Article
Mathematics, Applied
Kerrek Stinson
Summary: The research introduces the Cahn-Hilliard reaction model to explain phase separation in lithium-ion batteries. This model incorporates the Butler-Volmer kinetics for electrochemical consistency and allows lithium-ions to enter the domain through a nonlinear Robin-type boundary condition. The exponential dependence of the boundary condition on the chemical potential mu is of great importance. Fixed point methods are applied to ensure the existence of regular solutions in three dimensions and recover the exponential boundary conditions in the physical application.
JOURNAL OF NONLINEAR SCIENCE
(2023)
Article
Mathematics, Applied
Tim Laux, Kerrek Stinson
Summary: We propose a weak solution theory for the sharp interface limit of the Cahn-Hilliard reaction model for lithium-ion batteries. By introducing solution concepts and dissipation inequality, we show that the solutions of the Cahn-Hilliard reaction model converge to a Mullins-Sekerka type geometric evolution equation as the width of the transition layer vanishes.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2023)
Article
Mathematics
Charles Elbar, Jakub Skrzeczkowski
Summary: There has been a recent interest in rigorously deriving the Cahn-Hilliard equation from the nonlocal equation, particularly with regards to degenerate mobilities. In this study, a new method is presented to show the convergence of the nonlocal to the local degenerate Cahn-Hilliard equation, using nonlocal Poincare and compactness inequalities. This research is motivated by models for the biomechanics of living tissues.(c)2023 Elsevier Inc. All rights reserved.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Engineering, Mechanical
Junxiang Yang, Yibao Li, Chaeyoung Lee, Hyun Geun Lee, Soobin Kwak, Youngjin Hwang, Xuan Xin, Junseok Kim
Summary: In this paper, an explicit conservative Saul'yev finite difference scheme for the Cahn-Hilliard equation is presented. The proposed scheme has four main merits and outperforms in computational experiments.
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2022)
Article
Mathematics, Interdisciplinary Applications
Eylem Ozturk, Joseph L. Shomberg
Summary: In this study, a viscous Cahn-Hilliard phase-separation model with memory and a nonlocal fractional Laplacian operator in the chemical potential is examined. The existence of global weak solutions is proven using a Galerkin approximation scheme. Continuous dependence estimate provides uniqueness of weak solutions and existence of a compact connected global attractor in the weak energy phase space.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Applied
Keiichiro Kagawa, Mitsuharu Otani
Summary: This paper investigates the asymptotic behavior of solutions for the viscous Cahn-Hilliard equations as parameters tend to zero. It is shown that solutions of the viscous Cahn-Hilliard equations converge to solutions of the Allen-Cahn equation, the Cahn-Hilliard equation, and the viscous diffusion equation as suitable parameters tend to zero. Compared to existing results, a wider range of chemical potentials can be analyzed within our framework.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Correction
Mathematics
Sebastian Scholtes, Maria G. Westdickenberg
Summary: This article corrects a dissipation estimate from the original article, but the main result remains unchanged.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics, Applied
Pierluigi Colli, Gianni Gilardi, Andrea Signori, Juergen Sprekels
Summary: This note studies the optimal control of a nonisothermal phase field system with a conserved order parameter. The heat flux constitutive law assumes a possible thermal memory. The system also has a source term in the order parameter equation and the mass conservation of the order parameter is no longer satisfied. The paper analyzes the differentiable cases of the double-well potential and establishes the necessary optimality conditions for the optimal control problem.
APPLIED MATHEMATICS AND OPTIMIZATION
(2023)
Article
Mathematics, Applied
Marco Salvalaglio, Axel Voigt, Steven M. Wise
Summary: In this study, we discuss two doubly degenerate Cahn-Hilliard models for isotropic surface diffusion, focusing on degeneracy in the mobility function and a restriction function associated with the chemical potential. Our computational results indicate that the restriction functions provide more accurate approximations of surface diffusion. We also explore a slight generalization of a non-variational model and introduce a new variational and energy dissipative model, both of which can be related to the generalized non-variational model and show convergence to the sharp-interface limit of surface diffusion through formal matched asymptotics.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Applied
Seokjun Ham, Yibao Li, Darae Jeong, Chaeyoung Lee, Soobin Kwak, Youngjin Hwang, Junseok Kim
Summary: In this study, an explicit adaptive finite difference method is proposed for solving the Cahn-Hilliard equation. The method utilizes a narrow-band domain to improve the accuracy of the numerical calculations. Comparisons with previous methods demonstrate the superior performance of the proposed method.
