Article
Materials Science, Multidisciplinary
Maria Cinefra
Summary: This paper investigates the implementation of 3D finite elements in curvilinear coordinates using the fundamental equations of 3D elasticity and the Principle of Virtual Displacements. The mathematical model of the geometry is reviewed and the formulation of hexahedral finite elements is presented. These finite elements can handle curved geometries and can apply mixed methods to combat locking phenomenon.
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES
(2022)
Article
Computer Science, Interdisciplinary Applications
Christopher G. Albert, Patrick Lainer, Oszkar Biro
Summary: This paper presents a numerical method for solving three-dimensional linear magnetostatic problems by embedding the geometry into a symmetric domain and using Fourier expansion. The developed method allows for a decoupled set of two-dimensional problems, reducing computational complexity and improving efficiency. The approach has important applications in analyzing magnetic plasma confinement devices.
COMPUTER PHYSICS COMMUNICATIONS
(2022)
Article
Mathematics, Applied
Benedikt Perse, Katharina Kormann, Eric Sonnendrucker
Summary: Numerical schemes that preserve the structure of kinetic equations can provide stable simulation results. This paper extends the discrete Hamiltonian structure of the Vlasov-Maxwell equations to curvilinear coordinates and discusses various discretization methods for time with conservation properties and computational efficiency.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2021)
Article
Neurosciences
Uzair Hussain, Corey A. Baron, Ali R. Khan
Summary: Coordinate invariance of physical laws is crucial in physics, allowing freedom to express observations in computationally convenient coordinate systems. Transitioning from Cartesian to curvilinear coordinates in medical imaging can simplify visualization and operation. Introducing tools to enhance existing diffusion tractography approaches, testing showed that tracts from curvilinear coordinates generally have improved sensitivity and specificity compared to Cartesian coordinates. As an application, harmonic coordinates can enhance tractography for the hippocampus.
FRONTIERS IN NEUROSCIENCE
(2021)
Article
Mechanics
Seyed Rasoul Atashipour, Zahra Mohammadi, Peter D. Folkow
Summary: This paper introduces a unique representation of the three-dimensional Navier's equations in cylindrical coordinate system, presenting them in an exact simplified form without any approximation. By solving known elasticity problems, the correctness and effectiveness of this approach are demonstrated.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2022)
Article
Mathematics, Interdisciplinary Applications
Dang Phong Bach, Delphine Brancherie, Ludovic Cauvin
Summary: A numerical approach based on the Embedded Finite Element Method (E-FEM) has been developed to model size effect in nanocomposites by incorporating surface elasticity at the interface. The results from this approach have been compared to analytical solutions and other numerical methods, demonstrating its efficiency in evaluating and predicting the mechanical behavior of nanocomposite materials with both linear and nonlinear behaviors considered.
COMPUTATIONAL MECHANICS
(2022)
Article
Chemistry, Physical
Marco Mendolicchio, Julien Bloino, Vincenzo Barone
Summary: This paper presents the implementation and validation of a second-order perturbative approach for anharmonic vibrations based on curvilinear internal coordinates. The results confirm that curvilinear coordinates significantly reduce inter-mode couplings and increase the reliability of low-order perturbative treatments for semi-rigid molecules. The study also paves the way for accurately representing flexible molecules with different levels of theory.
JOURNAL OF CHEMICAL THEORY AND COMPUTATION
(2022)
Article
Computer Science, Software Engineering
Francis Lacombe, Jean -Pierre Hickey
Summary: Krypton is an open-source framework for solving stability equations on a curvilinear coordinate system, specifically predicting laminar-to-turbulent transition under transonic conditions. It is written in Python and includes a laminar flow solver using a consistent numerical scheme for modal stability calculations. The framework has been validated and can be used as a foundation for future development in aerospace engineering, geophysics, and multiphase flows.
Article
Mechanics
Kenta Suzuki, Sean E. Phenisee, Marco Salviato
Summary: This study explores the use of a NURBS-based Isogeometric Analysis framework for simulating complex curvilinear fiber composites, showing superior computational efficiency and estimation quality compared to standard Finite Element Analysis. Optimization studies demonstrate the ability to reduce stress concentration effectively without significantly affecting overall plate stiffness with the use of curvilinear anisotropy.
COMPOSITE STRUCTURES
(2021)
Article
Chemistry, Analytical
Gianluca Mezzanzanica, Olivier Francais, Stefano Mariani
Summary: Size sorting, line focusing, and isolation of microparticles or cells are essential for disease diagnostic tools in biology and biomedicine. This paper presents a finite element model of a microfluidic surface acoustic wave-based device for microparticle manipulation. Acoustic waves are used to create a standing surface acoustic wave in a microchannel, allowing for non-contact manipulation. The effects of microchannel size on microparticle actuation are discussed using sensitivity analysis and exemplary results.
Article
Mathematics, Interdisciplinary Applications
Frederic Marazzato
Summary: The variational discrete element method is adapted to compute the deformation of elastic Cosserat materials by adding rotational degrees of freedom and devising a reconstruction method to achieve constant strains and stresses in each cell. Numerical examples demonstrate the robustness of the method for static and dynamic computations in both two and three dimensions.
