Численное моделирование процессов динамического деформирования и усталостного разрушения гетерогенных сред / Numerical modeling of the dynamic deformation and fatigue destruction processes of heterogeneous media тема диссертации и автореферата по ВАК РФ 00.00.00, кандидат наук Халид Валид

• Халид Валид
• кандидат наук
• 2025

Оглавление диссертации кандидат наук Халид Валид

Contents

Introduction

Chapter 1. Literature Review

1.1 Heterogeneous Material s

1.2 Ice Deformation Simulation

1.3 Fatigue Fracturing Process

Chapter 2. Mathematical Models and Numerical Methods

2.1 Isotropic Linear Elastic Model

2.2 Grid-Characteristic Method

2.2.1 B ackground Rectangul ar Grid

2.2.2 Overlapping Structured Grid

2.2.3 Interpolation between Background and Overlapping Grids

2.3 Fatigue Fracturing Model

Chapter 3. Algorithm Implementation Details

3.1 Fatigue Fracturing

3.2 Ice Deformation Simulation

Chapter 4. Simulation Results

4.1 Fatigue Fracturing

4.1.1 Comparison of 3D and 2D Problems

4.1.2 Comparison with OpenFOAM results

4.1.3 Comparison of static and dynamic simulations

4.1.4 Complex hole shapes

4.1.5 Complex stress state

4.2 Steel Ball - Ice Plate Low-Speed Interaction

4.2.1 Linear Elastic Model Usage

4.2.2 Elastoplastic Model Usage

5 Conclusion

6 Acknowledgments

7 References

Введение диссертации (часть автореферата) на тему «Численное моделирование процессов динамического деформирования и усталостного разрушения гетерогенных сред / Numerical modeling of the dynamic deformation and fatigue destruction processes of heterogeneous media»

Introduction

Failure models based on the concept of damageability belong to the class of continuum models and were first proposed in the works of Soviet scientists Rabotnov Yu.N. and Kachanov L.M. Fatigue failure models of this type as applied to cyclic loads were also developed in the works of Russian authors Petukhov D.S. and Tumanov A.V. for various cyclic loading modes. When constructing cyclic damageability models, fatigue failure criteria are used, which serve to generalize fatigue curves under uniaxial cyclic loading to the case of a multiaxial stress state.

Recently, in articles published by Nikitin I.S. and Burago N.G. with their colleagues, the theory of cyclic damage is employed to illuminate the fatigue fracturing process in solid media. Initially, the problem is solved in ANSYS to determine the stresses on the computational grid. Subsequently, an algorithm is utilized to identify the quasicrack, cyclic loading, and damage function on the grid. Two distinct complex methods are employed to define the equivalent stresses on the computational grid.

The grid-characteristic method was presented for multidimensional hyperbolic problems in 1960x. It was further extended to the curvilinear and movable grids. Also, the hybrid grid-characteristic scheme and the quasilinear grid-characteristic scheme based on the free coefficients space were developed. Then, the generalization of these schemes on the irregular tetrahedral meshes was done. Combined grid-characteristic/smoothed-particle hydrodynamics and grid-characteristic/discontinuous Galerkin method schemes were invented. Major improvements were made related to the support of hierarchical and overlapping meshes. Recently, new approaches for the achievement of the high approximation order in multidimensional cases and near to the integration domain boundaries were proposed.

This work is devoted to the extension of the numerical grid-characteristic method on structured overlapping grids to the problem of fatigue fracturing under very-high-cycling loadings. The second research task is to provide numerically proved approach for simple reproduction of ice deformation experiment data under low-energy impact.

Primary Goal and Objectives. The central goal of the current research was the development of the numerical algorithm, based on the full-wave solution of a single cycle deformation problem and provided the correct simulation of the fatigue fracturing process in high-cycle and very-high-cycle loading modes. It led to the consideration of such tasks:

1) Adaptation of the grid-characteristic method on overlapping grids for the full-wave problem of the metal plate with hole of a given geometry loading.

2) Combination and implementation of a multi-mode fatigue fracturing model based on the kinetic equation solution on the additional damage function.

