List of publications

Books:

1. Co-editor and major contributor to

Topics in the mathematical modeling of composite materials, A.Cherkaev and R. Kohn editors, Birkhausen, NY, 1997.
2. A. Cherkaev. Variational methods for structural optimization. Springer Verlag NY 2000

Patent:

A. Cherkaev. A.Melnic, T.Romanova, I.Poljakova, A.Mjagy. Dynamic head of loud-speaker.- Author's certificate N1304177 of 12.15.1986. (in Russian)

Papers (in the chronological order):

1. K. Lurie, A. Cherkaev. On applying Prager`s theorem to the problems of optimal design of thin plates. - Mechanics of Solids (Izv. Acad. Sci. USSR, MTT), 1976, N.6, pp. 157-159.
2. A. Cherkaev. On the problem of formulating the problem of optimal design of freely oscillating structures.- PMM (J. Appl. Math. and Mech.), 1978, 42, N.1, pp. 194-197.
3. J.-L.Armand, K.Lurie, A. Cherkaev. On solution of problems of optimization of eigenvalues in designing elastic constructions. - Mechanics of Solids (Izv. Acad. Sci. USSR, MTT), 1978.
4. K.Lurie, A.Cherkaev. Inhomogeneous bar of extremal torsion rigidity.- in: Nonlinear problems of engineering mechanics. Optimization of constructions, Kiev, 1978. pp. 80-89. (in Russian)
• the note "in Russian" means that there is no English translation available.
5. Yu.Bulatov, A.Cherkaev. On the optimal form of an axis of an elastic curved bar. - in: Methods and facilities of mathematical modeling, Alma-Ata, pp. 87-93. (in Russian)
6. A. Cherkaev. Some problems of optimal design of elements of elastic structures. - Ph.D. Thesis, 130p., 1979. (in Russian)
7. N.Lavrov, K.Lurie, A.Cherkaev. Inhomogeneous bar of extremal torsion rigidity. - Mechanics of Solids (Izv. Acad. Sci.), 1980, N.6.
8. K.Lurie, A.Fedorov, A.Cherkaev. On limiting facilities of design of elastic plates. - Proceedings of XII Soviet Conference on theory plates and shells, Yerevan, 1980, v. 3, pp. 25-30. (in Russian)
9. K.Lurie, A.Fedorov, A.Cherkaev. Regularization of optimal problems of design of bars and plates and solving the contradictions in a system of necessary conditions of optimality. J. Opt. Theory Appl. , 1982, v. 37, N. 4, pp. 499-522 (part 1), 523-542 (part 2).
* The preliminary version of two parts of the last paper has been earlier published separately in Russian as:
• Regularization of optimal problems of design of bars and plates and solving the contradictions in a system of necessary conditions of optimality. - Report N. 667, Physical Technical. Inst. Acad. Sci. USSR, 1980, 60 pp. (in Russian)
• On existence of the solutions of some problems of optimal design of bars and plates.- Report N. 668, Physical Technical. Inst. Acad. Sci. USSR., 1980, 43 pp. (in Russian)
10. N.Olhoff, K.Lurie, A.Fedorov, A. Cherkaev. Sliding regimes and anisotropy in optimal design of vibrating axisymmetric plates. Int. J. of Solids and Structures, 1981, 17, No. 10, pp. 931-948.
* Preliminary version has been published as:
• Report N. 192, The Technical University of Denmark, 1980, 34 pp.
11. K.Lurie, A. Cherkaev. Editor's supplement to the Russian translation of the book by N.Olhoff ``Optimal design of elastic construction elements (problems of vibration and loss of stability)" M. Mir, 1981. 16p. (in Russian).
12. K.Lurie, A. Cherkaev. Exact estimates of conductivity of mixtures composed of two materials taken in prescribed proportion (plane problem).- Doklady Akademii Nauk SSSR, 1982, 264, N.5, pp. 1128-1130.
13. K.Lurie, A. Cherkaev. Exact estimates of conductivity of mixtures composed of two isotropic media taken in prescribed proportion. Proceed. Roy. Soc. Edinburgh, sect. A, 1984, 99 (P1-2), pp. 71-87.
* First has been published in Russian in 1982 :
• K.Lurie, A. Cherkaev. Report 783, Physical Technical. Inst. Acad. Sci. USSR, 1982, 32p. (in Russian).
14. A.Fedorov, A. Cherkaev. Choosing of optimal orientation of axes of elastic symmetry of orthotropic plate. - Mech. Solids, (Izv. Acad. Sci. USSR, MTT) ,1983, No. 3, pp. 135-142.
15. K.Lurie, A. Cherkaev. G-closure of a set of conducting media ( two-dimensional problem). - Doklady Akademii Nauk SSSR, 1981, 259, N.2, pp. 238-241.
16. K. Lurie, A. Cherkaev. G-closure of a set of anisotropic conducting media in the two-dimensional case. J. Opt. Theory Appl. , 1984, 42, N.2, pp. 283-304.
17. K.Lurie, A. Cherkaev. G-closure of some particular sets of admissible material characteristics for the problem of bending of the thin elastic plates. J. Opt. Theory Appl. , 1984, 42, N.2, pp. 305-316.
 