COMPUTATIONAL MECHANICS
(2021)
Article
Mechanics
K. A. Hasim, A. Kefal
Summary: A new IsoGeometric formulation (IG-RZT) based on Refined Zigzag Theory has been proposed for static analysis of laminated plates with curvilinear fiber paths. This method accurately predicts in-plane displacement of composite materials with curved fibers, addressing the challenges of variable angle tow composites. The integration of IG-RZT with Non-Uniform Rational B-Splines (NURBS) functions ensures accuracy and efficiency in predicting displacement and stress distributions in VAT composite structures.
COMPOSITE STRUCTURES
(2021)
Article
Mathematics, Applied
Lu Zhang, Siyang Wang, N. Anders Petersson
Summary: The developed method is a fourth order accurate finite difference method for the three dimensional elastic wave equation in isotropic media with piecewise smooth material property. It discretizes governing equations in second order form on curvilinear meshes using a fourth order finite difference operator with a summation-by-parts property. The method is energy stable, allows for mesh size selection based on material velocity structure, and enforces physical interface conditions at mesh refinement interfaces with hanging nodes.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2021)
Article
Engineering, Civil
K. S. Akhil, P. M. Anilkumar, A. Haldar, B. N. Rao
Summary: This paper investigates the potential applications of variable stiffness bistable laminates in morphing and energy harvesting devices, and presents a semi-analytical model based on the Rayleigh-Ritz approach to predict their natural frequencies. The results are validated using a fully geometrically nonlinear finite element model, and the effects of different external forces on the dynamic characteristics of the laminates are studied.
INTERNATIONAL JOURNAL OF STRUCTURAL STABILITY AND DYNAMICS
(2023)
Article
Mathematics, Applied
Danny Smyl, Liang Chen, Li Lai, Dong Liu
Summary: This method applies non-cooperative game theory to finite element problems, treating each element as a player to reach Nash equilibrium in the overall game. Numerical demonstrations show matching with analytical solutions in linear elasticity and convergence to a prescribed precision in two-player nonlinear problems.
APPLIED NUMERICAL MATHEMATICS
(2021)
Article
Computer Science, Interdisciplinary Applications
E. Schaller, A. Javili, I Schmidt, A. Papastavrou, P. Steinmann
Summary: In this study, a nonlocal bone remodelling framework was proposed and implemented using a peridynamic formulation on the macroscale. The implementation was validated using a benchmark test and two load cases of the proximal femur.
COMPUTER METHODS IN BIOMECHANICS AND BIOMEDICAL ENGINEERING
(2022)
Article
Mechanics
E. Ekiz, P. Steinmann, A. Javili
Summary: Continuum-kinematics-inspired Peridynamics (CPD) is a geometrically exact, thermodynamically and variationally consistent formulation of peridynamics. Unlike the original peridynamics formulation (PD), CPD can capture the Poisson effect exactly and does not suffer from zero-energy modes and displacement oscillations. The two-neighbor interactions in CPD preserve the basic notions of classical continuum kinematics, length and area, and play a key role. This manuscript establishes the relationships between CPD material parameters and isotropic linear elasticity and determines the admissible ranges for CPD material parameters.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2022)
Article
Materials Science, Multidisciplinary
Jiong Wang, Chengkai Fan, Paul Steinmann
Summary: The governing equation system for modeling the high-frequency dynamic magneto-mechanical response of MSMAs is formulated based on Hamilton's principle. The system includes Maxwell's equations, mechanical dynamic equations, evolution laws for internal variables, and criteria for predicting twin interface motion. This lays the foundation for future numerical simulations and mechanism analyses.
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
(2022)
Article
Materials Science, Multidisciplinary
A. Derya Bakiler, Ali Javili
Summary: This paper proposes a generic theoretical framework to study the instability behavior of compressible bilayer systems and explores the effects of different parameters. The accuracy of the framework is validated by comparing it with numerical simulation results. It is found that the critical stretch of the system is significantly dependent on the film thickness in the presence of an interface.
MATHEMATICS AND MECHANICS OF SOLIDS
(2023)
Article
Mathematics, Interdisciplinary Applications
Ludwig Herrnboeck, Ajeet Kumar, Paul Steinmann
Summary: This work compares two different computational approaches for geometrically exact elastoplastic rods. The first approach uses a constitutive model based on stress resultants, while the second approach applies an FE2 approach that couples the macro-scale and micro-scale of the rod. A novel aspect of this work is the determination of a hardening tensor for use in the stress resultant approach. The mechanical response of both approaches is compared on material point level and for finitely and non-uniformly strained rods.
