Article
Mathematics, Interdisciplinary Applications
Jorg Schroeder, Mohammad Sarhil, Lisa Scheunemann, Patrizio Neff
Summary: Modeling the mechanical properties of metamaterials using the relaxed micromorphic model with finite element method is discussed in this paper. Different formulations and their convergence behavior are presented, along with the implementation of higher-order Nedelec elements. The effect of characteristic length on the model and its capturing of the size-effect property are also analyzed.
COMPUTATIONAL MECHANICS
(2022)
Article
Engineering, Multidisciplinary
Adam Sky, Michael Neunteufel, Ingo Muench, Joachim Schoeberl, Patrizio Neff
Summary: The classical continuum theory fails to capture the mechanical behavior of materials with pronounced microstructure, but the relaxed micromorphic continuum provides an alternative method. By enriching the kinematics of the mathematical model, this theory introduces a microdistortion field with nine extra degrees of freedom for each material point. We describe the construction of appropriate finite elements using Nedelec and Raviart-Thomas subspaces and explore the numerical behavior of the relaxed micromorphic model.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Engineering, Multidisciplinary
Adam Sky, Ingo Muench, Patrizio Neff
Summary: In this study, we test the numerical behavior of matrix-valued fields approximated by finite element subspaces of [H-1](3x3), [H(curl)](3), and H(sym Curl) for a linear abstract variational problem related to the relaxed micromorphic model. We introduce the formulation of the corresponding finite elements, perform numerical benchmarks, and present our conclusions. The introduction of the newly appropriate space H(sym Curl) reduces the continuity assumptions of the classical micromorphic model and provides a larger solution space for the microdistortion.
JOURNAL OF ENGINEERING MATHEMATICS
(2022)
Article
Materials Science, Multidisciplinary
Ryan Alberdi, Joshua Robbins, Timothy Walsh, Remi Dingreville
Summary: Metamaterials are artificial structures that can manipulate and control sound waves in unique ways. The relaxed micromorphic model is used in this paper to study wave propagation in heterogeneous metastructures composed of different unit cells, showing the versatility of this model in accurately simulating wave propagation. Through spatially arranging multiple unit cells into metastructures, tailored and unique properties such as spatially-dependent broadband wave attenuation, rainbow trapping, and pulse shaping can be achieved.
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
(2021)
Article
Mathematics, Applied
Adam Sky, Ingo Muench, Gianluca Rizzi, Patrizio Neff
Summary: This work applies the polytopal template methodology for the construction of Nedelec elements in the relaxed micromorphic model. Dual numbers are used in conjunction with Bernstein-Bezier polynomials to compute hp-FEM solutions of the model. The Nedelec base functions inherit the optimal complexity of the underlying Bernstein-Bezier basis through the polytopal template methodology.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Materials Science, Multidisciplinary
F. Demore, G. Rizzi, M. Collet, P. Neff, A. Madeo
Summary: This paper presents a unit cell that exhibits a band-gap in the lower acoustic domain, and confirms its viability through manufacturing and experimental tests. The introduction of a micromorphic model allows for focusing elastic energy, enabling the optimization of complex structures. This opens up new possibilities in metastructural design.
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
(2022)
Article
Multidisciplinary Sciences
Gianluca Rizzi, Patrizio Neff, Angela Madeo
Summary: In this paper, a coherent boundary value problem based on the relaxed micromorphic model is established to model metamaterials' behavior. The well-posed boundary conditions in this problem allow for exploring the scattering patterns of finite-size metamaterial specimens. The simplified model's structure enables the unveiling of the scattering response for a wide range of frequencies and angles. These results are crucial for the development of large-scale meta-structures that can control elastic waves and recover energy. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 1)'.
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2023)
Article
Mechanics
Plastiras Demetriou, Gianluca Rizzi, Angela Madeo
Summary: This paper proposes an approach to describe wave propagation in finite-size microstructured metamaterials using a reduced relaxed micromorphic model. This model introduces an additional kinematic field to capture the effects of microstructure and is effective for numerical simulations and analysis. It is an essential tool for designing and optimizing metamaterial structures with specific wave propagation properties.
ARCHIVE OF APPLIED MECHANICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Mohammad Sarhil, Lisa Scheunemann, Joerg Schroeder, Patrizio Neff
Summary: In this paper, the size-effects of metamaterial beams under bending are modeled using the relaxed micromorphic continuum. The size-dependent bending stiffness of fully discretized metamaterial beams is analyzed. Two equivalent loading schemes are introduced to achieve a constant moment along the beam length. The relaxed micromorphic model is used to retrieve the size-effects, and a procedure is presented to determine the material parameters of the model based on well-defined scales.