JOURNAL OF NONLINEAR SCIENCE
(2022)
Article
Mechanics
S. Sampaoli, A. Agosti, G. Pozzi, P. Ciarletta
Summary: This study proposes a toy partial differential model that considers both the short-term dynamics of misfolded proteins and the long-term evolution of tissue damage in neurodegenerative diseases. By using mixture theory, the brain is considered as a biphasic material consisting of misfolded protein aggregates and healthy tissue. Numerical simulations show that the spreading front of neural damage follows the direction of the largest eigenvalue of the mobility tensor.
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS
(2022)
Article
Mathematics, Applied
Junseok Kim, Zhijun Tan, Junxiang Yang
Summary: This article proposes linear temporally first- and second-order accurate methods for simulating phase change in binary fluid mixtures, and proves mass conservation and unconditional energy stability of the proposed schemes. The methods are efficient and easy to implement, and capable of simulating spinodal decomposition in irregular domains.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Engineering, Multidisciplinary
Revanth Mattey, Susanta Ghosh
Summary: A physics informed neural network (PINN) is a method that incorporates the physics of a system into a neural network's loss function by satisfying the system's boundary value problem. To address the accuracy issue for highly non-linear and higher-order time-varying partial differential equations, a novel backward compatible PINN (bc-PINN) scheme is proposed, which solves the PDE sequentially over successive time segments using a single neural network and re-trains the network to satisfy the already obtained solutions for previous time segments. Two techniques, using initial conditions and transfer learning, are introduced to improve the accuracy and efficiency of the bc-PINN scheme.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Mathematics, Applied
Andrej Novak, Nora Reinic
Summary: This paper focuses on the problem of digital image inpainting using the modified Cahn-Hilliard equation and a shock filter. The existence and uniqueness of the solution are proven using fixed point arguments and Aubin-Lions lemma. Additionally, a numerical method based on convexity splitting is introduced to approximate the solutions. The method is applied to various binary images, demonstrating its ability to extend image features and preserve edges.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)
Article
Engineering, Mechanical
Xiaofang Zhou, Changxin Qiu, Wenjing Yan, Biao Li
Summary: This paper presents a cell-average-based neural network (CANN) method for approximating the solutions of nonlinear Cahn-Hilliard equation and Camassa-Holm equation. The CANN method utilizes neural networks to approximate the evolution of solutions, allowing for larger time steps and the ability to handle corrupted data.
NONLINEAR DYNAMICS
(2023)
Article
Mechanics
V. Govorukha, M. Kamlah
ARCHIVE OF APPLIED MECHANICS
(2020)
Article
Mechanics
Verena Becker, Marc Kamlah
Summary: This paper presents a theoretical model for normal contact force of elastoplastic ellipsoidal bodies for use in mechanical discrete element method. The model is an extension of the Thornton model, incorporating elliptical contact areas and focusing on normal contact force description as a continuous function of time.
JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME
(2021)
Article
Nuclear Science & Technology
M. Moscardini, S. Pupeschi, M. Kamlah
Summary: The research focuses on defining the macroscopic plastic strain of the bed by simulating the plastic deformation of individual pebbles, investigating different theories, and validating numerical results in the development of tritium breeder and neutron multiplier in the solid blanket concept.
FUSION ENGINEERING AND DESIGN
(2021)
Article
Chemistry, Physical
Tao Zhang, Marc Kamlah
Summary: A chemo-mechanical phase-field model is developed to capture the complex phase segregation processes in NaxFePO4 (0 < x < 1), along with the structural changes during charging/discharging. The model constructs a multi-well potential for NaxFePO4 for the first time and investigates the microstructure evolution during sodiation and desodiation processes. Results suggest that the formation of an intermediate phase can reduce stress and improve mechanical stability, leading to better battery performance.
