Alexander M. Linkov

Office Address

Institute for Problems in Mechanical Engineering
Russian Academy of Sciences (IPME RAS)

V.O., Bol'shoy Pr., 61, St.Petersburg 199178, Russia
Tel.: +7-812-3214774; Fax: +7-812-2696171
E-mail: voknilal@hotmail.com





Current Positions

1993 - Present

Chief Scientist, Department of Mathematical Methods in Mechanics of Materials and Structures, Laboratory of Numerical Models in Mechanics of Materials and Structures, Institute for Problems in Mechanical Engineering of Russian Academy of Science







Academic Degrees

• Doctor of Sciences, Physics and Mathematics, 1977
  Leningrad State University, Leningrad, USSR
  
• Ph.D., Physics and Mathematics, 1969
  Leningrad State University, Leningrad, USSR
  
• M.Sc., Mechanical Engineering, 1963
  Leningrad State Mechanical Institute, Leningrad, USSR

Specialization

(i) main field: solid, fracture and computational mechanics;
(ii) other fields: fluid dynamics, integral equations;
(iii) current research interests: micromechanics, homogenization problem, hypersingular equations, singular points, blocky and layered systems, fracture propagation, synthetic seismicity, hydraulic fractures

Honours, Awards

Silver Medal - Leningrad secondary school No 155, 1957, Leningrad (USSR)
Cum laude - Leningrad State Mechanical Institute, 1963, Leningrad (USSR
Prizes and Diplomas - Sci. and Tech. Soc., 1975 - 1982, Leningrad (USSR)
Russian State Stipend to Outstanding Scientists - 1995 - 1996, Russia
MTS Honourable Visiting Professor - University of Minnesota (USA); 1992, 2002
International Schlumberger Award for Fundamental Researches in Rock Mechanics - International Society for Rock Mechanics; 1994
Visiting Professor - University of Minnesota (USA) 1994, 1997; Colorado School of Mines (USA), 1997
Invited Researcher - INERIS, France, 1996, 1997, 2000
Invited Researcher - CSIR, South Africa 1996, 1997
Visiting Fellowship - Gledden Visiting Senior Fellowship, Australia, 1999
Prize of the Journal of Applied Mathematics and Mechanics (Russian Academy of Sciences) for the best paper published in 1999, Russia, 2000
Salamon Award - SANIRO, South Africa, 2002
Marie Curie Professorship - University of Liverpool (UK), 2005
Honoured Scientist of the Russian Federation - Award by the President of the Russian Federation, 2008

Key-Note Addresses

4-th South American Congress on Applied Rock Mechanics (1994, Santiago-de-Chile, Chile): Key-note address "Rockbursts and Dynamic Phenomena in Mines".
1-st North American Rock Mechanics Symposium (1994, Austin, USA): Key-note address "Rockbursts and Instability of Rock Masses".
8-th Int. Congress on Rock Mechanics (1995, Tokyo, Japan): Key-note address "Equilibrium and Stability of Rock Masses".
1st Australasian Congress on Applied Mechanics, ACAM-96 (1996, Melbourne, Australia): Key-note address "Computational Mechanics; Subject and Problems".
4-th Int. Symposium on Rockbursts and Seismicity in Mines (1997, Krakow, Poland):Key-note address "New Geomechanical Approaches to Develop Quantitative Seismicity".
Int. Conference in Memory of Professor Neville Cook (1998, Berkeley, USA); Key-note address "Wave Amplification on Softening Surfaces".
20-th Int. Conference on Mathematical Modeling in Mechanics of Solids and Constructions (2003, St-Petersburg, Russia): Key-note address "Hypersingular BIE and BEM in Computational Mechanics".
29-th Summer School-Conference on Advanced Problems of Mechanics APM-2004 (2004, Repino, Russia): Key-note address "In Memory of Professor Lazar Kachanov".

