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Modelling of Deformation Characteristics of Materials or Structures
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Modelling of Deformation Characteristics of Materials or Structures

A special issue of Materials (ISSN 1996-1944). This special issue belongs to the section "Materials Simulation and Design".

Deadline for manuscript submissions: 20 August 2025 | Viewed by 2641

Special Issue Editor

Prof. Dr. Tomasz Strek

E-Mail Website1 Website2
Guest Editor
Institute of Applied Mechanics, Poznan University of Technology, 60-965 Poznan, Poland
Interests: computational mechanics; auxetic; smart materials; finite element analysis; modeling and simulation
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Nowadays, simulation techniques and numerical methods have been rapidly evolving in order to apply increasingly complex models and to meet the growing requirements of engineering applications. Also, newly developed analytical solutions have covered a wider range of scientific problems and are benchmark solutions for numerical simulations.

This Special Issue of Materials is devoted to analytical and computational methods in the modelling of material characteristics. Among others, the following topics are the main fields of interest of this Issue: linear and non-linear behavior elasticity and plasticity models; materials with anomalous characteristics; metamaterials; auxetic cellular materials; smart materials; porous materials; functionally graded materials, dynamics and fatigue of materials; the topological optimization of structures; heat transfer in materials and structures; as well as other topics relating to computational methods in the engineering and modelling of materials.    

We invite you to submit research articles concerning the latest research work in these areas, with an emphasis on applications in all areas of materials and mechanics engineering.

Prof. Dr. Tomasz Strek
Guest Editor

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. Materials 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

  • computational materials
  • auxetic cellular materials
  • smart materials
  • negative materials
  • porous materials
  • material strain-rate dependency
  • porous materials
  • mechanics of materials
  • heat transfer
  • thermal stresses
  • dynamics
  • biomechanics

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Published Papers (4 papers)

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Research

20 pages, 4919 KiB  
Article
Analytical and Finite Element Solution for Functionally Graded Pressure Vessels Subjected to Finite Strain Coupled Axial and Torsional Deformations
by Mohammad Shojaeifard, Arash Valiollahi, Davood Rahmatabadi, Ali Taheri, Eunsoo Choi, Alireza Ostadrahimi and Mostafa Baghani
Materials 2025, 18(9), 2136; https://doi.org/10.3390/ma18092136 - 6 May 2025
Viewed by 246
Abstract
This study presents an analytical solution to examine the mechanical behavior of an incompressible, functionally graded hyperelastic cylinder under combined extension and torsion. The exp-exp strain energy density function characterizes the hyperelastic material, with parameters varying exponentially along the radial direction. To validate [...] Read more.
This study presents an analytical solution to examine the mechanical behavior of an incompressible, functionally graded hyperelastic cylinder under combined extension and torsion. The exp-exp strain energy density function characterizes the hyperelastic material, with parameters varying exponentially along the radial direction. To validate the solution, finite element simulations using a custom UHYPER in ABAQUS are performed. The analytical and numerical results show strong agreement across different stretch and twist levels. The stress distribution and maximum stress are significantly influenced by the exponential parameter governing material gradients. Unlike axial stretch, torsion induces a more intricate longitudinal stress distribution, with large twisting producing two extrema that shift toward the cylinder’s center and outer surface. Longitudinal stress primarily governs von Mises stress and strain energy density variations across the radial direction. A critical axial stretch is identified, below which torsion-induced axial force transitions to compression, elongating the cylinder during twisting. Beyond this stretch, the axial force shifts from tensile to compressive with increasing twist, causing initial shortening before further elongation. Full article
(This article belongs to the Special Issue Modelling of Deformation Characteristics of Materials or Structures)
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23 pages, 11800 KiB  
Article
Numerical Analysis of Incinerator Refractory Brick with Coupled Parameters Based on Thermodynamic Theory
by Yu Mou, Sisi Han, Yanrong Zhang, Kai Wu and Xinrui Shen
Materials 2025, 18(4), 824; https://doi.org/10.3390/ma18040824 - 13 Feb 2025
Viewed by 445
Abstract
The selection of refractory bricks significantly impacts the operational performance of brick structures in high-temperature environments. In this study, a coupled thermal stress model of a refractory brick structure was established and validated by means of thermal expansion experiments. This paper innovatively combined [...] Read more.
The selection of refractory bricks significantly impacts the operational performance of brick structures in high-temperature environments. In this study, a coupled thermal stress model of a refractory brick structure was established and validated by means of thermal expansion experiments. This paper innovatively combined the brick number, brick thickness, and brick material to investigate their influence on brick structural performance. The results indicated that the influence of the brick number on the temperature was less significant than that of brick thickness. However, the brick number had a greater effect on vertical displacement and principal compressive stress than brick thickness, with the maximum differences being 342.3% and 28.9%. Compared to brick thickness, brick material had a more significant effect on vertical displacement and principal compressive stress, with the maximum differences being 77.1% and 67.4%. Additionally, the influence of brick material properties on vertical displacement and principal compressive stress was greater than that of the brick number, with the maximum differences being 77.6% and 65%. Therefore, when selecting refractory bricks, it is advisable to consider the brick material first, the brick number second, and the brick thickness last. This study offers theoretical guidance for refractory brick structure design and material selection in high-temperature applications. Full article
(This article belongs to the Special Issue Modelling of Deformation Characteristics of Materials or Structures)
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Graphical abstract

