Article
Mechanics
Vinh Tu, Fredrik Larsson, Kenneth Runesson, Ralf Jaenicke
Summary: In this study, a multi-scale modeling framework is developed to address the electro-chemically coupled ion transport in a Structural Battery Electrolyte (SBE). The governing equations are established by coupling Gauss law with mass conservation for each species. Through variationally consistent homogenization, a two-scale model is formulated where both macro-scale and sub-scale equations are derived from a single-scale problem. The transient effects in the investigated sub-scale RVE problem are found to be negligible, leading to the assumption of micro-stationarity. In the case of linear constitutive response, a numerically efficient solution scheme for the macro-scale problem is obtained based on a priori upscaling. Finally, the efficiency of the solution scheme is demonstrated by solving a 2D macro-scale problem using upscaled constitutive quantities from a 3D RVE.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2023)
Article
Mathematics, Applied
Monia Capanna, Jean C. Nakasato, Marcone C. Pereira, Julio D. Rossi
Summary: This paper considers the homogenization problem for a nonlocal equation involving different smooth kernels, and shows the existence of a homogenized limit system with three kernels and a limit function under specific conditions. Both Neumann and Dirichlet boundary conditions are addressed, and a probabilistic interpretation of the results is also provided.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
(2021)
Article
Mathematics, Applied
Monia Capanna, Jean C. Nakasato, Marcone C. Pereira, Julio D. Rossi
Summary: This paper discusses the homogenization of an evolution problem involving a jump process with three different smooth kernels. By dividing the spatial domain into two subdomains and assuming weak convergence of certain functions, the existence of a homogenized limit system is proven. The probabilistic interpretation of the evolution equation is also presented, along with the convergence of the underlying process to a limit process. The analysis focuses on Neumann type boundary conditions, with a brief mention of how to handle Dirichlet boundary conditions.
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics, Applied
Santiago Cano-Casanova
Summary: This article investigates the existence of positive weak solutions for a non-uniform elliptic boundary value problem of logistic type in a general annulus. The novelty of this research lies in considering non-classical mixed glued boundary conditions, specifically Dirichlet conditions on one part of the boundary and glued Dirichlet-Neumann conditions on the other part. The paper provides a comprehensive analysis of the existence of positive weak solutions, presenting necessary and sufficient conditions depending on the lambda parameter, spatial dimension N >= 2, and exponent q > 1 of the reaction term. The main mathematical techniques employed in this study are variational and monotonicity techniques. The results obtained in this paper are pioneering in this field as, to the author's knowledge, this is the first analysis of such logistic problems.
Article
Mathematics
Delfina Gomez, Sergei A. Nazarov, Rafael Orive-Illera, Maria-Eugenia Perez-Martinez
Summary: In this paper, we establish uniform bounds for the convergence rates of low frequencies in a parametric family of Laplace operator problems on a rectangular perforated domain. The perforations are periodically placed at a distance O(ε) along the ordinate axis, where ε is a parameter that tends to zero. The Floquet-parameter, η, varies within the interval [-π, π]. The boundary conditions consist of quasi-periodicity conditions on the lateral sides of the rectangle and Neumann conditions elsewhere. Precise bounds for the convergence rates, which are uniform on both ε and η parameters, are obtained and heavily depend on the height H. The analysis is particularly challenging near the nodes of the limit dispersion curves.
MATHEMATISCHE NACHRICHTEN
(2023)
Article
Mathematics
Pierpaolo Omari
Summary: We establish the existence of infinitely many regular weak solutions for the prescribed mean curvature problem in a bounded domain Omega in R-N. The functions f(x,s) and F(x,s) are odd with respect to s and have certain properties. Our findings improve and expand upon previous results in the literature.
JOURNAL OF GEOMETRIC ANALYSIS
(2023)
Article
Mechanics
Remi Cornaggia, Marie Touboul, Cedric Bellis
Summary: This paper establishes a formulation of band problems into fully periodic cell problems on bounded domains by introducing a Dirichlet-to-Neumann operator and a boundary corrector in a Fourier framework, and proposes a fixed-point algorithm and an example choice of corrector. Comparisons with other computational methods support this proposition.
COMPTES RENDUS MECANIQUE
(2022)
Article
Mathematics, Applied
Jana Bjorn, Abubakar Mwasa
Summary: In this paper, we study a mixed boundary value problem for the p-Laplace equation in an open infinite circular half-cylinder, proving the existence of weak solutions and obtaining a boundary regularity result for the point at infinity.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2021)
Article
Mathematics, Applied
Yahya Alnashri, Hasan Alzubaidi
Summary: The paper explores the application of the gradient discretisation method (GDM) in anisotropic reaction-diffusion problems, proving both the existence of weak solutions and the uniform-in-time convergence of the discrete solution and strong convergence of its gradient. It also examines the use of non-conforming numerical schemes on a generic grid.
COMPUTATIONAL METHODS IN APPLIED MATHEMATICS
(2021)
Article
Mathematics, Interdisciplinary Applications
Fredrik Ekre, Fredrik Larsson, Kenneth Runesson, Ralf Janicke
Summary: This paper further develops the previous work by proposing a combined basis constructed using both SD and POD modes with an adaptive mode selection strategy. The performance of the combined basis is compared to pure SD and pure POD bases through numerical examples, showing that the combined basis can yield a smaller error estimate.