JOURNAL OF POWER SOURCES
(2021)
Article
Engineering, Chemical
Oleg Birkholz, Matthias Neumann, Volker Schmidt, Marc Kamlah
Summary: The study investigates the relationships between microstructure characteristics and effective transport properties of granular materials through modeling and simulation of sphere packings. It establishes formulas expressing effective transport properties of the considered sphere packings in terms of the mean contact angle and the standard deviation of the particle radii.
Article
Energy & Fuels
Adrian Schmidt, Elvedin Ramani, Thomas Carraro, Jochen Joos, Andre Weber, Marc Kamlah, Ellen Ivers-Tiffee
Summary: Porous electrode models are crucial for predicting the performance and lifetime of lithium-ion batteries inexpensively, but some simplifications in existing models may lead to limitations in accuracy, especially under high charge and discharge rates. By studying the effects of various microstructural characteristics on the validity of the models, insights are gained to improve the homogenized model and overcome existing limitations of the pseudo-2D approach.
Article
Energy & Fuels
Oleg Birkholz, Marc Kamlah
Summary: The hierarchically structured half-cell model for lithium-ion battery electrodes with porous secondary particles has been developed and validated through experiments. The study shows that the rate-limiting factor in this model differs from classical half-cell models, being the combination of electronic conductivity and inner morphology of the secondary particles.
Article
Energy & Fuels
Verena Becker, Oleg Birkholz, Yixiang Gan, Marc Kamlah
Summary: This article investigates the influence of particle shapes on the micromechanical responses during calendering in lithium-ion battery manufacturing, and their impact on the effective transport properties of battery electrodes. The study presents a novel algorithm for generating stress-free particle assemblies and calculates effective conductivities using a resistor network approach. The research provides insights into the interplay between calendering process, electrode microstructure, and effective conductivities of solid and pore phases.
Article
Materials Science, Multidisciplinary
Friedemann A. Streich, Alexander Martin, Kyle G. Webber, Marc Kamlah
Summary: A fully electromechanically coupled, three-dimensional phenomenological constitutive model was developed for relaxor ferroelectric materials, which can simulate the macroscopic electromechanical response of lead-free and non-lead-free relaxor materials. The model accounts for unique material properties, and its accuracy is validated through comparison with experimental data.
JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES
(2022)
Article
Materials Science, Multidisciplinary
Jay Santoki, Simon Daubner, Daniel Schneider, Marc Kamlah, Britta Nestler
Summary: Transport mechanisms in battery systems are influenced by microstructural properties such as particle size, porosity, and tortuosity. A simulation study using a multiple particle model system and ellipsoid-like particles as an example was conducted. Results suggest that electrode structures impact transportation rates, with smaller particles limited by surface reactions and larger particles tending towards bulk-transport limited theory.
MODELLING AND SIMULATION IN MATERIALS SCIENCE AND ENGINEERING
(2021)
Editorial Material
Energy & Fuels
Thomas Wetzel, Wolfgang G. Bessler, Marc Kamlah, Hermann Nirschl
Article
Engineering, Chemical
Si Suo, Marigrazia Moscardini, Verena Becker, Yixiang Gan, Marc Kamlah
Summary: This study improved and adapted a thermo-mechanical discrete element method to investigate the evolution of thermal conductivity and stress on the grain scale of gas-filled granular materials. The simulation results showed that the thermal conductivity dropped significantly due to plastic deformation, but this effect could be suppressed by increasing the packing factor.
Article
Instruments & Instrumentation
Alexander Martin, Juliana G. Maier, Friedemann Streich, Marc Kamlah, Kyle G. Webber
Summary: The study examined the impact of ceramic-ceramic composite structures on the electromechanical response of lead-free ferroelectrics by manipulating local electrical and mechanical fields, and separating the relative contributions of PSC mechanisms.
