Article
Computer Science, Interdisciplinary Applications
Brendan J. Meade, T. Ben Thompson
Summary: The linear elastic boundary element model is a common tool for understanding the mechanics of earthquake cycle processes and their impact on tectonic structure growth. This study introduces a two-dimensional plane strain linear elastic boundary element approach based on the displacement discontinuity method, incorporating three node quadratic elements and the classic particular integral approach. The accuracy of three node quadratic elements provides a more exact representation of displacements, stresses, and tractions on elements with slip gradients, demonstrating the recovery of analytic solutions and the combined effects of faulting and gravitational body forces in the presence of topographic relief.
COMPUTERS & GEOSCIENCES
(2022)
Article
Thermodynamics
Sorin Vlase, Marin Marin, Andreas Oechsner, Omar El Moutea
Summary: This paper presents the main methods offered by classical mechanics for the analysis of elastic multibody systems using a unified description, and reviews relevant literature. It also introduces the main methods used in the research of MBS systems.
CONTINUUM MECHANICS AND THERMODYNAMICS
(2023)
Article
Mathematics, Applied
Shangyou Zhang
Summary: The paper proposes a stable and effective finite element method that satisfies both the discrete Korn inequality and the requirements of the Stokes problem. The linear conforming finite element is enriched by introducing some nonconforming bubbles.
JOURNAL OF NUMERICAL MATHEMATICS
(2023)
Article
Engineering, Biomedical
Luca Heltai, Alfonso Caiazzo, Lucas O. Muller
Summary: This study introduces a computational multiscale model for simulating vascularized tissues efficiently, comprising an elastic matrix and a vascular network. The model is capable of reproducing tissue responses at the effective scale while modeling microscale vasculature.
ANNALS OF BIOMEDICAL ENGINEERING
(2021)
Article
Mathematics, Applied
Jichun Li, Li Zhu, Todd Arbogast
Summary: In this paper, a new variational form is developed to simulate the propagation of surface plasmon polaritons on graphene sheets. Graphene is treated as a thin sheet of current with an effective conductivity, and modeled as a lower-dimensional interface. A novel time-domain finite element method is proposed to solve this graphene model, which couples an ordinary differential equation on the interface with Maxwell's equations in the physical domain. Discrete stability and error estimate are proved for the proposed method. Numerical results are presented to demonstrate the effectiveness of this graphene model for simulating the surface plasmon polaritons propagating on graphene sheets.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Mathematics, Applied
Francesco Dell'Accio, Filomena Di Tommaso, Allal Guessab, Federico Nudo
Summary: This study proposes a method of enriching the standard simplicial linear finite element by non-polynomial functions, and provides necessary and sufficient conditions for the existence of enriched element families. It is also shown that the enriched basis functions can be represented in a closed form using enrichment functions and functionals. Finally, numerical tests are conducted. This approach can address the under-performance of low-order elements in nearly incompressible materials.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Materials Science, Multidisciplinary
Zhanhua Li, Jingtao Han, Yufeng Zhang, Ruilong Lu, Yong Yang
Summary: Stacer, as a vital component of long-distance telescopic driving device, has been widely used in aerospace with its unique advantages. This paper proposes a new method called continuous stretch bending to produce Stacer and investigates its forming process through numerical simulation. The results show that both forward and reverse bending occur during the forming process and the residual stress of cold formed Stacer can be released or directed to favorable direction without heat treatment. Optimal forming parameters are obtained for smooth deployment of Stacer and the bending stiffness of Stacer is comparable to thin-walled tubes with equivalent wall thickness. High-quality Stacers with good mechanical properties are achieved using continuous stretch bending.
MATERIALS TODAY COMMUNICATIONS
(2023)
Article
Mathematics, Applied
Grigor Angjeliu, Matteo Bruggi, Alberto Taliercio
Summary: Sequential Linear Analysis (SLA) is a valid alternative for brittle material analysis compared to incremental-iterative finite element solutions. In SLA framework, the no-tension masonry-like material model is implemented in plane stress conditions, with sequential alignment of material axes and reduction of directional stiffness at critical points. It results in compressive stress fields with virtually no tensile stresses.