Discovery

Discovery No 337 "Regularity of underground fracture of rocks", 1988, State Committee on Discoveries, USSR

Teaching Courses

• Selected problems of mathematics lecture course for PhD students of mechanical and airplane engineering
• Basics of continuum mechanics lecture course for PhD students of mechanical and airplane engineering

Membership in Professional Societies

• M. of St.-Petersburg Scientific Society (Russian Academy of Sciences)
• M. of Int. Assoc. for Boundary Element Method
• M. of the American Geophysical Union
• M. of New York Academy of Sciences
• M. of Society of Petroleum Engineers

Grants

• Grant of the International Science Foundation by George Soros in support of Russian scientists, 1994.
• Investigation of the Constitution Properties of Fluid Saturated Poorly Consolidated Rock (Civilian Research & Development Foundation, CRDF, 1999-2000, No RG0-821, head of project)
• Investigation of time processes prior and during dynamic phenomena, 1997-1999 (Russian Foundation for Basic Research, No 97-05-64191, head of project)
• Investigation of fracture amplification in time near openings and faults, 2000-2002 (Russian Foundation for Basic Research, No 00-05-64316, head of project)
• Elaboration of the theoretical and computational basis for joining geomechanical numerical simulation and seismic monitoring of dynamic phenomena in rock, 2003-2005 (Russian Foundation for Basic Research, No 03-05-64888, head of project)
• Theory and new methods for assessment and control of rock state and fluids fluxes in oil and gas production, 2006-2008 (Russian Foundation for Basic Research, No 06-05-64089, head of project)
• Computational micromechanics methods for characterizing effective properties and the strength of micro-heterogeneous materials, 2006-2008 (Russian Foundation for Basic Research, No 06-01-00107, team member)
• Theory and enhanced methods for interpretation of microseismic and geodesic data in oil, gas and geothermal heat production, 2009-2011 (Russian Foundation for Basic Research, No 09-05-00104, head of project)
• Enhancing hydraulic fracturing on the basis of numerical simulation of coupled geomechanical, hydrodynamic and microseismic processes, 2010-2014 (EU Marie Curie Industry-Academia Partnerships and Pathways Program FP7-PEOPLE-2009-IAPP, "HYDROFRAC", scientific leader of the Polish-Russian team)

Publications

The list of publications counts 9 books and over 300 scientific papers.


Selected Monographs


1. Petukhov I. M., Linkov A. M. et al. The Theory of Protective Seams.- Moscow, Nedra Publ. House, 1976. 224 p. (In Russian)
2. Petukhov I. M., Linkov A.M. Mechanics of Rockbursts and Outbursts. - Moscow, Nedra Publishing House, 1983, 280p. (in Russian).
3. Linkov A. M. Dynamic Phenomena in Mines and the Problem of Stability. Int. Soc. Rock Mech., Lisboa, Cedex, Portugal, 1994. 133 p.
4. Linkov A. M. Complex Variable Boundary Integral Equations of Elasticity Theory. Saint-Petersburg, Nauka, 1999. 382 p. (In Russian).
5. Linkov A. M. Boundary Integral Equations in Elasticity Theory. Dordrecht-Boston-London, Kluwer Academic Publishers, 2002. 268 p.
6. Linkov A.M., Mishuris G., Rybarska-Rusinek L. Selected Topics of Mathematics for Engineers. Oficyna Wydawnicza Politechiki Rzeszowskiey, Rzeszow, 2014, 186 p