COMPUTATIONAL MECHANICS
(2023)
Article
Mathematics
Haiying Li, Yulian Wu, Fenghui Wang
Summary: In this paper, two inertial relaxed CQ algorithms are proposed for solving the split feasibility problem in real Hilbert spaces, involving metric projections and a new variable step size. The weak and strong convergence of the algorithms are established under certain conditions, and a numerical experiment is conducted to illustrate the performance.
JOURNAL OF MATHEMATICS
(2021)
Article
Materials Science, Multidisciplinary
Gianluca Rizzi, Geralf Hutter, Hassam Khan, Ionel-Dumitrel Ghiba, Angela Madeo, Patrizio Neff
Summary: In this study, we addressed the St. Venant torsion problem for an infinite cylindrical rod using various isotropic generalized continua models, including the relaxed micromorphic and classical micromorphic model. Special attention was given to the potential nonphysical stiffness singularity that may occur for slender specimens with vanishing rod diameter.
MATHEMATICS AND MECHANICS OF SOLIDS
(2022)
Article
Materials Science, Multidisciplinary
Gianluca Rizzi, Manuel Collet, Felix Demore, Bernhard Eidel, Patrizio Neff, Angela Madeo
Summary: This paper addresses the challenge of exploring the interactions between metamaterials and other materials to enhance their behaviors and enable real engineering applications. The relaxed micromorphic model is shown to be useful for describing the refractive properties of simple meta-structures, and changing the elastic properties of specific elements can drastically alter the overall refractive behavior of the structure.
FRONTIERS IN MATERIALS
(2021)
Article
Acoustics
Gianluca Rizzi, Domenico Tallarico, Patrizio Neff, Angela Madeo
Summary: This paper introduces an enriched continuum model of the micromorphic type for simulating metamaterials' response in meta-structural design. Experimenting with different combinations of metamaterials and classical-materials bricks using the reduced model's structure and well-posed interface conditions allows for the creation of an optimized meta-structure with enhanced diode-behaviour.
Article
Mathematics, Applied
Haiying LI, Fenghui Wang, Hai Yu
Summary: This paper examines the inertial relaxed CQ algorithm for solving split feasibility problems in Hilbert spaces and establishes two convergence theorems under different conditions, with the first condition being weaker and the second condition being completely different from existing ones. Preliminary numerical experiments show that the proposed algorithms converge faster than existing ones.
JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS
(2021)
Article
Materials Science, Multidisciplinary
Gianluca Rizzi, Marco Valerio d'Agostino, Patrizio Neff, Angela Madeo
Summary: This paper establishes well-posed boundary and interface conditions for the relaxed micromorphic model and implements it in finite-element simulations. The results show that the relaxed micromorphic model is suitable for describing dynamic anisotropy and can be used to design a metastructure combining metamaterials and classical materials.
MATHEMATICS AND MECHANICS OF SOLIDS
(2022)
Article
Engineering, Multidisciplinary
Michael Neunteufel, Joachim Schoeberl
Summary: In this paper, a method to overcome membrane locking of thin shells is proposed by inserting an interpolation operator into the membrane energy term to weaken implicitly given kernel constraints. The approach decreases the number of constraints on triangular meshes compared to reduced integration techniques, and can be easily incorporated into existing shell elements. The performance of the method is demonstrated through several benchmark examples.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Computer Science, Interdisciplinary Applications
Michael Neunteufel, Joachim Schoberl
Summary: This study presents a novel application of the (high-order) H(div)-conforming Hybrid Discontinuous Galerkin finite element method for monolithic fluid-structure interaction (FSI), which yields exact divergence free fluid velocity solutions by introducing the Piola transformation. With the use of hp-refinement strategies, singularities and boundary layers are overcome leading to optimal spatial convergence rates. Copyright (C) 2020 Elsevier Ltd.