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2023)
Article
Mechanics
Congzhe Wang, Anastasios P. Vassilopoulos, Thomas Keller
Summary: This study numerically investigated the two-dimensional delamination growth in FRP laminates under Mode I loading condition using finite element analyses. The results showed that flatter pre-crack or loading zone shapes could result in higher initial structural stiffness and less uniform distribution of the strain energy release rate along the pre-crack perimeter. The final crack shape was dependent on the loading zone shape and area, but the effects were relatively weak.
ENGINEERING FRACTURE MECHANICS
(2021)
Article
Mathematics, Applied
Yuzhi Fang, Yuan Feng, Minqiang Xu, Lei Zhang
Summary: In this paper, two novel gradient recovery based linear element methods are proposed for solving the quad-curl equation in two dimensions. Compared to existing finite element methods, our approach is the simplest as it only utilizes finite elements with 3 degrees of freedom (DOFs). Numerical experiments show that our proposed methods have excellent convergence properties, with optimal convergence rates under L2 and H1 norms and superconvergence phenomena under the recovery derivative.
APPLIED MATHEMATICS LETTERS
(2023)
Article
Mathematics, Applied
Xu Zhang, Nan Jiang, Qigui Yang, Guanrong Chen
Summary: This article introduces Li-Yorke chaos of linear differential equations in a finite-dimensional space with a weak topology. Based on this topology on the Euclidean space, it is proved that a flow generated from a linear differential equation can be Li-Yorke chaotic under certain conditions, which is in sharp contrast to the well-known fact that linear differential equations cannot exhibit chaos in a finite-dimensional space with a strong topology.
Article
Mathematics, Applied
Xiaohua Zhang, Xinmeng Xu
Summary: This paper presents a method for obtaining stable and high-precision numerical solutions for the coupled Burgers' equations at high Reynolds numbers using the moving finite element method. The method decouples the mesh equation and partial differential equation into two unrelated parts and reconstructs the mesh structure iteratively to maintain harmonics.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Mechanics
Chu Zhang, Huimin Dong, Chuang Zhang, Delun Wang, Shudong Yu
Summary: This paper presents an effective node-to-surface contact scheme for handling three-dimensional quasi-static contact between deformable bodies with prescribed rigid body motion. Through testing and comparisons with standard solutions, the scheme's accuracy and efficiency were verified, demonstrating its versatility and effectiveness in mechanical system design.
Article
Mathematics, Applied
Yunqing Huang, Jichun Li, Wei Yang
Summary: This paper investigates a graphene-based absorber model, incorporating both interband and intraband conductivity. Energy identity and stability are established for the continuous model, and a finite element time-domain method is proposed for solving the model. Numerical stability and optimal error estimate are proven for the scheme, with numerical results justifying the error estimate and demonstrating the wave absorbing phenomenon by graphene slab.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)
Article
Engineering, Multidisciplinary
Alfonso Pagani, Marco Enea, Erasmo Carrera
Summary: This study investigates quasi-static crack propagation in brittle materials using a combination of local and non-local elasticity models. The failure initiation and propagation are modeled using three-dimensional bond-based peridynamics (PD), while the rest of the structure is analyzed using high order one-dimensional finite elements based on the Carrera unified formulation (CUF). The coupling between the two zones is achieved through Lagrange multipliers, and static solutions for different fracture problems are provided through sequential linear analysis. The proposed approach effectively combines the advantages of CUF-based classical continuum mechanics models and PD, providing both the failure load and crack pattern shape for three-dimensional problems.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2022)
Article
Materials Science, Multidisciplinary
Marin Marin, Erasmo Carrera, Sorin Vlase
Summary: The paper focuses on a mixed initial-boundary value problem in thermoelasticity of piezoelectric bodies with a dipolar structure. It considers the case of an inhomogeneous and anisotropic thermoelastic body with the added effect of piezoelectricity. The paper establishes the existence of a unique solution for the mixed problem by imposing some intermediate conditions and obtains a generalized form of Hamilton's principle to cover this context.
