Visualization of tensor fields based on geometric representation of tensors

Dimitrienko, Yu. I.; Губарева, Е. А.; Sborshikov, S.V.

doi:10.26583/sv.10.2.08

Cited by 5 publications

(7 citation statements)

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“…In all cases, fracture cracks grow from a defect of initial length 𝑙 0 along the normal to the direction of maximum tensile stress. To characterize the crack, scale relations are fulfilled Where λ is the fluctuation crack propagation upon rupture of one or a group of bonds (for organic polymers 𝜆 = 12𝛢 ∘ [5,6]), 𝜏 𝑓 (𝜎, 𝑇) is the duration of the slow (thermofluctuation) stage of crack growth from the initial to the critical length. Scale relations (2) are the substantiating experimental result for the construction of mathematical models.…”

Section: Ideological Schemes Of Researchmentioning

confidence: 99%

“…Where 𝑈 = 𝑈 0 − 𝑞𝑇 в is the activation energy for breaking bonds, decreasing linearly with increasing temperature; 𝑈 0 is the activation energy of the rupture process, extrapolated to absolute zero; q is the coefficient of temperature dependence of the activation energy (for polymeric organic glasses) 𝑞 ∼ (15 − 20)J/molK; 𝜎 0 *thermal fluctuation threshold of destruction (safe overvoltage at the crack tip). The fluctuation volume, an important molecular structural characteristic of polymers, is calculated on the basis of data on the structure of polymers and the mechanism of their destruction [5,6]: 𝑉 𝑎 = 𝜆𝜆 𝜋 𝜆 𝑚 , where 𝜆 𝜋prebreak bond elongation; 𝜆 𝑚bond elongation. For non-oriented polymers, (polymer glasses formed by linear polymers), for oriented (fibers) 𝑉 𝑎 = 6𝜆 0 2 ⋅ 𝜆 𝑚 = 1.4 ⋅ 10 −28 м 3 ; 𝜆 𝑚 = 1.5 𝐴 ∘ , 𝜆 0 = 4𝐴 ∘ is the average intermolecular distance in the polymer) [7,8].…”

Section: Ideological Schemes Of Researchmentioning

confidence: 99%

“…Structure-sensitive materials are obtained by various methods: nanopowder compaction, deposition on a substrate, crystallization of amorphous alloys, etc. [1][2][3][4][5][6] and have unique mechanical and thermal properties that allow them to be used in structures subject to various external influences [7,8]. An important step in the creation and use of these materials is the development of appropriate mathematical models to describe their behavior in a wide range of changes in external operational factors.…”

Section: Introductionmentioning

confidence: 99%

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Kinetic characteristics of cracks in polymers and composites based on mechanical and thermal loads

Valishin

Карташов²,

Dzhemesyuk³

2023

E3S Web of Conf.

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Theoretical ratios of important kinetic characteristics for brittle polymers with cracks under mechanical and thermal effects are obtained, which underlie the study of the thermokinetics of the process of polymer fracture in terms of the theory of the time dependence of strength-durability. Rectilinear (internal and surface) cracks in plate-type specimens and internal circular (disk-shaped) cracks in polymer fibers are considered. Two test modes are considered successively: constant tensile stress, constant absolute temperature, unchanging structure, inactive medium, as well as a more complex mode of purely thermal loading - the case least developed in the theory of destruction. The calculated ratios of a number of limiting characteristics and parameters of the destruction process are given: safe and critical stress; initial length of a microcrack and its relative critical length; safe and critical voltage; local stress at the crack tip (in the fluctuation volume); the value of the free surface energy. The above relations are the basis for the development of the theory of the time dependence of strength-durability.

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Section: Ideological Schemes Of Researchmentioning

confidence: 99%

Section: Ideological Schemes Of Researchmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Kinetic characteristics of cracks in polymers and composites based on mechanical and thermal loads

Valishin

Карташов²,

Dzhemesyuk³

2023

E3S Web of Conf.

View full text Add to dashboard Cite

show abstract

“…This approach has already been applied to natural science and mathematical training based on information and educational environment for the mathematical training of engineers NOMOTEX [48,49]. In this environment, specialized software modules are used to visualize the most complex mathematical concepts, for example, tensor fields [50]. Moreover, created on the principles of artificial intelligence, this environment includes a mathematical knowledge base founded on a neural network structure [51].…”

Section: Experience In Engineering Education Transformationmentioning

confidence: 99%

Engineering Education: Key Features of the Digital Transformation

Александров¹,

Tsvetkov²,

Zhileykin³

2020

ITM Web Conf.

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The paper deals with the digital transformation of engineering education. Such transformation is justified in terms of an engineering education paradigm change. Based on a comprehensive analysis of the didactic system of engineering education, the authors specify the requirements for such important engineering education components as goal setting, content, educational technologies, assessment tools and methods in current educational environment. They provides examples of a practical digital transformation of a number of engineering curricula and syllabi by integrating blended learning based on a Small Private Online Course (SPOC). The authors share their best practices in designing e-learning taking into account the features of the learning-forgetting process, they demonstrate how to make use of the saved time for students’ practical work, how to implement gamification techniques based on such new forms as the Hackathon, Internet of things (IoT) for engineering education. They also provide examples of creating a digital educational environment with specialized software modules to visualize complex mathematical concepts as well as examples of applying principles of artificial intelligence and machine learning to shape a student’s adapted educational trajectory. They discuss how to identify student’s problems with learning material assimilation and suggest a specially developed course including propaedeutic unit for additional study.

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“…4. Development of applications for CAE, designed to solve specific visualization problems in the environment of a particular CAE system [7][8][9]. This paper considers the solution of a particular visualization problem for CAD/CAE Solid-Works (Simulation).…”

Section: Introductionmentioning

confidence: 99%

Visualization of energy efficiency of using a material in a deformable solid

Chugunov¹,

Polunina²

2020

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Visualization of tensor fields based on geometric representation of tensors

Cited by 5 publications

References 0 publications

Kinetic characteristics of cracks in polymers and composites based on mechanical and thermal loads

Kinetic characteristics of cracks in polymers and composites based on mechanical and thermal loads

Engineering Education: Key Features of the Digital Transformation

Visualization of energy efficiency of using a material in a deformable solid

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