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Symmetry
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Symmetry in Finite Element Modeling and Mechanics
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Symmetry in Finite Element Modeling and Mechanics

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Engineering and Materials".

Deadline for manuscript submissions: 30 November 2024 | Viewed by 8330

Special Issue Editors

Dr. Sina Niazi

E-Mail Website
Guest Editor
Department of Civil and Environmental Engineering, Virginia Tech, Blacksburg, VA 24061, USA
Interests: computational mechanics; fracture mechanics; peridynamics; advanced finite element methods; composites; mechanics of complex materials
Dr. Rodrigo C. V. Coelho

E-Mail Website
Guest Editor
1. Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal
2. Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal
Interests: fluid dynamicslattice; boltzmann method; soft condensed matter; liquid crystals

Special Issue Information

Dear Colleagues,

Symmetry is one of the most important notions that lies at the heart of the fundamental laws of nature, and it acts as an important tool for understanding the features of complex systems. Symmetry in systems may appear in various forms, such as in domain geometry, boundary conditions, model definitions, solutions, etc.

Computational and theoretical techniques in mechanics, such as finite element modeling, have been intensively developed in recent years. The existence of abundant literature shows that such techniques have proven their efficiency, robustness, and ability to handle challenging problems. However, an aspect that has not been so widely considered in the literature is the handling of symmetries, in various forms, within the problems. Therefore, the present Special Issue aims to emphasize the phenomena that lie at the intersection between the concept of symmetry, modeling, and mechanics.

In this Special Issue, we welcome contributions covering a broad range of topics that include—but are not limited to—theoretical and computational mechanics, finite element modeling, damage and fracture mechanics, geometric modeling, numerical methods, continuum mechanics, and boundary conditions. We hope that this Special Issue will serve as a platform for innovation and will provide up-to-date findings for readers and the scientific community.

Dr. Sina Niazi
Dr. Rodrigo C. V. Coelho
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. Symmetry is an international peer-reviewed open access monthly 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 2400 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

  • theoretical and computational mechanics
  • finite element modeling
  • damage and fracture mechanics
  • geometric modeling
  • numerical methods
  • continuum mechanics
  • boundary conditions

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Further information on MDPI's Special Issue polices can be found here.

Published Papers (5 papers)