SMART MATERIALS AND STRUCTURES
(2022)
Article
Energy & Fuels
Nils Klasen, Friedemann Heinz, Angela De Rose, Torsten Roessler, Achim Kraft, Marc Kamlah
Summary: This work reports on the cracking mechanism observed on shingle solar cells in PV modules subjected to thermal cycling. Experimental investigations and structural mechanic simulations show that the cracks are limited to the joint area and occur on the rear side of the solar cells. The cracks are caused by the thermal contraction of the encapsulant.
SOLAR ENERGY MATERIALS AND SOLAR CELLS
(2022)
Article
Engineering, Multidisciplinary
Raghuram Karthik Desu, Yixiang Gan, Marc Kamlah, Ratna Kumar Annabattula
Summary: The macroscopic behavior and damage of an assembly of polydisperse spherical particles were studied using a numerical model based on DEM. The analysis revealed that the initial packing fraction, damage rate, and particle size variation all influence the macroscopic stress-strain response. Experimental data showed varying crush strengths for particles of the same size.
INTERNATIONAL JOURNAL OF ADVANCES IN ENGINEERING SCIENCES AND APPLIED MATHEMATICS
(2021)
Article
Mechanics
Alireza Enferadi, Majid Baniassadi, Mostafa Baghani
Summary: This study presents the design and analysis of an SMP microvalve, where the thermomechanical response of the SMP is investigated using a nonlinear constitutive model that incorporates hyperelasticity and viscoelasticity. The model accounts for fluid-solid interaction and heat transfer in both fluid and solid physics. Numerical simulations are carried out to examine the important characteristics of the SMP valve. The results demonstrate the significance of employing fluid-solid interaction conjugated heat transfer analysis for the efficient development of microvalves in diverse applications.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2024)
Article
Mechanics
Hridya P. Lal, B. R. Abhiram, Debraj Ghosh
Summary: Higher-order elasticity theories are used to model mechanics at the nanoscale, but the length-scale parameters in these theories need to be evaluated through experiments or MD simulations. This study shows that the length-scale parameter in the modified strain gradient theory varies with dimensions, boundary conditions, and deformation level for carbon and boron nitride nanotubes. To address this issue, a supervised ML-based framework is developed, combining MD simulations, continuum formulation, and ML to predict the length-scale parameter for a given material, dimension, and boundary condition. This predictive tool reduces the need for expensive MD simulations and opens up possibilities for applying non-classical continuum theories to nanoscale mechanics problems.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2024)
Article
Mechanics
Geng Chen, Shengzhen Xin, Lele Zhang, Min Chen, Christian Gebhardt
Summary: This paper develops a multiscale numerical approach to predict the failure probability of additive manufacturing (AM) structures subjected to time-varied loadings. The approach combines statistical homogenization, shakedown analyses, and reliability methods to consider the influence of microstructural features on load bearing capacity. Through case studies on exemplary structures and different material randomness assumptions, the robustness of the results is confirmed and the mechanism of how micropores influence structural reliability is explained.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2024)
Article
Mechanics
Guillaume Cadet, Manuel Paredes
Summary: This study proposes a comprehensive solution for calculating the stress field on the surface of a curved beam with a circular cross section, which is crucial for probabilistic fatigue life analysis.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2024)
Article
Mechanics
Hongshi Ruan, Xiaozhe Ju, Junjun Chen, Lihua Liang, Yangjian Xu
Summary: This paper proposes a data-driven approach to improve the efficiency of computational homogenization for nonlinear hyperelastic materials. By combining clustering analysis, Proper Orthogonal Decomposition (POD), and efficient sampling, a reduced order model is established to accurately predict elastoplasticity under monotonic loadings. The numerical results show a significant acceleration factor compared to a purely POD-based model, which greatly improves the applicability for structural analysis.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2024)
Article
Mechanics
Pep Espanol, Mark Thachuk, J. A. de la Torre
Summary: The motion of a rigid body, described by Euler's equations in Classical Mechanics, assumes that the distances between constituent particles are fixed. However, real bodies cannot meet this assumption due to thermal fluctuations. In order to incorporate dissipative and thermal fluctuation effects into the description, a generalization of Euler's equations is proposed. This theory explains the origin of these effects as internal, rather than caused by an external thermal bath, and derives the stochastic differential equations governing the body's orientation and central moments.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2024)