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES
(2023)
Article
Thermodynamics
Marin Marin, Andreas Ochsner, Sorin Vlase
Summary: In this study, we investigate a thermoelastic Cosserat body with dual-phase lag. To develop a dual-phase-lag model, a time differential equation is introduced to capture both the thermal effects and the coupling with deformation from an elastic perspective. A mixed problem with initial data and boundary conditions is associated with this model. Qualitative estimates of the solutions to this mixed problem are obtained without imposing restrictive conditions on the thermoelastic coefficients. The uniqueness of the solution is established using a Lagrange-type identity and a previously demonstrated conservation law. Additionally, an inequality of Gronwall's type is derived, which proves the continuous dependence of the solutions on the initial values and loads, representing another key finding of our study.
CONTINUUM MECHANICS AND THERMODYNAMICS
(2023)
Article
Materials Science, Multidisciplinary
Marin Marin, Erasmo Carrera, Ahmed E. Abouelregal
Summary: In this paper, we study the linear mixed problem with initial and boundary values for a Cosserat body that is both elastic and porous. We couple the equations governing the evolution of the pores with the equations describing the elastic deformations of the Cosserat body. The coupling is achieved through predetermined coefficients. To prove the continuity of the solutions, we introduce a suitable measure that helps in estimating the gradients of the elastic deformations and the behavior of the pores.
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES
(2023)
Article
Mathematics, Applied
Marin Marin, Holm Altenbach, Ibrahim Abbas
Summary: In this study, we utilize basic results from abstract theory of differential equations of elliptic type to obtain fundamental results for a specific type of media. Specifically, we formulate the boundary values problem in the context of elasticity of Cosserat bodies with voids and prove the existence and uniqueness of a generalized solution.
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK
(2023)
Review
Polymer Science
Mostafa Katouzian, Sorin Vlase, Marin Marin, Maria Luminita Scutaru
Summary: The paper aims to present important practical cases in analyzing the creep response of unidirectional fiber-reinforced composites. Various models including the micromechanical model, homogenization techniques, Mori-Tanaka method, and finite element method (FEM) are described and analyzed for their advantages and disadvantages. The accuracy of the results obtained is compared with experimental tests. The methods discussed can be applied not only to carbon-fiber-reinforced composites but also to other types of composite materials.
Article
Thermodynamics
Marin Marin, Sorin Vlase, Andreas Oechsner
Summary: First, we establish the boundary value problem for elastic orthotropic beams in the context of elastostatics, where the beams are loaded at the ends and on the lateral surface. Then, we solve this problem by using stress functions, which leads to an extension of Prandtl's method and naturally extends the known Almansi's problem from the classical plane problem of torsion.
CONTINUUM MECHANICS AND THERMODYNAMICS
(2023)
Article
Thermodynamics
Marin Marin, Andreas Oechsner, Sorin Vlase, Dan O. Grigorescu, Ioan Tuns
Summary: In this study, we establish a boundary value problem for elasticity of porous piezoelectric bodies with a dipolar structure. By defining two operators on suitable Hilbert spaces, we prove their positivity and self-adjointness, demonstrating that eigenvalues are real numbers and corresponding eigenfunctions are orthogonal. A variational formulation is provided for the eigenvalue problem using a Rayleigh quotient type functional. Additionally, a disturbance analysis in a specific case is investigated. It is important to note that the porous piezoelectric bodies with dipolar structure considered in this study are of a general form, i.e., inhomogeneous and anisotropic.
CONTINUUM MECHANICS AND THERMODYNAMICS
(2023)
Article
Mathematics, Applied
Ahmed E. Abouelregal, Marin Marin, Holm Altenbach
Summary: This article presents the first investigation of the thermoelectric vibration of microscale Euler-Bernoulli beams resting on an elastic Winkler base. The system of equations for thermoelastic microbeams was developed using elastic basis theory and the generalized Moore-Gibson-Thompson (MGT) thermal transport framework. The effects of different inputs on mechanical fields were analyzed and it was found that an increase in the Winkler modulus and shear modulus of the foundation decreased the deflection and axial deformation in the microbeams.