* First has been published as:
• Report N. 213, The Technical University of Denmark, 1981, 18 pp.; J. Opt. Theory Appl. , 1984, 42, N.2, pp. 305-316.
18. J.-L.Armand, K.Lurie, A. Cherkaev. Optimal control theory and structural design. - In: New directions in optimal structural design, H.Atreck, R.H.Gallagher, O.C.Zienkewicz eds., Wiley, 1984, pp. 211-229.
19. L.Gibiansky, A. Cherkaev. Optimal design of composite plates.- Proceedings of Soviet Conference ``Problems of reduction of specific consumption of materials of load bearing units". Gorkiy, 1984, pp. 27-28. (in Russian)
20. K.Lurie, A. Cherkaev. Exact estimates of conductivity of a binary mixture of isotropic compounds. Proceedings R. Soc. Edinburgh, sect. A, 1986, 104 (P1-2), pp. 21-38.
* First has been published in Russian as:
• Report N.894, Physical Technical. Inst. Acad. Sci. USSR, 1984, 26 pp.
21. K.Lurie, A. Cherkaev. The problem of formation of an optimal isotropic multicomponent composite. - Report No. 895, Physical Technical. Inst. Acad. Sci. USSR, 1984, 32 pp. (in Russian)
22. K.Lurie, A. Cherkaev. Optimal design of elastic bodies and the problem of regularization. - Dynamics and strength of mechanisms, 1984, No. 40/80, pp. 25-31. (in Russian)
23. K.Lurie, A. Cherkaev. Effective characteristics of composites and problems of optimal design. - Advances of mathematical sciences, 1984, v.39, N.4(238), pp. 122.
English translation in: Topics in the mathematical modeling of composite materials, A.Cherkaev and R. Kohn editors, Birkhausen, NY, 1997.
24. L. Gibiansky, A. Cherkaev. Design of composite plates of extremal rigidity.- Report 914. Physical Technical. Inst. Acad. Sci. USSR, Leningrad, 1984, 60 pp.
English translation in: Topics in the mathematical modeling of composite materials, A.Cherkaev and R. Kohn editors, Birkhausen, NY, 1997.
25. L. Gibiansky, A. Cherkaev. Exact estimates of energy of deformation of elastic composite plates; application to the problems of optimal design. - Proceedings of II Soviet ``Strength, rigidity and adaptability to manufacture structures from composite materials", Yerevan, 1984, v.1, pp. 171-176. (in Russian)
26. K. Lurie, A. Cherkaev. Method of deriving the exact estimates of effective constants of composites.- Problems of nonlinear mechanics of continuous medium, 1985, Tallinn, pp. 63-72. (in Russian)
27. S. Vigdergauz, A. Cherkaev. A hole in a plate, optimal for its biaxial extension compression.- PMM J. Appl. Math. and Mech., 1986, v.50, N.3, pp. 401-404.
28. K. Lurie, A. Cherkaev. Optimization of properties of multicomponent isotropic composites. - J. Optimization. Theory and Applications., 1985, 46, N.4, pp. 571-580.
29. L. Gibiansky, K. Lurie, A. Cherkaev. Optimum focusing of heat flux by means of a inhomogeneous heat conducting medium. - Report 305, The Technical University of Denmark, 1985. 11 pp.
30. A. Cherkaev. Relaxation of non-convex multidimensional problems by means of constructing quasi-convex envelopes.- Advances of mathematical sciences, 1986, v. 41, No. 4 (250). (in Russian)
31. L.Gibiansky, A. Cherkaev. Microstructures of composites of extremal rigidity and exact estimates of provided energy density. - Report 1115. Physical Technical. Inst. Acad. Sci. USSR, Leningrad, 1987. (in Russian) .
English translation in: Topics in the mathematical modeling of composite materials, A.Cherkaev and R. Kohn editors, Birkhausen, NY, 1997.
32. L.Gibiansky, Yu. Malinin, A. Cherkaev. Optimal Distribution of Visco-elastic Materials in axisymmetric Constructions. - Report N.1116, Physical Technical. Inst. Acad. Sci. USSR, Leningrad, 1987, 41 pp. (in Russian)
33. A. Cherkaev. A.Melnic, T.Romanova, I.Poljakova, A.Mjagy. Dynamic head of loud-speaker.- Author's certificate N1304177 of 12.15.1986. (in Russian)
34. L. Gibiansky, A. Cherkaev. Optimal design of nonlinear elastic and plastic-elastic bars under torsion. - Mechanics of solids ( Izv. Acad. Sci. USSR, MTT), 1988, N. 5, pp. 168-174.
35. K.Lurie, L.Gibiansky, A. Cherkaev. Optimal focusing of heat flow by heterogeneous heat conducting media (thermo-lens problem). - J. Tech.. Physics. (Zhurnal. Tech. Fiziki.) Acad. Sci. USSR, 1988, 58, N.1, pp. 67-74.