Article
Mechanics
Prateek Chandrakar, Narayan Sharma, Dipak Kumar Maiti
Summary: The current study focuses on the deterioration in thermal buckling performance of variable angle tow laminated (VATL) plates caused by damages in various composite and damage characteristics. Through numerical simulations and surrogate models, it was found that damages reduce the sensitivity of composite properties to buckling response, and a distinctive pattern of buckling response was observed when composite properties vary.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2024)
Article
Mechanics
Liangteng Guo, Shaoyu Zhao, Jie Yang, Sritawat Kitipornchai
Summary: This study introduces composites reinforced with graphene origami nanofillers into functionally graded multilayered phononic crystals. Numerical investigations reveal that these materials possess negative Poisson's ratio and offer unique mechanical properties, which can be tuned by adjusting the weight fraction and hydrogen coverage of the graphene fillers.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2024)
Article
Mechanics
Kai Li, Haiyang Wu, Yufeng Liu, Yuntong Dai, Yong Yu
Summary: This paper presents a novel self-oscillating liquid crystal elastomer fiber-beam system that can sway continuously and periodically under steady illumination. The governing equations of the system are established and the self-swaying process and motion mechanism are described in detail. Numerical results show the system undergoes supercritical Hopf bifurcation and the effects of system parameters on the self-swaying amplitude and frequency are discussed quantitatively.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2024)
Article
Mechanics
Lingkang Zhao, Peijun Wei, Yueqiu Li
Summary: This paper proposes a spatial-temporal fractional order model to study the dynamic behavior of thermoelastic nanoplates in a thermal environment. The model provides a flexible approach to describe the small-scale effects and complex history-dependent effects. Analytical and numerical methods verify the reliability of the model, and the effects of parameters on the dynamic response are discussed.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2024)
Article
Mechanics
A. N. O'Connor, P. G. Mongan, N. P. O'Dowd
Summary: This research presents an autonomous framework that combines Bayesian optimization and finite element analysis to identify ductile damage model parameters. The framework has been successfully applied to P91 material datasets and demonstrates the impact of algorithm hyperparameters on the resulting non-unique ductile damage parameters.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2024)
Article
Mechanics
S. V. Sorokin, S. Lenci
Summary: This paper reconsiders the nonlinear coupling between flexural and longitudinal vibrations of ideally straight elastic beams, using a nonlinear theory of curved beams and employing class-consistent boundary conditions. A paradoxical difference in the nonlinear parts of the Duffing equations obtained in the limit of vanishing curvature and in the case of an ideally straight beam is demonstrated and explained.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2024)
Article
Mechanics
C. Hari Manoj Simha
Summary: Dynamic Mode Decomposition (DMD) can be used to construct deformation fields for linear solids without making constitutive assumptions or knowing material properties. It operates on time-shifted data matrices and selects dominant modes using singular value decomposition. DMD can be used for reconstructing displacement states in elastic solids and identifying the onset of plasticity in elastic-plastic solids.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2024)
Article
Mechanics
C. Ren, K. F. Wang, B. L. Wang
Summary: An electromechanical model is established to investigate the characteristics of a bilayer structure consisting of a piezoelectric semiconductor film and an elastic substrate. The combined effects of piezoelectricity and flexoelectricity are considered, and closed-form expressions for the distributions of electron concentrations and relevant electromechanical fields are obtained. The effects of interfacial parameter, flexoelectricity, and initial carrier concentration are discussed. The research highlights the importance of the interfacial parameter and the weakening effect of flexoelectricity on the imperfect interface of the bilayer system.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2024)
Article
Mechanics
Yu Sun, Qiang Han, Chunlei Li
Summary: This paper presents the design of a tunable functionally graded metamaterial beam for flexural wave attenuation through the integration of a piezomagnetic shunt damping system and an inertial amplification mechanism. The proposed system demonstrates tunable and strong wave attenuation capability through local resonance and energy consumption. The theoretical and numerical results verify that the system can achieve significant wave attenuation at defined frequencies and also be optimized for maximal attenuation at various frequency ranges.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2024)
