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Mathematics
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Applied Mathematics and Mechanics 2019
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Applied Mathematics and Mechanics 2019

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: closed (31 July 2020) | Viewed by 3589

Special Issue Editors

Dr. Reza Abedi

E-Mail Website
Guest Editor
Department of Mechanical Aerospace and Biomedical Engineering, University of Tennessee Space Institute, Tullahoma, TN 37388, USA
Interests: spacetime discontinuous Galerkin; computational mechanics; fracture mechanics; computational electromagnetics
Special Issues, Collections and Topics in MDPI journals
Dr. Raj Kumar Pal

E-Mail Website
Guest Editor
Department of Mechanical and Nuclear Engineering, Kansas State University, Manhattan, KS 66506, USA
Interests: wave propagation; lattices; metamaterials; granular media; computational mechanics; solid mechanics

Special Issue Information

Dear Colleagues,

The advances in technology and material science have required constitutive modeling of modern materials and the formulation of computational tools necessary for their analyses. For example, many new designs, such as microelectromechanical and nanoelectromechanical systems (MEMS and NEMS), smart materials and multifunctional materials, are inherently multiphysic and require rigorous constitutive modeling. Successful experimental demonstration of negative electrical permittivity, magnetic permeability, effective elastic modulus, and mass density in metamaterials and extreme solids are other examples that emphasize the importance of classical applied mechanics fields, such as continuum mechanics in recent years. Of particular importance have been multiscale and homogenization approaches, given the role of specific microstructural designs on the response of modern materials. There has also been a greater emphasis in nondeterministic approaches, given the higher sensitivity of the aforementioned materials to design deviations and the importance on the stochastic distribution on small scale features in overall response, for example, in fracture mechanics and turbulence. Such advances have, in turn, necessitated the formulation of computational methods capable of efficient and accurate rendering of these material models. Theoretical and computational tools, including but not limited to multiscale and high-order methods, rigorous analysis of numerical errors and efficiency, homogenization schemes, and efficient approaches for the solution of discrete lattices, periodic media, and ordinary, partial and stochastic partial differential equations are a few of the relevant topics.

Prof. Dr. Reza Abedi
Dr. Raj Kumar Pal
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Solid mechanics
  • Fluid mechanics
  • Thermodynamics
  • Fracture mechanics
  • Continuum mechanics
  • Constitutive models for modern materials
  • Multiphysics problems
  • Homogenization
  • Multiscale methods
  • Stochastic partial differential equations
  • Computational mechanics including error and efficiency analysis
  • Finite element methods
  • Metamaterials
  • Wave propagation
  • Granular media
  • Instabilities in solids
  • Acoustics and ultrasonics
  • Smart materials

Published Papers (2 papers)

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15 pages, 10142 KiB  
Article
An Image-Based Double-Smoothing Cohesive Finite Element Framework for Particle-Reinforced Materials
by Xiaoming Bai, Xue Mi, Hai Xie, Kaikai Shi, Furui Xiong, Yixiong Zhang and Licheng Guo
Mathematics 2020, 8(4), 543; https://doi.org/10.3390/math8040543 - 07 Apr 2020
Viewed by 1671
Abstract
In order to simulate the fracture process of particle-reinforced materials on the micro-scale, an image-based double-smoothing cohesive finite element framework is proposed in the present paper. Two separate smoothing processes are performed to reduce the noise in the digital image and eliminate the [...] Read more.
In order to simulate the fracture process of particle-reinforced materials on the micro-scale, an image-based double-smoothing cohesive finite element framework is proposed in the present paper. Two separate smoothing processes are performed to reduce the noise in the digital image and eliminate the jagged elements in the finite element mesh. The main contribution of the present study is the proposed novel image-based cohesive finite element framework, and this method improved the quality of the meshes effectively. Meanwhile, the artificial resistance due to the jagged element is reduced with the double-smoothing cohesive finite element framework during the crack propagation. Therefore, the image-based double-smoothing cohesive finite element framework is significant for the simulation of fracture mechanics. Full article
(This article belongs to the Special Issue Applied Mathematics and Mechanics 2019)
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18 pages, 1343 KiB  
Article
A Closed-Form Solution of Prestressed Annular Membrane Internally-Connected with Rigid Circular Plate and Transversely-Loaded by Central Shaft
by Zhi-Xin Yang, Jun-Yi Sun, Zhi-Hang Zhao, Shou-Zhen Li and Xiao-Ting He
Mathematics 2020, 8(4), 521; https://doi.org/10.3390/math8040521 - 03 Apr 2020
Cited by 5 | Viewed by 1579
Abstract
In this paper, we analytically dealt with the usually so-called prestressed annular membrane problem, that is, the problem of axisymmetric deformation of the annular membrane with an initial in-plane tensile stress, in which the prestressed annular membrane is peripherally fixed, internally connected with [...] Read more.
In this paper, we analytically dealt with the usually so-called prestressed annular membrane problem, that is, the problem of axisymmetric deformation of the annular membrane with an initial in-plane tensile stress, in which the prestressed annular membrane is peripherally fixed, internally connected with a rigid circular plate, and loaded by a shaft at the center of this rigid circular plate. The prestress effect, that is, the influence of the initial stress in the undeformed membrane on the axisymmetric deformation of the membrane, was taken into account in this study by establishing the boundary condition with initial stress, while in the existing work by establishing the physical equation with initial stress. By creating an integral expression of elementary function, the governing equation of a second-order differential equation was reduced to a first-order differential equation with an undetermined integral constant. According to the three preconditions that the undetermined integral constant is less than, equal to, or greater than zero, the resulting first-order differential equation was further divided into three cases to solve, such that each case can be solved by creating a new integral expression of elementary function. Finally, a characteristic equation for determining the three preconditions was deduced in order to make the three preconditions correspond to the situation in practice. The solution presented here could be called the extended annular membrane solution since it can be regressed into the classic annular membrane solution when the initial stress is equal to zero. Full article
(This article belongs to the Special Issue Applied Mathematics and Mechanics 2019)
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