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Mathematics
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Numerical and Qualitative Methods in Solid Mechanics
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Numerical and Qualitative Methods in Solid Mechanics

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

Deadline for manuscript submissions: closed (31 August 2023) | Viewed by 2192

Special Issue Editor

Dr. Elena A. Lyamina

E-Mail Website
Guest Editor
Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, 119526 Moscow, Russia
Interests: fracture; mechanics; mechanical engineering; materials science; metal forming; plastics; mechanical behavior of materials; solid mechanics; fracture mechanics

Special Issue Information

Dear Colleagues,

Numerical and qualitative methods are essential parts of solid mechanics. These methods are necessary for understanding the general features of well-established and new constitutive equations, as well as for obtaining results ready for engineering applications. However, the results derived by qualitative methods can be useful for developing finite element methods such as the generalized finite element method. Special numerical methods are important for design problems in the mechanics of structures and processes.

This Special Issue focuses on the following:

  1. Asymptotic methods in solid mechanics;
  2. Perturbation techniques in solid mechanics;
  3. Constitutive modeling for engineering materials;
  4. Design of structures using continuum mechanics methods;
  5. Design of processes using continuum mechanics methods;
  6. Development of numerical techniques for solving boundary value problems in solid mechanics.

Manuscripts reporting results using commercial software packages are not encouraged.

Dr. Elena A. Lyamina
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. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

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Published Papers (2 papers)

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Research

21 pages, 11181 KiB  
Article
The Effect of Preloaded Compressive Stress and Curvature of Defect on Blast-Induced Fracture Behavior by Caustic and Numerical Models
by Chen Huang, Zong-Xian Zhang, Adeyemi Aladejare, Xianbo Guan, Bingbing Yu and Liyun Yang
Mathematics 2023, 11(21), 4532; https://doi.org/10.3390/math11214532 - 3 Nov 2023
Cited by 2 | Viewed by 894 | Correction
Abstract
In this study, the effects of preloaded uniaxial compressive stress and defect (prefabricated by laser cutting) curvature on blast-induced cracks and stress wave propagation were investigated in polymethyl methacrylate (PMMA) specimens using caustics theory. Based on the mathematical relationship between stress and optics, [...] Read more.
In this study, the effects of preloaded uniaxial compressive stress and defect (prefabricated by laser cutting) curvature on blast-induced cracks and stress wave propagation were investigated in polymethyl methacrylate (PMMA) specimens using caustics theory. Based on the mathematical relationship between stress and optics, the fracture behavior (the propagation path, dynamic stress intensity factors (DSIFs), propagation velocity, initiation angle of the main crack, and damage degree between the defect and the blasthole) was calculated and analyzed quantitatively. The results show that the preloaded stress could mainly restrain the main crack propagation in the horizontal direction and reduce the initiation angle and damage degree at the defects. Meanwhile, the crack initiation position of the positive curvature defect was not at the end of the defect. In addition, the curvature of the defect significantly affected the blast-induced fracture compared to preloaded stresses. Comparing the main crack with other curvature defects, the DSIFs, velocity, crack arrest time, crack length, and horizontal offset distance of the main crack with negative curvature defect were the largest. The variation in the full stress field in the specimen under blasting and preloaded stress was simulated by a numerical model. The results show that the curvature of the defect has a significant effect on tensile waves at the end of defects, and the tensile stress from high to low was C-25, C0, and C25, in that order. Full article
(This article belongs to the Special Issue Numerical and Qualitative Methods in Solid Mechanics)
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19 pages, 5035 KiB  
Article
Design of Dies of Minimum Length Using the Ideal Flow Theory for Pressure-Dependent Materials
by Sergei Alexandrov and Vyacheslav Mokryakov
Mathematics 2023, 11(17), 3726; https://doi.org/10.3390/math11173726 - 30 Aug 2023
Cited by 1 | Viewed by 918
Abstract
This paper develops the ideal plastic flow theory for the stationary planar flow of pressure-dependent materials. Two rigid plastic material models are considered. One of these models is the double-shearing model, and the other is the double slip and rotation model. Both are [...] Read more.
This paper develops the ideal plastic flow theory for the stationary planar flow of pressure-dependent materials. Two rigid plastic material models are considered. One of these models is the double-shearing model, and the other is the double slip and rotation model. Both are based on the Mohr–Coulomb yield criterion. It is shown that the general ideal plastic flow theory is only possible for the double slip and rotation model if the intrinsic spin vanishes. The theory applies to calculating the shape of optimal extrusion and drawing dies of minimum length. The latter condition requires a singular characteristic field. The solution is facilitated using the extended R–S method, commonly employed in the classical plasticity of pressure-independent materials. In particular, Riemann’s method is used in a region where all characteristics are curved. It is advantageous since determining the optimal shape does not require the characteristic field inside the region. The solution is semi-analytical. A numerical procedure is only required to evaluate ordinary integrals. It is shown that the optimal shape depends on the angle of internal friction involved in the yield criterion. Full article
(This article belongs to the Special Issue Numerical and Qualitative Methods in Solid Mechanics)
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