28 pages, 1200 KiB  
Article
Dynamics of One-Directional Functionally Graded Plates with Different Sizes of Microstructure: Theoretical Tolerance Modelling
by Jarosław Jędrysiak and Magda Kaźmierczak-Sobińska
Materials 2025, 18(2), 328; https://doi.org/10.3390/ma18020328 - 13 Jan 2025
Cited by 1 | Viewed by 601
Abstract
The dynamics of thin elastic one-directional non-periodic plates are considered in this paper. The structure of these plates is, at a macro level, functionally graded along the x1-axis, but at the micro level it is non-periodic (tolerance-periodic). In the plates, the [...] Read more.
The dynamics of thin elastic one-directional non-periodic plates are considered in this paper. The structure of these plates is, at a macro level, functionally graded along the x1-axis, but at the micro level it is non-periodic (tolerance-periodic). In the plates, the effect of a microstructure size on their behaviour can play a crucial role. The tolerance modelling method allows for this effect to be taken into account. This paper mainly proposes that tolerance modelling leads to model equations of two different tolerance models for one-directional functionally graded plates with two kinds of tolerance-periodic microstructures, i.e., (a) those having a microstructure size that is an order of the plate thickness, d~l, and (b) those having the plate thickness that is smaller than a microstructure size, d << l. Derived model equations are characterised by slowly varying coefficients. A subset of these coefficients is contingent on the microstructure size. The models presented herein determine formulas for both fundamental lower-order vibration frequencies and higher-order vibration frequencies, which are related to the microstructure. These models of such plates are implemented in a rudimentary example of free vibrations. Using the Ritz method, formulas of frequencies are obtained. Full article
(This article belongs to the Special Issue Modelling of Deformation Characteristics of Materials or Structures)
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25 pages, 7189 KiB  
Article
Design Optimization of the Mechanics of a Metamaterial-Based Prosthetic Foot
by Agata Mrozek-Czajkowska and Tomasz Stręk
Materials 2025, 18(1), 96; https://doi.org/10.3390/ma18010096 - 29 Dec 2024
Viewed by 800
Abstract
This paper is dedicated to the analysis of a foot prosthesis optimization process, with a particular focus on the application of optimization algorithms and unconventional materials, such as auxetic materials. The study aims to enhance prosthesis performance by minimizing the difference between the [...] Read more.
This paper is dedicated to the analysis of a foot prosthesis optimization process, with a particular focus on the application of optimization algorithms and unconventional materials, such as auxetic materials. The study aims to enhance prosthesis performance by minimizing the difference between the ground reaction force generated by the prosthetic foot and that of a natural limb. In the initial part of the study, the basic topics concerning the parameterization of the foot prosthesis geometry and the preparation of a finite element model for human gait are discussed. In the subsequent part of the study, the focus is on the optimization process, in which algorithms were applied to adjust the prosthesis structure to the patient’s individual needs. The optimization process utilized a finite element method gait model. After validating the FEM, an algorithm generating the prosthesis geometry based on the given parameters was developed. These parameters were optimized using the VOA, comparing FEM gait model data on vertical ground reaction force with experimental results. The results of the foot prosthesis optimization are presented through a comparison of different structural models. The study also demonstrates the application of auxetic materials, which, due to their unique mechanical properties, can enhance foot prosthesis efficiency. Simulations were performed using multi-material topology optimization. The results obtained for different gait phases were compared. Full article
(This article belongs to the Special Issue Modelling of Deformation Characteristics of Materials or Structures)
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