36. M. Avellaneda, A. Cherkaev, K. Lurie, G. Milton. On the effective conductivity of polycrystals and a 3 dimensional phase-interchange inequality.- J. Appl. Phys., 1988, 63, N.10, 4989-5003.
37. L. Gibiansky, A. Cherkaev. The set of tensor pairs of dielectric and magnetic permeabilities of two-phase composites.- Report N. 1286, Physical Technical. Inst. Acad. Sci. USSR, 1988, 51 pp. (in Russian)
38. A. Cherkaev. Optimization the structure of inhomogeneous bodies by variational methods. - Dissertation for degree ``Doctor of Physics and Mathematics". Leningrad State University, 1988. 330 pp. (in Russian)
39. K. Lurie, A. Cherkaev. On a certain variational problem of phase equilibrium. In: Material Instabilities in Continuum Mechanics and Related Mathematical Problems, ed. by J. Ball, Clarendon Press, Oxford, 1988, pp. 257-268.
40. M. Avellaneda, A. Cherkaev, K. Lurie, G. Milton. Conductivity of polycrystals and a phase interchange inequality.- Physica A, 1989, 157, N.1, pp. 148-153.
41. A. Cherkaev, L.Gibiansky, V.Serikov N. Serikova, Yu. Malinin. Membrane surface forms during local change of surface energy applications to endocytosis processes.- Biologicheskie membrany, 7, No. 3, 1990 pp. 326-334 (in Russian).
42. A. Cherkaev. On the optimization of rigidity of an elastic construction. - Proceedings of Leningrad Shipbuilding Inst. Seria ``Applied Mathematics". 1990, pp. 25-34. (in Russian)
43. A. Cherkaev, L. Gibiansky. The exact coupled bounds for effective tensors of electrical and magnetic properties of two-component two-dimensional composites. 42 pp. - Proceed. of Royal Soc. of Edinburgh, (1992) v, 122A, pp. 93-125 .
44. A. Cherkaev, L. Gibiansky. Coupled estimates for the bulk and shear moluli of a two-dimensional isotropic elastic composite. J. Mech. Pays. Solids 41 (5), 937-980, 1993.
45. A. Cherkaev, L. Gibiansky. Improving the Hashin-Strickman estimates by means of the translation method. - Proceedings of SIAM workshop in micromechanics. Leesburgh, Virginia, 1991.
46. A. Cherkaev, G.W.Milton and K.A.Lurie. Invariant properties of the stress in plane elasticity and equivalence classes of composites. Proc Royal Soc. London. A (1992), v. 438, pp. 519-529.
47. A. Cherkaev. Stability of optimal structures of elastic composites. In: Topology Design of Structures. M.Bendsoe and C.A.Mota Soares - editors. p. 547-558, Kluwer, 1992.
48. A. Cherkaev. Conducting and Elastic Composites of Optimal Structures. In: Structural Optimization 93, J.Hersovits - ed., vol. 1, pp. 377- 385. ABCM, Brazil, 1993
49. A. Cherkaev, L. Gibiansky. Variational principles for complex conductivity, viscoelasticity and similar problems in media with complex moduli. J. of Math. Physics 35 (1), pp. 1-19, 1994
50. A. Cherkaev. Relaxation of problems of optimal structural design. Int. J. of Solids and Structures 31, N0 16, pp 2251-2280, 1984.
51. A. Cherkaev. Reducing of optimal design problems to the minimal variational problem. 34 pp. Submitted to: Proceedings of the second Workshop on Composite Media and Homogenization in Truest. Dal Maso- editor.
52. A. Cherkaev, L. Gibiansky. Extremal structures of multiphase composites. Int. J. of Solids and Structures JSS 33(18), 2609-2623.
53. A. Cherkaev, L. Slepyan. Waiting element structures and stability under extension. J. of Appl. Mechanics, 4, (1995), pp 58--82.
54. A. Cherkaev, R.Palais Optimal design of three-dimensional axisymmetric structures. Int. J. of Structural optimization.
55. M. Avellaneda, A. Cherkaev, L.Gibiansky, G.W.Milton, M. Rudelson. Complete characterization of possible isotropic effective tensors of polycrystals in planar elasticity (orthotropic monocrystal). Journal of Mechanics and Physics of Solids 44(7) 1179-1218.
56. E.Cherkaeva and A.Cherkaev, Bounds for delectability of material damage by noisy electrical measurements, Structural and Multidisciplinary Optimization, WCSMO-1 First World Congress of Structural and Multidisciplinary Optimization. N.Olhoff and G.I.N.Rozvany - eds., Pergamon 1995. pp. 543-548.
57. A. Cherkaev, R.Palais. Optimal Design of three-dimensional Elastic Structures. WCSMO-1 First World Congress of Structural and Multidisciplinary Optimization N.Olhoff and G.I.N.Rozvany - eds., Pergamon 1995. pp. 201 - 206.