COMPUTATIONAL MECHANICS
(2022)
Article
Engineering, Multidisciplinary
Fredrik Ekre, Fredrik Larsson, Kenneth Runesson, Ralf Jaenicke
Summary: This paper adopts Numerical Model Reduction (NMR) to solve the nonlinear microscale problem in computational homogenization of porous media. It derives an explicit and computable a posteriori error estimator based on the linearized error equation and demonstrates its performance through numerical examples.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Mechanics
Mohammad Salahi Nezhad, Dimosthenis Floros, Fredrik Larsson, Elena Kabo, Anders Ekberg
Summary: The study examines the influence of different operational loading scenarios on the predicted crack growth direction for a propagating inclined railhead crack through 2D finite element simulations. It is found that a combination of thermal and contact loads results in a gradual divergence of the crack path from transverse growth to shallow growth, while a combination of bending and contact loads causes a discrete jump in the crack direction.
ENGINEERING FRACTURE MECHANICS
(2022)
Article
Mechanics
David Carlstedt, Kenneth Runesson, Fredrik Larsson, Vinh Tu, Ralf Jaenicke, Leif E. Asp
Summary: This paper presents a computational modelling framework for studying the electro-chemo-mechanical properties of structural batteries. The convective contribution to mass transport within the battery electrolyte is found to have a minor influence under certain conditions, but has a noticeable influence under externally applied mechanical loading or large current pulses. The porosity of the electrolyte is also shown to significantly influence the combined mechanical and electro-chemical performance.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2022)
Article
Mechanics
David Carlstedt, Kenneth Runesson, Fredrik Larsson, Leif E. Asp
Summary: This paper presents a fully coupled thermo-electro-chemo-mechanical computational modelling framework for carbon fibre-based structural batteries, which can capture the coupled thermo-electro-chemo-mechanical behavior. It is found that the heat generation during battery cycling is mainly due to discontinuities in the electrical and chemical potentials at the fibre/electrolyte interface. Additionally, the temperature change during electrochemical cycling is significantly influenced by the applied current, thermal properties of the constituents, and heat exchange with the surroundings. Moreover, in conditions with large temperature variations, the thermal strains in the structural battery electrolyte are similar to the insertion-induced strains.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2022)
Article
Construction & Building Technology
Adam Sciegaj, Fredrik Larsson, Karin Lundgren
Summary: This study developed an effective and robust method to consider the interfilament slip in textile reinforcement yarns and the slip between the yarns and concrete. Pull-out tests were carried out to determine the efficiency factors for strength and stiffness, which were found to be very similar.
CEMENT & CONCRETE COMPOSITES
(2022)
Article
Materials Science, Multidisciplinary
Soheil Firooz, Stefan Kaessmair, Vasily Zaburdaev, Ali Javili, Paul Steinmann
Summary: Cellular aggregates play a significant role in the evolution of biological systems. This study proposes a non-linear continuum mechanics formulation and finite element simulation framework to model the physics of cellular aggregate formation, focusing on bacterial colony formation as an example. The study describes the aggregation process as an active phase separation phenomenon and investigates the influence of various parameters on the dynamics of cellular aggregate formation through numerical examples.
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
(2022)
Article
Mechanics
Vinh Tu, Fredrik Larsson, Kenneth Runesson, Ralf Jaenicke
Summary: In this study, a multi-scale modeling framework is developed to address the electro-chemically coupled ion transport in a Structural Battery Electrolyte (SBE). The governing equations are established by coupling Gauss law with mass conservation for each species. Through variationally consistent homogenization, a two-scale model is formulated where both macro-scale and sub-scale equations are derived from a single-scale problem. The transient effects in the investigated sub-scale RVE problem are found to be negligible, leading to the assumption of micro-stationarity. In the case of linear constitutive response, a numerically efficient solution scheme for the macro-scale problem is obtained based on a priori upscaling. Finally, the efficiency of the solution scheme is demonstrated by solving a 2D macro-scale problem using upscaled constitutive quantities from a 3D RVE.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2023)
Article
Mechanics
D. R. Rollin, F. Larsson, K. Runesson, R. Jaenicke
Summary: A variationally consistent model-based computational homogenization approach is developed for transient chemomechanically coupled problems using the classical assumption of first order prolongation of displacement and chemical potential fields. An upscaling procedure based on micro-stationarity assumption is introduced, allowing for unique solvability of the RVE-problems with periodic boundary conditions. The effective macro-scale properties such as elastic stiffness, insertion strain tensor, and mobility tensor are derived through sensitivity analysis of the RVE.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2023)
Article
Engineering, Multidisciplinary
Caroline Ansin, Fredrik Larsson, Ragnar Larsson
Summary: To increase computational efficiency, Proper Generalized Decomposition (PGD) is adopted to solve a reduced-order problem of the displacement field for a three-dimensional rail head. By modeling the rail head as a two-dimensional cross-section and incorporating the coordinate along the rail and the distributed contact load as parameters in the PGD formulation, the full three-dimensional model can be solved with reduced computational cost. The accuracy and efficiency of the proposed strategy are assessed through verification examples, showing that the PGD solution converges towards the finite element (FE) solution with reduced computational cost.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)