COMPUTERS & STRUCTURES
(2021)
Article
Engineering, Multidisciplinary
David Melching, Michael Neunteufel, Joachim Schoeberl, Ulisse Stefanelli
Summary: This study introduces a three-dimensional model capable of describing coupled damage and plastic effects in solids at finite strains, with rate-independent, associative, and unidirectional damage evolution features. Numerical simulations are conducted using multiphysics finite element software for various 2D and 3D settings under different choices of boundary conditions and possibly in presence of pre-damaged regions.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Engineering, Multidisciplinary
Michael Neunteufel, Astrid S. Pechstein, Joachim Schoeberl
Summary: This paper extends the TDNNS method to nonlinear elasticity by lifting the distributional derivatives of the displacement vector to a regular strain tensor using the Hu-Washizu principle. Three different methods are introduced using either the deformation gradient, the Cauchy-Green strain tensor, or both as independent variables. The good performance and accuracy of the methods are demonstrated through numerical examples where stress and strain variables are locally eliminated in linear sub-problems, resulting in an equation system solely in terms of displacement variables.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Engineering, Multidisciplinary
Adam Sky, Michael Neunteufel, Ingo Muench, Joachim Schoeberl, Patrizio Neff
Summary: The classical continuum theory fails to capture the mechanical behavior of materials with pronounced microstructure, but the relaxed micromorphic continuum provides an alternative method. By enriching the kinematics of the mathematical model, this theory introduces a microdistortion field with nine extra degrees of freedom for each material point. We describe the construction of appropriate finite elements using Nedelec and Raviart-Thomas subspaces and explore the numerical behavior of the relaxed micromorphic model.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Engineering, Multidisciplinary
Adam Sky, Ingo Muench, Patrizio Neff
Summary: In this study, we test the numerical behavior of matrix-valued fields approximated by finite element subspaces of [H-1](3x3), [H(curl)](3), and H(sym Curl) for a linear abstract variational problem related to the relaxed micromorphic model. We introduce the formulation of the corresponding finite elements, perform numerical benchmarks, and present our conclusions. The introduction of the newly appropriate space H(sym Curl) reduces the continuity assumptions of the classical micromorphic model and provides a larger solution space for the microdistortion.
JOURNAL OF ENGINEERING MATHEMATICS
(2022)
Article
Engineering, Multidisciplinary
Adam Zdunek, Michael Neunteufel, Waldemar Rachowicz
Summary: We investigate the possibility to determine the divergence-free displacement independently from the pressure reaction for a class of boundary-value problems in incompressible linear elasticity. For convex domains, there is only one variational boundary value problem that allows the independent determination. The weakly divergence-free displacement can be computed pressure robustly by decomposing the total body force using the Helmholtz decomposition.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Engineering, Multidisciplinary
Adam Sky, Michael Neunteufel, Jack S. Hale, Andreas Zilian
Summary: In this work, new finite element discretisations of the shear-deformable Reissner-Mindlin plate problem are developed based on the Hellinger-Reissner principle. Conforming Hu-Zhang elements are used to discretise the bending moments and the rotation field, resulting in highly accurate approximations and satisfaction of the Kirchhoff-Love constraint. The formulation is extended using Raviart-Thomas elements for the shear stress to preserve optimal convergence rates for small thicknesses.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Computer Science, Interdisciplinary Applications
Michael Neunteufel, Joachim Schoeberl, Kevin Sturm
Summary: In this paper, a novel numerical scheme is proposed for the Canham-Helfrich-Evans bending energy. It employs a three-field lifting procedure to convert the distributional shape operator to an auxiliary mean curvature field. By introducing the energetic conjugate scalar stress field as a Lagrange multiplier, the resulting fourth order problem is transformed into a mixed saddle point problem involving second order differential operators. The authors also derive analytical first variations and discuss the computation of shape derivatives in the finite element software NGSolve. Numerical simulations are provided to demonstrate the effectiveness of the proposed scheme and method.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Computer Science, Theory & Methods
Adam Sky, Cesar Polindara, Ingo Muench, Carolin Birk
Summary: This paper focuses on the assembly process of the global stiffness matrix in finite element methods, exploring different algorithms and their efficiency on shared memory systems using C++. The use of atomic synchronization primitives for data-race free algorithms and data structures is a key aspect of the investigation. Additionally, a new flexible storage format for sparse matrices is proposed and its performance is compared with the compressed row storage format using abstract benchmarks based on common characteristics of finite element problems.
PARALLEL COMPUTING
(2023)
Article
Mathematics, Applied
Adam Sky, Ingo Muench, Gianluca Rizzi, Patrizio Neff
Summary: This work applies the polytopal template methodology for the construction of Nedelec elements in the relaxed micromorphic model. Dual numbers are used in conjunction with Bernstein-Bezier polynomials to compute hp-FEM solutions of the model. The Nedelec base functions inherit the optimal complexity of the underlying Bernstein-Bezier basis through the polytopal template methodology.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Peter Gangl, Kevin Sturm, Michael Neunteufel, Joachim Schoeberl
Summary: This paper presents a framework for automated shape differentiation in the finite element software NGSolve, combining the Lagrangian approach and automated differentiation capabilities. Users can customize the level of automation needed, with automatic generation of first- and second-order shape derivatives discussed for both constrained and unconstrained model problems. Numerical experiments validate the accuracy of computed derivatives, and first- and second-order shape optimization algorithms are demonstrated for various numerical optimization examples.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2021)