Selected papers



1. Linkov A. M. Integral equations of elasticity for a plane with slits loaded by equilibrated forces. Proc. Acad. Sci. USSR, 1974, 218, 1294-1297 (in Russian; translated into English in "Soviet Physics. Doklady").
2. Amusin B. Z., Linkov A. M. On applying variable modulus for one class of viscoelastic problems. Notes Acad. Sci. USSR. Mech. of Solids, 1974, N? 6, 162-166 (in Russian; translated into English in "Solid Mechanics").
3. Linkov A.M. On stability conditions in fracture mechanics. Proc. Acad. Sci.USSR, 1977, 233 (1), 45-48 (in Russian; translated into English in "Soviet Physics. Doklady").
4. Petukhov I. M., Linkov A. M. The theory of post-failure deformations and the problem of stability in rock mechanics. Int. J. Rock Mech. Mining Sci. & Geomech. Abstr., 1979, 16 (2), 57-76.
5. Linkov A.M. Plane problems for static loading of piece-wise homogeneous linear-elastic media. Notes Acad. Sci. USSR. Applied Math. Mech., 1983, 47 (1), 644-651 (in Russian; translated into English in "Applied Math. and Mech.").
6. Linkov A. M., Mogilevskaya S. G. Finite-part integrals in problems of three-dimensional cracks. Notes Acad. Sci.USSR. Applied Math. Mech., 1986, 50 (5), 841-850 (in Russian; translated into English: Journal of Applied Mathematics and Mechanics, 1986, 50 (5), 652-658).
7. Zubkov V. V., Linkov A. M. Boundary integral equations of fluid flow, electrical and heat conduction in a medium composed of blocks. Notes Acad. Sci. USSR. Mechanics of Liquids and Gases, 1986, N 6, 72-78 (in Russian; translated into English in "Fluid Mechanics").
8. Linkov A.M. Stability of inelastic, geometrically nonlinear, discrete systems. Proc. Acad. Sci.USSR, 1987, 294 (1), 44-47 (in Russian; translated into English in "Soviet Physics. Doklady").
9. Linkov A. M., Khodyrev E. D. On sources of hereditary type in transfer problems. Proc. Acad. Sci.USSR, 1988, 302 (2), 280-283 (in Russian; translated into English in "Soviet Physics. Doklady").
10. Linkov A. M., Khodyrev E. D. Model of flow through porous media with sources of hereditary type.- Notes Acad. Sci. USSR. Mechanics of Liquids and Gases, 1989, N 3, 174-177 (in Russian; translated into English in "Fluid Mechanics").
11. Linkov A. M., Mogilevskaya S. G. Hypersingular integrals in plane problems of elasticity. Notes Acad. Sci. USSR. Applied Math. Mech., 1990, 54 (1), 116-122 (in Russian; translated into English in "Applied Math. and Mech.").
12. Linkov A.M. Asymptotic relations, fracture acceleration and subcritical crack growth under creep. Proc. Acad. Sci. USSR, 1991, 319 (3), 280-283 (in Russian; translated into English in "Soviet Physics. Doklady").
13. Linkov A. M., Filippov N. A. Difference equations approach to the analysis of layered systems. Meccanica, 26, 195-209.
14. Linkov A.M.. Boundary value problem for crack growth in viscoelastic media. Int. J. Fracture, 1994, 65, 197-218.
15. Linkov A. M., Mogilevskaya S. G. Complex hypersingular integrals and integral equations in plane elasticity. Acta Mechanica, 1994, 105, 189-205.
16. Linkov A. M., Linkova A. A., Savitski A. A. An effective method for multi-layered media with cracks and cavities. Int. J. Damage Mech., 1994, 3 (4), 338-356.
17. Blinova V. G., Linkov A. M. A method to find asymptotic forms at the common apex of elastic wedges. J. Appl. Math. Mech., 1995, 59 (2), 187-195.
18. Linkov A.M. Rockbursts and instability of rock masses. Int. J. Rock Mech. Mining Sci. & Geomech. Abstr., 1996, 33, 727-732.
19. Linkov A.M. Elasticity problems involving coupled half-planes. J. Appl. Mech., 1999, 63(6), 927-938.
20. Linkov A. M., Koshelev V. F. Complex variables BIE and BEM for a plane doubly periodic system of flaws, Journal of the Chinese Institute of Engineers, 1999, 22 (6), 709-720.
21. Linkov A.M. Instability, fracture acceleration and wave amplification. Int. J. Rock Mech. Min. Sci., 2000, 37, 31-37.
22. Al Heib M., Linkov A. M., Zoubkov V. V. . On numerical modeling of subsidence induced by mining. Proc. Int. Symp. "EUROCK-2001: Rock Mechanics - a Challenge for Society ". Sarkka & Floranta (eds). Swets&Zeitinger Lisse. 2001, 795-799.
23. Linkov A.M. The complex variable hypersingular BIE of thermoelasticity for plane inhomogeneous bodies with cracks and cavities. Proc. Int. Conference "Mathematical Problems of Mechanics of Non-homogenous Structures". G. S. Kit (ed.). National Academy of Sciences of Ukraine, Lvov, 2003, 250-252.
24. Linkov A. M., Zoubkov V. V. On numerical modeling of multi-layered structures. Proc. XX International Conference "Mathematical Modeling in Solid Mechanics. Boundary & Finite Elements Methods". V. A. Postnov (ed.). St-Petersburg, 2003, 71-76.
25. De Bremaecker, J.-Cl., Ferris M. C., Linkov A. M. Including gravity in the Displacement Discontinuity Method when accounting for contact interaction. Int. J. Rock. Mech. Mining Sci., 2004, 41 (6), 1043-1044.
26. Linkov A.M. The size of the end zone and the propagation velocity of a displacement jump. Journal of Applied Mathematics and Mechanics, 2005, 69, 135-140 (Translation from Russian: Линьков А. М. О размере концевой зоны и скорости распространения разрыва смещений. Прикладная математика и механика, ПММ, 2005, 69, No 1, 144-149).
27. Linkov A.M. Numerical modeling of seismic and aseismic events in geomechanics. Journal of Mining Science, 2005, 41 (1), 14-26 (Translation from Russian: Линьков А. М. Численное моделирование сейсмических и асейсмических событий в геомеханике. Физико-технические проблемы разработки полезных ископаемых, ФТПРПИ, 2005, 1: 19-33).
28. Linkov A.M. Numerical modeling of seismic and aseismic events in geomechanics. Journal of Mining Science, 2005, 41 (1), 14-26 (Translation from Russian: Линьков А. М. Численное моделирование сейсмических и асейсмических событий в геомеханике. Физико-технические проблемы разработки полезных ископаемых, ФТПРПИ, 2005, 1: 19-33).
29. Dobroskok A. A., Ghassemi A., Linkov A. M Extended structural criterion for numerical simulation of crack propagation under compressive loads. Int. J. Fracture, 2005, 133, 223-246.
30. Dobroskok A., Ghassemi A., Linkov A. Numerical simulation of crack propagation influenced by thermal and porous liquid stresses. Int. J. Fracture, 2005, 134, L29-L34.
31. Linkov A.M. Response to the paper by Y. Z. Chen "Singular integral equation method for the solution of multiple curved crack problems" (Int. J. Solids and Structures, 2004, 41, 3505-3519). Int. J. Solids and Structures, 2005, 42, 6514-6516.
32. Linkov A. M., Koshelev V. F. Multi-wedge points and multi-wedge elements in computational mechanics: evaluation of exponent and angular distribution. Int. J. Solids and Structures, 2006, 43, 5909-5930.
33. Linkov A.M. A theory of rupture pulse on softening interface with application to the Chi-Chi earthquake. Journal of Geophysical Research, 2006, 111, No B09307, 1-14.
34. Linkov A.M. Numerical modeling of seismic and aseismic events in three-dimensional problems of rock mechanics. Journal of Mining Science, 2006, 42 (1), 1-14. (Translation from Russian: Линьков А. М. О численном моделировании сейсмических и асейсмических событий в трехмерных задачах геомеханики. Физико-технические проблемы разработки полезных ископаемых, ФТПРПИ, 2006, 1: 3-16.)