58. A. Cherkaev. What Structures are Optimal for a General Problem of Structural Design? WCSMO-1 First World Congress of Structural and Multidisciplinary Optimization N.Olhoff and G.I.N.Rozvany - Des, Pergamon 1995. pp. 219-224.
59. G.W.Milton, A.Cherkaev. Which elasticity tensors are realizable? J of Eng. Mat. and Technology, 117, 1995 pp 483-493
60. A. Cherkaev, R.Palais. NIST-CTCMS International Workshop on Optimal Design for Materials and Structures. Structural Optimization 13 (1) 1997. pp 1-4.
61. T. Burns A. Cherkaev. Optimal distribution of multimaterial composites for torsion beams. Structural Optimization 13 (1) 1997. pp 1-4.
62. A. Cherkaev, R. Kohn. Introduction. In: Topics in the Mathematical Modeling of Composite Materials, A.Cherkaev and R. Kohn eds., Birkhauser, 1997.
63. Cherkaev, A. V., Grabovsky, Y., Movchan, A. B. and Serkov, S. K. Optimality of dilute composites under shear load, in "IUTAM Symposium on Transformation Problems in Composite and Active Materials" Proceedings of the IUTAM Symposium held in Cairo, Egypt, 9-12 March 1997 G. M. L. Gladwell, Yehia A., Y. A. Bahei-el-Din and G. J. Dvorak, eds., pp. 285-300, Springer Netherlands, 2002. final publication.
64. Cherkaev, A. V., Grabovsky, Y., Movchan, A. B. and Serkov, S. K. The cavity of the optimal shape under shear stresses, Int. J. Solids Struct., 35, No. 33, pp. 4391-4410, 1998.
65. E. Cherkaeva and A. Cherkaev, Bounds for detectability of material damage by noisy electrical measurements. In: Structural and multidisciplinary optimization, N. Olhoff and G.I.N.Rozvany eds, Pergamon, 1995, pp. 543-548.
66. A. Cherkaev. Necessary conditions technique in optimization of structures. Accepted in J. Mech. Phys. Solids.
67. E.Cherkaeva and A.Cherkaev. Optimal design for uncertain loading conditions. In: Homogenization, V.Berdichevsky, V.Jikov, and G.Papanicolaou, eds., World Scientific, 1999, 193-213.
68. A. Cherkaev. L. Krog and I. Kucuk. Stable Optimal design of two-dimensional structures made from optimal composites. Control and Cybernetics, v.27, n.2, 1998, pp. 265-282,
69. E.Cherkaeva, A.Cherkaev. Structural optimization and biological "designs". In: Proceedings of IUTAM Symposium: Synthesis in bio solid mechanics. M.Bendsoe and P.Pedersen eds., Kluwer, 1998.
70. A. Cherkaev, R.Palais. Optimization of Elastic Structures. Axisymmetric Problem. In: Structural Dynamic Systems. Computational Techniques and Optimization. Optimization Techniques. C.T. Leondes- ed, Gorgon and Breach Sc. Publ. 1999, pp. 237- 267.
71. A. Cherkaev. Variational Approach to Structural Optimization. In: Structural Dynamic Systems. Computational Techniques and Optimization. Optimization Techniques. C.T. Leondes- ed, Gorgon and Breach Sc. Publ. 1999, pp. 199 - 237.
72. A.Cherkaev and I. Kucuk. Equally stressed structures: Two-dimensional perspective. In: Topology Optimization of Structures and Composite Continua, G.I.N.Rozvany and N.Olhoff eds. Kluwer 2000,  251-266.
73. A. Balk, A. Cherkaev, and L. Slepyan Dynamics of solids with non-monotone stress-strain relations. I. Model and numerical experiments. J. Mech. Phys. Solids, 49 (2001) 131-148.
74. A. Balk, A. Cherkaev, and L. Slepyan Dynamics of solids with non-monotone stress-strain relations. II. Nonlinear waves and  waves of phase transition. J. Mech. Phys. Solids. 49 (2001) 149-172.
75. Andrej Cherkaev, Ismail Kucuk Detecting stress fields in an Optimal Structure I: Two-dimensional Case and Analyzer Int.J Struct. Opt. January 2004 pp 1-15
76. Andrej Cherkaev, Ismail Kucuk Detecting stress fields in an Optimal Structure II: Three-dimensional Case, Int. J Struct. Opt. January 2004 pp 15-24.
77. Andrej Cherkaev, Liya Zhornitskaya Dynamics of damage in two-dimensional structures with waiting links In: Asymptotics, Singularities and Homogenisation in Problems of Mechanics, A.B.Movchan editor, Kluwer 2004. pp 273 - 284,
78. E. Cherkaev and A. Cherkaev, Principal compliance and robust optimal design, The Rational Spirit in Modern Continuum Mechanics, Essays and Papers Dedicated to the Memory of Clifford Ambrose Truesdell III, 2003, Also in: Journal of Elasticity, 2003, 72, 71-98.