COMPUTATIONAL MECHANICS
(2023)
Article
Computer Science, Interdisciplinary Applications
David N. De Klerk, Thomas Shire, Zhiwei Gao, Andrew T. McBride, Christopher J. Pearce, Paul Steinmann
Summary: A novel implicit integration scheme for the Discrete Element Method (DEM) is proposed, which provides an accurate description of particle systems in both quasi-static and dynamic situations. Compared to the velocity-Verlet method, the proposed scheme achieves equivalent accuracy.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Chemistry, Physical
Miguel Angel Moreno-Mateos, Mokarram Hossain, Paul Steinmann, Daniel Garcia-Gonzalez
Summary: This study explores the design and performance of ultra-soft hybrid magnetorheological elastomers (MREs) through experimental and computational methods. Experimental results show that the magnetomechanical performance of hybrid MREs can be optimized by selecting an appropriate mixing ratio between particles. Computational results reveal the magneto-mechanical interactions between soft and hard particles, which are crucial for the effective response of hybrid MREs. The study uncovers new possibilities to push the frontiers of MRE solutions.
NPJ COMPUTATIONAL MATERIALS
(2022)
Article
Materials Science, Multidisciplinary
Lin Zhan, Siyu Wang, Shaoxing Qu, Paul Steinmann, Rui Xiao
Summary: Many classic hyperelastic models cannot accurately predict the stress responses of soft materials in complex loading conditions. We propose a new micro-macro transition approach integrated into a full network framework, which successfully captures the stress responses in multi-axial deformation modes for soft materials. We further develop a two-parameter hyperelastic model that exhibits greatly improved predictive ability for complex loading types compared to other existing models.
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
(2023)
Article
Materials Science, Multidisciplinary
Miguel Angel Moreno-Mateos, Mokarram Hossain, Paul Steinmann, Daniel Garcia-Gonzalez
Summary: Pre-existing flaws in highly stretchable elastomers can cause fractures under large deformations. This study shows that ultra-soft magnetorheological elastomers with remanent magnetization have 50% higher fracture toughness compared to non-pre-magnetized samples. The opening of cracks in pre-magnetized elastomers is delayed due to crack closure induced by the magnetic field. Numerical simulations also reveal that pre-magnetized elastomers have reduced stress concentration at the crack tip. This work reveals potential applications for functional actuators with improved fracture behavior and performance under cyclic loading.
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
(2023)
Article
Computer Science, Interdisciplinary Applications
Anna Titlbach, Areti Papastavrou, Andrew McBride, Paul Steinmann
Summary: In this study, a novel phenomenological approach based on a micromorphic formulation is proposed to consider the trabecular microstructure and non-local characteristics of bone in continuum bone remodelling. The influence of characteristic size and coupling between macro- and microscale deformation is analyzed through benchmark examples. The results demonstrate that the micromorphic formulation effectively captures the interaction between continuum points at the macroscale and their neighborhood, affecting the distribution of bone density at the macroscale.
COMPUTER METHODS IN BIOMECHANICS AND BIOMEDICAL ENGINEERING
(2023)
Article
Materials Science, Multidisciplinary
Lucie Spannraft, Paul Steinmann, Julia Mergheim
Summary: This article proposes a generalized mechanical interface model for nonlinear kinematics. The interface's response allows for jump in deformations, cohesive failure, and interfacial (in)elasticity. An anisotropic cohesive law is formulated to induce additional shear-like stresses within the interface. Damage variables are used to couple cohesive and membrane degradations, considering the interaction between different deformation modes. The model is thermodynamically consistent and fulfills the balance equations and material frame indifference. Numerical examples demonstrate the influence of damage coupling on the mechanical response of adhesive layers.
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
(2023)
Article
Materials Science, Multidisciplinary
Lin Zhan, Siyu Wang, Shaoxing Qu, Paul Steinmann, Rui Xiao
Summary: In this work, a general approach based on continuum damage mechanics is proposed to model the Mullins effect in soft composites. One-dimensional and three-dimensional damage models are formulated, which successfully describe the stress response in loading-unloading cycles and the anisotropic response of predeformed materials.
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
(2023)
Article
Engineering, Manufacturing
Julia Mergheim, Christoph Breuning, Christian Burkhardt, Daniel Hubner, Johannes Kopf, Ludwig Herrnbock, Zerong Yang, Carolin Korner, Matthias Markl, Paul Steinmann, Michael Stingl
Summary: This paper introduces a multiscale and multi-purpose simulation framework for investigating selective beam melting processes in metallic cellular structures. Process simulation methods are used to analyze the relationship between process strategies and resulting properties of the cellular materials. Numerical homogenization methods are applied to study the influence of grain structure and topology on the mechanical properties of the cellular materials. A two-scale optimization of components made of cellular material is performed to improve the buckling resistance of the structures. The results show that consistent simulations of additive manufacturing of cellular materials provide important insights into process-structure interactions and enable tailored additive manufacturing processes.
JOURNAL OF MANUFACTURING PROCESSES
(2023)
Article
Engineering, Multidisciplinary
Simon Wiesheier, Julia Mergheim, Paul Steinmann
Summary: This article introduces a new data-adaptive approach for modeling hyperelastic rubber-like materials at finite strains. This approach combines the advantages of phenomenological modeling with data-driven methods by directly including experimental data in calculations. Numerical examples demonstrate the ability of the approach to re-identify a certain number of parameters.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
