L. V. Gibiansky, and O. Sigmund, Multiphase composites with extremal bulk modulus, Journal of the Mechanics and Physics of Solids, 48(3), pp. 461-498 (2000).

       L. Gibiansky, Effective properties of a plane two-phase elastic composites: coupled bulk-shear moduli bounds, in Series on Advances in Mathematics for Applied Sciences - Vol. 50, Homogenization, edited by V. Berdichevsky, V. Jikov and G. Papanicolaou, 1999.

       L.V. Gibiansky, G.W. Milton, and J.G. Berryman, On the effective viscoelastic moduli of two-phase media. III. Rigorous bounds on the complex shear modulus in two dimensions, Proc. R. Soc. Lond. A, V.455, pp. 2117-2148 (1999).

       L. V. Gibiansky and S. Torquato, Matrix Laminates: Realizable approximations for the effective moduli of piezoelectric composites, Journal of Materials Research, 15, 569 (1999).

       S. Pecullan, L. V. Gibiansky, and S. Torquato, Scale effects on the effective elastic moduli of hierarchical Composites, Journal of the Mechanics and Physics of Solids, 47, 1509 (1999).

       L.V. Gibiansky, Effective moduli of plane polycrystals with a rank-one local compliance tensor, Proc. Roy. Society of Edinburgh, 128A, 1325-1354 (1998).

       L. V. Gibiansky and S. Torquato, New method to generate three-point bounds on effective properties of composites: application to viscoelasticity, Journal of the Mechanics and Physics of Solids, 46 (1998).

       L. V. Gibiansky and S. Torquato, New approximation for the effective energy of non-linear conducting composites, Journal of Applied Physics, 84, 301 (1998).

       L. V. Gibiansky and S. Torquato, Rigorous connection between physical properties of porous rocks, Journal of Geophysical Research (Solid Earth), 103, 23911 (1998).

       S Torquato, LV Gibiansky, MJ Silva, LJ Gibson, Effective mechanical and transport properties of cellular solids, International Journal of Mechanical Sciences 40 (1), 71-82 (1998).

       L. V. Gibiansky and S. Torquato, Effective energy of nonlinear elastic and conducting composites: Approximations and Cross-Property Bounds, Journal of Applied Physics, 84, 5969 (1998).

       L.V. Gibiansky and S. Torquato, Optimal design of 1-3 composite piezoelectrics, Structural Optimization, 13, 23 (1997).

       L.V. Gibiansky and S. Torquato, Thermal expansion of isotropic multiphase composites and polycrystals Journal of the Mechanics and Physics of Solids, 45, 1223 (1997).

       L. Gibiansky, A. Cherkaev. Design of composite plates of extremal rigidity.-Report 914. Phys.-Tech. Inst. Acad. Sci. USSR, Leningrad,1984, 60 pp. English translation in: Topics in the mathematical modelling of composite materials, A. Cherkaev and R. Kohn editors, Birkhausen, NY, 1997.

       L.Gibiansky, A. Cherkaev. Microstructures of composites of extremal rigidity and exact estimates of provided energy density. - Report 1115. Phys.-Tech. Inst.Acad. Sci. USSR, Leningrad, 1987 (in Russian); English translation in: Topics in the mathematical modelling of composite materials, A.Cherkaev and R. Kohn editors, Birkhausen, NY, 1997.

       Gibiansky, L. V. and Lakes, R. S., Bounds on the complex bulk modulus and shear modulus of a two-dimensional viscoelastic composite, Mechanics of Materials, 25, 79-95, (1997).

       L. V. Gibiansky and S. Torquato, Connection between the conductivity and elastic moduli of

       isotropic composite materials, Proceedings of the Royal Society of London A, 452, 253 (1996).

       L. V. Gibiansky and S. Torquato, Phase-interchange relations for the elastic moduli of two-phase composites, International Journal of Engineering Science, 34, 739 (1996).

       S. Torquato and L. V. Gibiansky, Rigorous link between the electrical and mechanical properties of composite materials, Symposium on Electrically Based Microstructural Characterization, Materials Research Society Proceedings eds. R.A. Gerhardt, S.R. Taylor and E.J. Garboczi, vol. 411, pp. 387-392 (1996).