79. Andrej Cherkaev. Approaches to nonconvex variational problems of mechanics In: Nonlinear homogenization and its applications to composites, polycrystals and smart materials. P.Ponte Castaneda, J.J.Telega and B. Gamblin eds., Kluwer 2004. pp. 65-106. (NATO Science Series, Mathematics, Physics and Chemistry v. 170)

80. Seubpong Leelavanishkul and Andrej Cherkaev. Why grains in the tree's trunk spiral: mechanical perspective Structural and Multidisciplinary Optimization, 28, 2-3, 2004, pp. 127 - 135.

81. A. Cherkaev, E. Cherkaev, and L. Slepyan, Transition waves in bistable structures I: Delocalization of damage, J. Mech. Phys. Solids, Vol 53/2 pp 383-405, 2005.

82. L. Slepyan, A. Cherkaev, and E. Cherkaev, Transition waves in bistable structures II: Analytical solution, wave speed, and energy dissipation, J. Mech. Phys. Solids, Vol 53/2 pp 407-436, 2005.

83. A.Cherkaev and L.Zhornitskaya. Protective Structures with waiting links and their damage elovulion. Multibody System Dynamics Journal. Multibody System Dynamics Journal. Volume 13, Number 4 May, 2005

84. Andrej Cherkaev, Vladimir Vinogradov, Seubpong Leelavanishkul. The waves of damage in elastic-plastic lattices with waiting links: design and simulation. Mechanics of Materials 38, 748-756, 2005.