3) Validation of the written program algorithm on the results, obtained with other available open-source and commercial software.

4) Numerical simulation of applied fatigue fracturing problems for different stress states and domain geometries.

Scientific Novelty. While completing the present research the following new results were obtained:

1) The application area of the numerical grid-characteristic method on structured grids was significantly extended on the problems of the fatigue fracturing process under cycling loadings.

2) The research software that implements a multi-mode fatigue fracturing model on Python language was developed and tested in combination with different deformation problem solvers.

3) The reproduction of the available experiment data about low-energy metal ball with ice plate interaction was achieved by a tuning of a single-parameter mechanical model.

Theoretical and Practical Significance.

The theoretical significance of the research relates to the extension of the available numerical methods for solving dynamic deformation and damage problems of heterogeneous media. The combination of the grid-characteristic method on structured overlapping grids with a multi-mode fatigue fracturing model provides the possibility of robust inclusion of multiple holes with different geometries into the simulation of the metal specimens life testing. It also allows the direct consideration of the dynamic deformation process, that is crucial for used in laboratory experiments with high loading frequencies.

The practical significance of the research is connected to the development of the in-house research software, that can be used to the simulation of metal plates fatigue fracturing process. The straightforward process of the grid's generation for the wide range of the considered hole geometries, potentially can be used for automatization of the specimen design process. The tuned elastoplastic mechanical model of the ice plate can be used for the rough estimations of the impact interaction consequences, that is important in the frame of the dynamic exploration of the Arctic region.

Research Methods and Results Validity.

The dissertation work uses classical mechanical models that describe dynamic deformations of isotropic linear elastic and elastoplastic media. The widely applied numerical methods, including the grid-characteristic method (in-house software), the finite-element method (ANSYS, ABAQUS) and the

6

finite-volume method (OpenFOAM). The numerical simulations were carried out with the available at the laboratory personal computers and small high-performance computer systems (up to 12 CPU cores).

The validity of the research results is ensured by the usage of well-known and verified mechanical and mathematical models and numerical methods. The reliability is further confirmed by the direct comparison with ones obtained by the available open-source and commercial software (ANSYS, ABAQUS, OpenFOAM). Also, good agreement with the experiment results published by other researchers was achieved.

Personal Contribution. All results presented in the dissertation were obtained personally by the author. All included in the thesis numerical solutions of the considered mechanical problems were obtained directly by the applicant himself. The original text was written independently. The research direction was formulated with the assistance of the scientific advisor.

Statements to be Defended.

1) The numerical algorithm for the fatigue fracturing process calculation during the cycling loading based on the single loading cycle full-wave simulation by the grid-characteristic method on overlapping grids combined with the multi-mode continual damage model was constructed and the research software was developed.

2) The numerical solutions of the metal plate fatigue fracturing problems with different geometry and number of holes under high-cycle and very-high-cycle stretch and shear loadings were obtained.

3) Single-parameter computational model, reproducing the experimental data of low-energy steel ball - ice plate interaction, was derived, based on the series of computational experiments.

Presentations at Conferences. The candidate's involvement in the following conferences is noteworthy:

1) "32nd International Scientific Conference for Undergraduate and Postgraduate Students and Young Scientists (LOMONOSOV)", Moscow, Russia, 11-25 April 2025;

2) "67th All-Russian Scientific Conference of MIPT", Dolgoprudny, Russia, 31 March - 5 April 2025;

3) "Marchukovsky Readings-2024", Novosibirsk, Russia, 7-11 October 2024;

4) "66th All-Russian Scientific Conference of MIPT", Dolgoprudny, Russia, 1-6 April 2024;

5) "65th All-Russian Scientific Conference MIPT in honor of the 115th anniversary L.D. Landau", Dolgoprudny, Russia, 3-6 April 2023;

6) VI All-Russian conference with international participation "POLAR MECHANICS", Nizhniy Novgorod, Russia, 23-24 March 2023;

7) International Conference "Numerical Methods and Experimental Techniques for Sustainable and Disaster Resilient Infrastructure", Indore, India, 8-9 September 2023.