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Research

12 pages, 2184 KiB  
Article
Non-Linear Elastic Beam Deformations with Four-Parameter Timoshenko Beam Element Considering Through-the-Thickness Stretch Parameter and Reduced Integration
by Nasser Firouzi and Ahmed S. M. Alzaidi
Symmetry 2024, 16(8), 984; https://doi.org/10.3390/sym16080984 - 2 Aug 2024
Viewed by 653
Abstract
In this work, non-linear elastic deformations of beams are investigated. The kinematics of the beam is derived based on an element with four-parameter containing a through-the-thickness stretch parameter to avoid Poisson locking. Moreover, the Kirchhoff-Saint Venant model is used to derive kinetic quantities. [...] Read more.
In this work, non-linear elastic deformations of beams are investigated. The kinematics of the beam is derived based on an element with four-parameter containing a through-the-thickness stretch parameter to avoid Poisson locking. Moreover, the Kirchhoff-Saint Venant model is used to derive kinetic quantities. Next, a non-linear FE formula in Total Lagrangian form is obtained, and three-node beam element with two-node reduced integration is employed to avoid shear locking. Finally, to evaluate the performance of the derived formulations, some examples are provided. The results prove that the current formulation is in very good agreement with those available in the literature. More importantly, the formulation is capable of predicting the experimental results with high accuracy. Full article
(This article belongs to the Special Issue Symmetry in Finite Element Modeling and Mechanics)
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17 pages, 455 KiB  
Article
A Non-Second-Gradient Model for Nonlinear Electroelastic Bodies with Fibre Stiffness
by Mohd Halim Bin Mohd Shariff, Jose Merodio, Roger Bustamante and Aymen Laadhari
Symmetry 2023, 15(5), 1065; https://doi.org/10.3390/sym15051065 - 11 May 2023
Cited by 1 | Viewed by 1279
Abstract
The study of the mechanical behaviour of fibre-reinforced electroactive polymers (EAPs) with bending stiffness is beneficial in engineering for mechanical design and problem solving. However, constitutive models of fibre-reinforced EAPs with fibre bending stiffness do not exist in the literature. Hence, to enhance [...] Read more.
The study of the mechanical behaviour of fibre-reinforced electroactive polymers (EAPs) with bending stiffness is beneficial in engineering for mechanical design and problem solving. However, constitutive models of fibre-reinforced EAPs with fibre bending stiffness do not exist in the literature. Hence, to enhance the understanding of the mechanical behaviour of fibre-reinforced EAPs with fibre bending stiffness, the development of a relevant constitutive equation is paramount. In this paper, we develop a constitutive equation for a nonlinear nonpolar EAP, reinforced by embedded fibres, in which the elastic resistance of the fibres to bending is modelled via the classical branches of continuum mechanics without using the second gradient theory, which assumes the existence of contact torques. In view of this, the proposed model is simple and somewhat more realistic, in the sense that contact torques do not exist in nonpolar EAPs. Full article
(This article belongs to the Special Issue Symmetry in Finite Element Modeling and Mechanics)
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12 pages, 378 KiB  
Article
A Generalised Time-Dependent Mathematical Formulation for Magnetoelectrically Coupled Soft Solids at Finite Strains
by Mohd Halim Bin Mohd Shariff, Roger Bustamante and Mokarram Hossain
Symmetry 2023, 15(3), 628; https://doi.org/10.3390/sym15030628 - 2 Mar 2023
Cited by 3 | Viewed by 1344
Abstract
To date, the mechanical models of magnetoelectric couplings at finite strains have mainly been limited to time-independent constitutive equations. This paper enhances the literature by developing a time-dependent electromagnetic constitutive equation to characterise the mechanical behaviour of soft solids at finite strains and [...] Read more.
To date, the mechanical models of magnetoelectric couplings at finite strains have mainly been limited to time-independent constitutive equations. This paper enhances the literature by developing a time-dependent electromagnetic constitutive equation to characterise the mechanical behaviour of soft solids at finite strains and take into account the full form of the Maxwell equations. Our formulation introduces a symmetrical total stress and uses recently developed spectral invariants in the amended energy function; as a result, the proposed constitutive equation is relatively simple and is amenable to a finite-element formulation. Full article
(This article belongs to the Special Issue Symmetry in Finite Element Modeling and Mechanics)
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13 pages, 4332 KiB  
Article
Mathematical Modeling of Spherical Shell-Type Pattern of Tumor Invasion
by Meitham Amereh, Henning Struchtrup and Ben Nadler
Symmetry 2023, 15(2), 283; https://doi.org/10.3390/sym15020283 - 19 Jan 2023
Cited by 2 | Viewed by 1756
Abstract
Cancer cell migration, as the principal element of tumor invasion, involves different cellular mechanisms. Various modes of cell migration including single and collective motions contribute to the invasion patterns. The competition between adhesive cell–cell and cell–matrix forces is a key factor that determines [...] Read more.
Cancer cell migration, as the principal element of tumor invasion, involves different cellular mechanisms. Various modes of cell migration including single and collective motions contribute to the invasion patterns. The competition between adhesive cell–cell and cell–matrix forces is a key factor that determines such patterns. In this paper, we study a distinct shell-type mode of tumor invasion observed in brain and breast tumors. In this mode, cells at the outer layer of the tumor collectively move away from the core and form a shell-type shape. Both the core and the shell sustain a sharp interface between cells and the surrounding matrix. To model the preserved interface, we adopted a Cahn–Hilliard-type free energy relation with the contribution of the interfacial stress. This nonconvex form of free energy allows for cells to remain together and preserve the tumor core via adhesive cell–cell forces while separating the core from the surrounding matrix across a continuous sharp interface. In addition, the motion of the shell was modeled using the chemotactic migration of cells in response to the gradient of nutrients. The associated fluxes of cells were implemented in a general form of balance law. A non-Michaelis–Menten kinetics model was adopted for the proliferation rate of cells. The flux of nutrients was also modeled using a simple diffusion equation. The comparison between the model predictions and experimental observations indicates the ability of the model to manifest the salient features of the invasion pattern. Full article
(This article belongs to the Special Issue Symmetry in Finite Element Modeling and Mechanics)
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17 pages, 2212 KiB  
Article
A Low-Cost Algorithm for Uncertainty Quantification Simulations of Steady-State Flows: Application to Ocular Hemodynamics
by Georgios Ninos, George Sofiadis, Aikaterini Skouroliakou and Ioannis E. Sarris
Symmetry 2022, 14(11), 2305; https://doi.org/10.3390/sym14112305 - 3 Nov 2022
Cited by 2 | Viewed by 1408
Abstract
An algorithm for the calculation of steady-state flowing under uncertain conditions is introduced in this work in order to obtain a probabilistic distribution of uncertain problem parameters. This is particularly important for problems with increased uncertainty, as typical deterministic methods are not able [...] Read more.
An algorithm for the calculation of steady-state flowing under uncertain conditions is introduced in this work in order to obtain a probabilistic distribution of uncertain problem parameters. This is particularly important for problems with increased uncertainty, as typical deterministic methods are not able to fully describe all possible flow states of the problem. Standard methods, such as polynomial expansions and Monte Carlo simulations, are used for the formation of the generalized problem described by the incompressible Navier-Stokes equations. Since every realization of the uncertainty parameter space is coupled with non-linear terms, an incremental iterative procedure was adopted for the calculation. This algorithm adopts a Jacobi-like iteration methodology to decouple the equations and solve them one by one until there is overall convergence. The algorithm was tested in a typical artery geometry, including a bifurcation with an aneurysm, which consists of a well-documented biological flow test case. Additionally, its dependence on the uncertainty parameter space, i.e., the inlet velocity distribution, the Reynolds number variation, and parameters of the procedure, i.e., the number of polynomial expansions, was studied. Symmetry exists in probabilistic theories, similar to the one adopted by the present work. The results of the simulations conducted with the present algorithm are compared against the same but unsteady flow with a time-dependent inlet velocity profile, which represents a typical cardiac cycle. It was found that the present algorithm is able to correctly describe the flow field, as well as capture the upper and lower limits of the velocity field, which was made periodic. The comparison between the present algorithm and the typical unsteady one presented a maximum error of ≈2% in the common carotid area, while the error increased significantly inside the bifurcation area. Moreover, “sensitive” areas of the geometry with increased parameter uncertainty were identified, a result that is not possible to be obtained while using deterministic algorithms. Finally, the ability of the algorithm to tune the parameter limits was successfully tested. Full article
(This article belongs to the Special Issue Symmetry in Finite Element Modeling and Mechanics)
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