scholarly journals Application of mathematical fracture models to simulation of exploration seismology problems by the grid-characteristic method

2019 ◽  
Vol 11 (6) ◽  
pp. 1077-1082
Author(s):  
Maksim Viktorovich Muratov ◽  
I. B. Petrov
2021 ◽  
Vol 13 (1) ◽  
pp. 71-78
Author(s):  
Maxim V. Muratov ◽  
◽  
Polina V. Stognii ◽  
Igor B. Petrov ◽  
Alexey A. Anisimov ◽  
...  

The article is devoted to the study of the propagation of elastic waves in a fractured seismic medium by methods of mathematical modeling. The results obtained during it are compared with the results of physical modeling on similar models. For mathematical modeling, the grid-characteristic method with hybrid schemes of 1-3 orders with approximation on structural rectangular grids is used. The ability to specify inhomogeneities (fractures) of various complex shapes and spatial orientations has been implemented. The description of the developed mathematical models of fractures, which can be used for the numerical solution of exploration seismology problems, is given. The developed models are based on the concept of an infinitely thin fracture, the size of the opening of which does not affect the wave processes in the fracture area. In this model, fractures are represented by boundaries and contact boundaries with different conditions on their surfaces. This approach significantly reduces the need for computational resources by eliminating the need to define a mesh inside the fracture. On the other hand, it allows you to specify in detail the shape of fractures in the integration domain, therefore, using the considered approach, one can observe qualitatively new effects, such as the formation of diffracted waves and a multiphase wavefront due to multiple reflections between the surfaces, which are inaccessible for observation when using effective fracture models actively used in computational seismic. The obtained results of mathematical modeling were verified by physical modeling methods, and a good agreement was obtained.


2015 ◽  
Vol 7 (4) ◽  
pp. 875-887 ◽  
Author(s):  
I. B. Petrov ◽  
Maksim Viktorovich Muratov ◽  
Alena Vladimirovna Favorskaya ◽  
Vladimir Aleksandrovich Biryukov ◽  
A. V. Sannikov

2016 ◽  
Vol 58 (9) ◽  
pp. 788-793 ◽  
Author(s):  
İsmail Yasin Sülü ◽  
Apdulmutalip Şahinaslan

Materials ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3657
Author(s):  
Alexander E. Wilson-Heid ◽  
Erik T. Furton ◽  
Allison M. Beese

This study investigates the disparate impact of internal pores on the fracture behavior of two metal alloys fabricated via laser powder bed fusion (L-PBF) additive manufacturing (AM)—316L stainless steel and Ti-6Al-4V. Data from mechanical tests over a range of stress states for dense samples and those with intentionally introduced penny-shaped pores of various diameters were used to contrast the combined impact of pore size and stress state on the fracture behavior of these two materials. The fracture data were used to calibrate and compare multiple fracture models (Mohr-Coulomb, Hosford-Coulomb, and maximum stress criteria), with results compared in equivalent stress (versus stress triaxiality and Lode angle) space, as well as in their conversions to equivalent strain space. For L-PBF 316L, the strain-based fracture models captured the stress state dependent failure behavior up to the largest pore size studied (2400 µm diameter, 16% cross-sectional area of gauge region), while for L-PBF Ti-6Al-4V, the stress-based fracture models better captured the change in failure behavior with pore size up to the largest pore size studied. This difference can be attributed to the relatively high ductility of 316L stainless steel, for which all samples underwent significant plastic deformation prior to failure, contrasted with the relatively low ductility of Ti-6Al-4V, for which, with increasing pore size, the displacement to failure was dominated by elastic deformation.


Author(s):  
Meng Fan ◽  
Yan Jin ◽  
Thomas Wick

AbstractIn this work, we develop a mixed-mode phase-field fracture model employing a parallel-adaptive quasi-monolithic framework. In nature, failure of rocks and rock-like materials is usually accompanied by the propagation of mixed-mode fractures. To address this aspect, some recent studies have incorporated mixed-mode fracture propagation criteria to classical phase-field fracture models, and new energy splitting methods were proposed to split the total crack driving energy into mode-I and mode-II parts. As extension in this work, a splitting method for masonry-like materials is modified and incorporated into the mixed-mode phase-field fracture model. A robust, accurate and efficient parallel-adaptive quasi-monolithic framework serves as basis for the implementation of our new model. Three numerical tests are carried out, and the results of the new model are compared to those of existing models, demonstrating the numerical robustness and physical soundness of the new model. In total, six models are computationally analyzed and compared.


Author(s):  
Noriko Ishida

AbstractThe fact that Veblen was a keen critic of the neo-classical concept of “economic man” is well known. However, the following issues have not been discussed in enough depth: how he rebuilt the traditional theory of human nature through his new methodology of economics, how much his methodological revision broadened the scope of economics, and what kind of phenomena Veblen’s economic theory elucidates. This article examines these issues and aims to show the logical connection between Veblen’s controversial proposal on the methodology of economics and his analysis of economic phenomena. Specifically, it reconsiders Veblen’s analysis of economic action using a unique concept of instincts, his logic of explaining the relation between society and human nature, his way of drawing history from the relativistic worldview, and his characteristic method of grasping the cause and effect of economic phenomena. Finally, it highlights the importance of modifying the concept of “economic man” by focusing on the qualitative aspect. Particular reference is made to the economic concepts of utility, efficiency, and intangibility.


2016 ◽  
Vol 47 (11) ◽  
pp. 5302-5312 ◽  
Author(s):  
František Šebek ◽  
Petr Kubík ◽  
Jindřich Petruška ◽  
Jiří Hůlka

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