35. Zubkov V. V., Koshelev V. F., Linkov A. M. Numerical modeling of hydraulic fracture initiation and development. Journal of Mining Science, 2007, 43 (1), 40-56. (Translation from Russian: Зубков В.В., Кошелев В. Ф., Линьков А. М. Численное моделирование инициирования и роста трещин гидроразрыва. Физико-технические проблемы разработки полезных ископаемых, ФТПРПИ, 2007, 1: 45-63.)
36. Dobroskok A., Fradkin L., Linkov A., Mishuris G. Crack redirection with thermal secondary loading. Eng. Fracture Mech., 2007, 74, 1719-1726.
37. Linkov A., Rybarska-Rusinek L. Numerical method and models for anti-plane strain of a system with a thin elastic wedge. Arch. Appl. Mech., 2008, 78, 821-831.
38. Linkov A.M. Numerical simulation of fluid flow and a hydraulically induced fracture propagation, Journal of Mining Science, 2008, 44 (1), 24-42 (Translation from Russian: Линьков А. М. Численное моделирование течения жидкости и продвижения трещины гидроразрыва. Физико-технические проблемы разработки полезных ископаемых, ФТПРПИ, 2008, 1: 26-46).
39. Dobroskok A. A., Linkov A. M. Complex variable equations and numerical solution of harmonic problems for piece-wise homogeneous media. Journal of Applied Mathematics and Mechanics, 2009, 73 (3), 313-325 (Translation from Russian: Доброскок А. А., Линьков А. М. Комплексные уравнения и численное решение гармонических задач для кусочно-однородных сред. Прикладная математика и механика, ПММ, 2009, 73 (3): 439-458).
40. Linkov A. M., Szynal-Liana A. CV circular-arc ordinary and (multi-) wedge elements for harmonic problems. Engineering Analysis with Boundary Elements, 2009, 33, 611-617.
41. Dobroskok A. A., Linkov A. M. CV dual reciprocity BEM for transient flow in blocky systems with singular points and lines of discontinuities. Engineering Analysis with Boundary Elements, 2010, 34 (3), 238-247.
42. Dobroskok A., Linkov A. CV BEM for transient poro-(thermo-) elastic problems concerning with blocky systems with singular points and lines of discontinuities. Int. Journal of Engineering Science. 2010, 48, 658-669.
43. Dobroskok A., Linkov A., Zoubkov V. V On joint geomechanical and geophysical monitoring in mines. Journal of Mining Science, 2010, 46 (1), 13-20 (Translation from Russian: Доброскок А. А., Линьков А. М., Зубков В. В. О совместном геомеханическом и геофизическом мониторинге на шахтах и рудниках. Физико-технические проблемы разработки полезных ископаемых, ФТПРПИ, 2010, 1: 16-24).
44. Linkov A. The end zone of a shear crack propagating at an intersonic velocity. Journal of Applied Mathematics and Mechanics, 2010, 74 (2), 223-231 (Translation from Russian: Линьков А. М. О концевой зоне сдвиговой трещины, распространяющейся с межзвуковой скоростью. Прикладная математика и механика, ПММ, 2010, 74 (2), 311-323).
45. Linkov A., Rybarska-Rusinek L. Plane elasticity problem for a multi-wedge system with a thin wedge. Int. J. Solids and Structures, 2010, 47, 3297-3304
46. Koshelev V. F., Linkov A. M. Numerical modelling of regular systems with randomly perturbed structural elements. Journal of Applied Mathematics and Mechanics, 2010, 74, 6, 735-744 (Translation from Russian: Кошелев В. Ф., Линьков А. М. Численное моделирование структур со случайно возмущенными структурными элементами. Прикладная математика и механика, ПММ, 2010, 74 (6), 1053-1067).
47. Linkov A. Loss of stability, characteristic length and Novozhilov-Neuber criterion in fracture mechanics. Mechanics of Solids, 2010, No 6, 844-854 (Translation from Russian: Линьков А. М. Потеря устойчивости, характерный линейный размер и критерий Новожилова-Нейбера в механике разрушения. Механика твердого тела, МТТ, 2010, 6: 98-111).