Publications. The publications in peer-reviewed scientific journals also support the credibility of research results. The dissertation materials were published in 8 works, including 1 paper in Q2 journal indexed by Scopus, 4 extended abstracts at international conferences. In 4 publications, the author of the dissertation is the first author.

The volume and structure of the work. The dissertation consists of an introduction, 4 chapters, conclusion, acknowledgments, lists of figures, tables. The full thesis' volume is 105 pages, including 50 figures and 10 tables. The list of references consists of 130 sources.

Chapter 1. Literature Review

The use of modeling and simulation is an increasingly powerful method in the modern era. The process begins with the construction of a mathematical model, followed by the execution of simulations and the interpretation of the results. The process ends with the conclusion of the experiment [1]. It is imperative to distinguish between the terms "modeling" and "simulation". Modeling involves the development of a model using software or mathematical equations, while simulation entails the execution of the numerical experiment on the chosen model. Figure 1.1 provides an illustration of the modeling and simulation process.

In the current research, two different mechanical problems are considered. In the first one, the fatigue fracturing process of the metal plate with the given hole shape under cycling loading is investigated. Even though initially the plate is treated as isotropic homogeneous medium, after the destruction initiation it transforms into a heterogeneous object. In the second one, the low-energy impact of metal ball on the ice plate is investigated. For the sake of simplicity, in the current research the ice treated in homogeneous approximation. However, a more complex loading mode of the ice should be simulated, considering its inhomogeneous internal structure too. Thus, in both cases, the heterogeneity of the materials plays an important role.

Заключение диссертации по теме «Другие cпециальности», Халид Валид

Conclusion

This work was devoted to the numerical simulation of the dynamic deformation process of heterogeneous media. The well-tested grid-characteristic method on structured numerical grids was used. The highly practical important problem of fatigue fracturing was considered. The thin metal plate under high-frequency and very-high-frequency loadings (with first kHz frequency) was investigated. The application of the overlapping structured grids approach to the integration domain description led to the correct and straightforward procedure of holes with different shapes incorporation. The multimode continual model based on the kinetic equation for the additional damage function was combined with the full-wave simulation of the loading cycle. This proved to be feasible for the description of the fatigue fracturing process and its development over cycles. The implemented numerical procedure was successfully applied to obtain numerical solutions of multiple applied problems. Also, the low-energy metal ball - ice plate interaction was considered. The formulated goal was to present the simple mode, that fits good enough known experimental data. The commercial software ABAQUS was utilized to simulate this direct collision problem. Based on these results, a single-parameter model for the ice deformation simulations was proposed and calibrated.

The following are the main results of this research:

1) The novel numerical algorithm for the fatigue fracturing simulation of a given metal specimen with possible multiple holes of complex geometries was proposed and implemented. It is based on the full-wave simulation of single loading cycle by the grid-characteristic method on structured grids. To incorporate the hole, the overlapping grids approach was utilized. Further, the multi-mode continual model, based on the kinetic equation for the additional damage function, was used.

2) This numerical procedure was successfully tested on open-source and commercial software (ANSYS, OpenFOAM) for static and dynamic treatment of a single loading cycle. Multiple applied problems were numerically solved.

3) Based on the series of computational experiments, carried out with the usage of the commercial software ABAQUS, the simple mechanical model for the ice dynamic description in the case of the low-energy interaction was formulated and tuned.

It should be noticed that the prominent directions of further research may be pointed out. Firstly, different mechanisms of fracturing may be considered and incorporated into the model. For example, to

describe the development of shear-type microcracks, the CVS (Carpinteri-Spagnoli-Vantadori) criterion is often used. Secondly, the fatigue failure model can be regularized with the normalized delocalization operator to eliminate the mesh element size influence on the destruction process. Thirdly, instead of the variation of the yield stress value for the ice elastoplastic model, the diving the whole ice specimen into number of regions with different rheologies may be utilized.

Список литературы диссертационного исследования кандидат наук Халид Валид, 2025 год

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