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK
(2023)
Article
Multidisciplinary Sciences
Ahmed E. Abouelregal, Marin Marin, Sameh S. Askar
Summary: This study investigates the effects of laser light on the heat transfer of a thin beam heated by an applied current and voltage. Laser heating pulses are simulated as endogenous heat sources with discrete temporal properties. The heat conduction equation is developed using the energy conservation equation and the modified Moore-Gibson-Thompson (MGT) heat flow vector. Thermal and structural analysis of Euler-Bernoulli microbeams is provided with the support of visco-Pasternak's base with three parameters. An approximation of an analytical solution is found for the field variables being examined using the Laplace transform method. A comparison is made of the impacts of laser pulse length, the three foundation coefficients, and the thermal parameters on the responses to changes in measured thermophysical fields, such as deflection and temperature.
Article
Multidisciplinary Sciences
Kamal Berrada, Mariam Algarni, Marin Marin, Sayed Abdel-Khalek
Summary: We investigate the temporal behavior of entanglement formation and quantum coherence in a quantum system consisting of two superconducting charge qubits (SC-Qs) under two different classes of nonlinear field. The study discusses the impact of time-dependent coupling (T-DC) and dipole-dipole interaction (D-DI) on the temporal behavior of quantum coherence and entanglement in ordinary and nonlinear fields. Furthermore, it is shown that the main parameters of the quantum model affect the entanglement of formation and coherence of the system in a similar manner.
Article
Mathematics
Ahmed E. Abouelregal, S. S. Askar, Marin Marin
Summary: This article presents a new model for describing elastic thermal vibrations in elastic nanobeams caused by temperature changes. It uses nonlocal elasticity and the dual-phase lagging thermoelastic model to explain small-scale effects. The proposed theory is verified by studying the thermodynamic response of nanobeams subjected to a periodic thermal load. The numerical results show that the behavior of the thermal nanobeam changes with phase delay factors and the length scale parameter.
Article
Mathematics
Ahmed E. Abouelregal, Marin Marin, Sahar M. Abusalim
Summary: By laminating piezoelectric and flexible materials, their performance can be improved. Therefore, the electrical and mechanical properties of layered piezoelectric materials under electromechanical loads and heat sources need to be analyzed theoretically and mechanically. Extended thermoelasticity models have been derived to address the problem of infinite wave propagation, as classical thermoelasticity cannot address this issue. This paper focuses on the thermo-mechanical response of a piezoelectric functionally graded (FG) rod due to a movable axial heat source, using the dual-phase-lag (DPL) heat transfer model. The physical characteristics of the FG rod vary exponentially along the axis of the body. The Laplace transform and decoupling techniques are used to analyze the physical fields obtained. The results are compared with those in previous literature, considering a range of heterogeneity, rotation, and heat source velocity measures.
Article
Thermodynamics
Marin Marin, Andreas Ochsner, M. M. Bhatti, Sorin Vlase
Summary: The aim of this study is to establish a new criterion for the analyticity of a complex function. Specifically, we will derive specific restrictions that a complex function defined on the unit disc must satisfy in order to be analytic on the open unit disc. We will then apply these findings to derive Schwartz-Villat's formula and obtain the well-known Joukowski's function.
CONTINUUM MECHANICS AND THERMODYNAMICS
(2023)
Article
Multidisciplinary Sciences
Haroon D. S. Adam, Khalid I. A. Ahmed, Mukhtar Yagoub Youssif, Marin Marin
Summary: In this manuscript, analytical solutions for coupled mKdV with a time-dependent variable coefficient are implemented using the Hirota bilinear technique. Multiple wave kink and wave singular kink solutions are constructed based on the similarity transformation. The results demonstrate the effectiveness of the method and the ability to control the characteristics of soliton waves, allowing for more applications in applied sciences.
Article
Mathematics, Applied
Sami F. Megahid, Ahmed E. Abouelregal, Sameh S. Askar, Marin Marin
Summary: In this study, the Moore-Gibson-Thompson (MGT) concept of thermal conductivity is applied to a two-dimensional elastic solid in the form of a half-space. The model constructed addressed the infinite velocity problem of heat waves using Green and Naghdi's thermoelastic model. The effect of rotation and modified Ohm's law modulus on the responses of field distributions is discussed.
