PUBLICATIONS

2015

L.X. Hu*, L. P. Liu, From atomistics to continuum: effects of a free surface and determination of surface elasticity properties, Mechanics of Material, submitted, 2015.
Z. Alameh, Q. Deng, L. P. Liu and P. Sharma. Using electrets to design concurrent magnetoelectricity and piezoelectricity in soft materials. Journal of Material Research, In press, 2014.

L. P. Liu. Feasibility of Large-scale power plants based on thermoelectric effects. New Journal of Physics, 16, 123019, 2014.
L.P. Liu. An energy formulation of continuum magneto-electro-elastics with applications, J. Mech. Phys. Solids 63:451-480, 2014.
D. Qian*, L. P. Liu and P. Sharma. Flexoelectricity in Soft and Biological Materials, J. Mech. Phys. Solids, 62:209-227, 2014.
Y. Hanlumyuang*, L.P. Liu and P. Sharma. Revisiting the entropic force between fluctuating biological membranes? J. Mech. Phys. Solids, 63:179-186, 2014.
L. P. Liu. A differential approach to microstructure-dependent bounds for multiphase heterogeneous media. Accepted to Acta Mechanica, 225, 1245-1266, 2014.
L. P. Liu. Geometries of minimum field concentration. Mechanics of Materials, 75, 95-102, 2014.
L. X. Hu* and L. P. Liu. Interfacial waves with surface elasticity. ASME J Appl. Mech, 81, 081007, 2014.

P. Mohamad*, L. P. Liu, Pradeep Sharma, R. V. Kukta. Surface Energy, Elasticity and the Homogenization of Rough Surfaces, J. Mech. Phys. Solids 61, 325-340, 2013.
L. P. Liu. Polynomial eigenstress inducingpolynomial strain of the same degreein an ellipsoidal inclusion and itsapplications, Mechanics and Mathematics of Solids, 18, 168-180, 2013. .
L. P. Liu. On energy formulations of electrostatics for continuum media. J. Mech. Phys. Solids 61, 968-990, 2013.
P. Mohammadi*, L. P. Liu, Pradeep Sharma. A Theory of Flexoelectric Membranes and Effective Properties ofHeterogeneous Membranes, ASME J. Appl. