers and vibrational dampers.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2023)
Article
Mechanics
Giacomo Elefante, Maria Laura De Bellis, Andrea Bacigalupo
Summary: An electrically-tunable metamaterial with active control of damped elastic waves is designed, where a dissipative electric circuit is used to adjust the impedance/admittance. A new derationalization strategy is proposed to solve the difficulty caused by the presence of a dissipative circuit, by exploiting an LU factorization of the matrix collecting the rational terms. The strategy is successfully applied to a three-phase metamaterial shunted by a series RLC circuit with rational admittance.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2023)
Article
Mechanics
Rosaria Del Toro, Maria Laura De Bellis, Andrea Bacigalupo
Summary: In this study, the magneto-electro-elastic (MEE) heterogeneous materials with periodic microstructure, specifically the layered MEE material, are investigated. The frequency dispersion spectrum is derived using the transfer matrix method and Floquet-Bloch boundary conditions, and an eigenproblem involving a 12 x 12 transfer matrix is solved. The problems of longitudinal and transverse elastic waves are uncoupled by assuming the cubic symmetry of layers, simplifying the treatment and subproblems to be solved.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2023)