85. N. Albin, A. Cherkaev Optimality conditions on fields in microstructures and controllable differential schemes (2006)- pdf Postscript version In: Inverse Problems, Multi-Scale Analysis, and Effective Medium Theory. Habib Ammari and Hyeonbae Kang - editors. Series: Contemporary Mathematics number 408 pp 137-150.

86. N. Albin, A. Cherkaev and V. Nesi A class of optimal two-dimensional multimaterial conducting laminates (2005)- pdf In: IUTAM Symposium on Topological Design Optimization of Structures, Machines and Materials Status and Perspectives, SERIES = {Solid Mechanics and Its Applications}, AMS 2006. VOLUME = {137},

87. Andrej Cherkaev, Elena Cherkaev and Leonid Slepyan. Dynamics of Structures with Bistable Links. In: Vibration Problems ICOVP 2005 Springer, 2007, Volume 111, 111-122,

88. Elena Cherkaev, Andrej Cherkaev. Minimax optimization problem of structural design. Computers and Structures 86 (2008) 1426-1435
89. A. Cherkaev *, V. Vinogradov, S. Leelavanichkul The waves of damage in elasticâplastic lattices with waiting links: Design and simulation. Mechanics of Materials, 2006

90. A. Cherkaev, Y. Zhang Optimal structures of multiphase elastic composites 8th World Congress on Structural and Multidisciplinary Optimization June 1 - 5, 2009, Lisbon, Portugal

91. A. Cherkaev, E. Cherkaev, S. Leelavanichkul Principles of optimization of structures against an impact, 8th World Congress on Structural and Multidisciplinary Optimization June 1 - 5, 2009, Lisbon, Portugal

92. A.Cherkaev, A, Kouznetsov, A.Panchenko. Still states of bistable lattices, compatibility, and phase transition. 2009. Continuum Mechanics and Thermodynamicsm 22, 6-8, 421-444,

93. N. Albin, A. Cherkaev and V. Nesi Optimal structures of multimaterial composites. Journal of the Mechanics and Physics of Solids Volume 55, Issue 7, July 2007, Pages 1513-1553

94. Cherkaev, A.; Vinogradov, V.; Leelavanichkul, S. 2006: The waves of damage in elastic-plastic lattices with waiting links: Design and simulation. In: /Mechanics of Materials/ *38*, pp. 748 -- 756

95. Leelavanichkul, S.; Cherkaev, A. 2009: Elastic Cylinder with Helicoidal Orthotropy: Theory and Applications. In: /International Journal of Engineering Science/. *47*(1), pp 1 -- 20

96. Leelavanichkul, S.; Cherkaev, A.; Adams, D.; Solzbacher, F. 2009: Energy Absorption of a Helicoidal Bistable Structure. In: /Journal of Mechanics of Materials and Structures/ *5*(2), pp. 305 -- 321

97. A.Movchan, A.Cherkaev, J.Dempsey, M.Ayzenberg-Stepanenko and E.Sher 2009. Preface to the special issue in honour of Leonid Slepya Continuum Mechanics and Thermodynamics Volume 22, Numbers 6-8, 413-419,

98. Cherkaev, A; Cherkaev, E.; Leelavanichkul, S. 2011: Principle of Optimization of Structures Against an Impact. In:/Journal of Physics: Conference Series/ *319*(1), pp. 1 -- 16

99. Cherkaev, A.; Leelavanichkul, S. 2011: An Impact Protective Structure with Bistable Links. In: /International Journal of Damage Mechanics/. In print.

100. Cherkaev, A., 2009. Bounds for effective properties of multimaterial two-dimensional conducting composites and fields in optimal composites. Mechanics of Materials 41, 411-433.

101. Cherkaev, A., Zhang, Y. Optimal anisotropic three-phase conducting composites: Plane problem 2011 International Journal of Solids and Structures 48 (20), pp. 2800-2813

102. Cherkaev, A. 2011. Optimal Three-Material Wheel Assemblage of Conducting and Elastic Composites. Accepted in Continuum Mechanics and Thermodynamics. http://arxiv.org/pdf/1105.4302