48. Dobroskok A. A., Linkov A. M. Modeling of fluid flow, stress state and seismicity induced in rock by instant pressure drop in a hydrofracture. Journal of Mining Science, 2011, 47 (1), 10-19 (Translation from Russian: Доброскок А. А., Линьков А. М. Моделирование течения, напряженного состояния и сейсмических событий в породах при сбросе давления в трещине гидроразрыва, ФТПРПИ, 2011, 1: 12-22).
49. Linkov A. Speed equation and its application for solving ill-posed problem of hydraulic fracturing. Doklady Physics, 2011, 56 (8), 436-438 (Translation from Russian: Линьков А. М. Уравнение скорости и его применение для решения некорректных задач о гидроразрыве. Доклады Академии наук, 2011, 439 (4), 473-475).
50. Linkov A., Rybarska-Rusinek L. Interface conditions simulating influence of a thin elastic wedge with smooth contacts. Arch. Appl. Mech., 2011, 81, 1203-1214
51. Linkov A. On efficient simulation of hydraulic fracturing in terms of particle velocity. Int. J. of Engineering Science, 2012, 52, 77-88.
52. Linkov A., Rybarska-Rusinek L. Evaluation of stress concentration in multi-wedge systemswith functionally graded wedges. Int. J. Eng. Sci., 2012, 61, 87-93
53. Mishuris G., Wrobel M., Linkov A. On modeling hydraulic fracture in proper variables : stiffness, accuracy, sensitivity. Int. J. Eng. Sci., 2012, 61, 10-23.
54. Linkov A. M. On efficient simulation of hydraulic fracturing in terms of particle velocity. Int. J. Eng. Sci., 2012, 52, 77-88.
55. Linkov A. M. Analytical solution of hydraulic fracture problem for a non-Newtonian fluid. Journal of Mining Science, 2013, 49(1), 8-18.
56. Rejwer, E., RybarskavRusinek, L., Linkov, A. а.(2014) The complex variable fast multipole boundary element method for the analysis of strongly inhomogeneous media. Engineering Analysis with Boundary Elements, 43, 105v106. DOI: 10.1016/j.enganabound.2014.04.001 (link)
57. Linkov, A.M. (2014) On comparison of thinning fluids used for hydraulic fracturing. International Journal of Engineering Science, 77, 14v23. DOI: 10.1016/j.ijengsci.2013.12.005 (link)
58. Jaworski, D., Linkov, A., RybarskavRusinek, L. (2015) A Note on Evaluation of Temporal Derivative of Hypersingular Integrals over Open Surface with Propagating Contour. Journal of Elasticity, 120 (1), 121v128. DOI: 10.1007/s10659v014v9499v9 (link)
59. Kuzkin, V.A., Krivtsov, A.M., Linkov, A.M. (2014) Computer simulation of effective viscosity of fluidvproppant mixture used in hydraulic fracturing. Journal of Mining Science, 50 (1), 1v9. DOI: 10.1134/S1062739114010013 (link)
60. Kuzkin, V.A., Krivtsov, A.M., Linkov, A.M. (2014) Comparative study of rheological properties of suspensions by computer simulation of Poiseuille and Couette flows. Journal of Mining Science, 50 (6), 1017v1025. DOI: 10.1134/S1062739114060039 (link)
61. Linkov, A.M. (2015) The particle velocity, speed equation and universal asymptotics for the efficient modelling of hydraulic fractures. Journal of Applied Mathematics and Mechanics, 79 (1), 54v63. DOI: 10.1016/j.jappmathmech.2015.04.018 (link)
62. Jaworski, D., Linkov, A., RybarskavRusinek, L. (2015) On solving 3D elasticity problems for inhomogeneous region with cracks, pores and inclusions. Computers and Geotechnics, 71, 295v309. DOI: 10.1016/j.compgeo.2015.04.017 (link)
63. Линьков А.М. (2016) Численное решение плоской задачи о гидроразрыве в модифицированной постановке при произвольных начальных условиях //Физико-технические проблемы разработки полезных ископаемых. 2016, 2:48-56. 0
64. Линьков А.М. (2016) Решение осесимметричной задачи о гидроразрыве для утончающихся жидкостей //Прикладная математика и механика. 2016, 2:207-217.



---