       L. V. Gibiansky and S. Torquato, Bounds on the effective moduli of cracked materials, Journal of the Mechanics and Physics of Solids, 44, 233 (1996).

       Cherkaev, L. Gibiansky. Extremal structures of multiphase composites. Int. J. of Solids and Structures JSS 33(18), 2609-2623(1996).

       M. Avellaneda, A. Cherkaev, L.Gibiansky, G.W.Milton, M. Rudelson. Complete characterization of possible isotropic effective tensors of polycrystals in planar elastisity (othotropic monocrystal). Journal of Mechanics and Physics of Solids 44(7), 1179-1218 (1996).

       L. V. Gibiansky and S. Torquato, Geometrical parameter bounds on effective properties of composites, Journal of the Mechanics and Physics of Solids, 43, 1587 (1995).

       L. V. Gibiansky and S. Torquato, Rigorous link between the conductivity and elastic moduli of fibre-reinforced composite materials, Philosophical Transactions of the Royal Society, 353, 243 (1995).

       Cherkaev, L. Gibiansky. Variational principles for complex conductivity, viscoelasticity and similar problems in media with complex moduli. J. Math. Physics 35 (1), pp. 1-19, (1994).

       Gibiansky, L.V.; Milton, G.W. On the effective viscoelastic moduli of two-phase media. I. Rigorous bounds on the complex bulk modulus, Proc. R. Soc. Lond. A, V.440, pp. 163-188, 1993

       Gibiansky, L. V., Lakes, R., and Milton, G. W., Viscoelastic composites with extremal properties, in Abstracts of the World Congress, 'Structural Optimization 1993, Rio de Janeiro, 1, 218-225, (1993).

       G. Allaire, A. Braides, G. Buttazzo, A Defranceschi, and L. Gibiansky. Two-scale convergence and homogenization of periodic structures. Technical Report Ref. 140/93/M, SISSA ISAS, (1993).

       Gibiansky, L.V. and Lakes, R.S., Bounds on the complex bulk modulus of a two-phase viscoelastic composite with arbitrary volume fractions of the components, Mechanics of Materials, 16, 317-331 (1993).

       L. V. Gibiansky and S. Torquato, Link between the conductivity and elastic moduli of composite materials, Physical Review Letters, 71, 2927-2930 (1993).

       Cherkaev, L. Gibiansky. Coupled estimates for the bulk and shear moluli of a two-dimensional isotropic elastic composite. J.Mech. Phys. Solids 41 (5), 937-980, (1993).

       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, 122A, 93-125 (1992).

       Cherkaev, L. Gibiansky. Improving the Hashin-Strickman estimates by means of the translation method. - Proceedings of SIAM workshop in micromechanics. Leesburgh, Virginia, 1991.

       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).

       L. Gibiansky, A. Cherkaev. Optimal design of nonlinear-elastic and plastic-elastic bars under torsion. - Mechanics of solids ( Izv. Acad. Sci. USSR, MTT), 5, 168-174, (1988).

       K.Lurie, L.Gibiansky, A. Cherkaev. Optimal focusing of heat flow by heterogeneous heat-conducting media (thermo-lens problem). - J. Techn. Phys. (Zh. Tech. Fiz.) Acad. Sci. USSR, 58, 1, 67-74, (1988).

       L. Gibiansky, A. Cherkaev. The set of tensor pairs of dielectric and magnetic permeabilities of two-phase composites.- Report N. 1286, Phys.-Tech. Inst. Acad. Sci. USSR, (1988) (in Russian).

       L. Gibiansky, Exact variational bounds of the effective properties and the optimal design problems. - (Ph.D Thesis). Leningrad Ioffe Physical-Technical Institute, (1988) (in Russian).

       L.Gibiansky, Ju. Malinin, A. Cherkaev. Optimal distribution of viscoelastic materials in axisymmetric constructions. - Report N.1116, Phys.-Tech. Inst.Acad. Sci. USSR, Leningrad, 1987, 41 pp. (in Russian)

       L. Gibiansky, K. Lurie, A. Cherkaev. Optimum focusing of heat flux by means of a non-homogeneous heat conducting medium. - Report 305, The Technical University of Denmark, (1985).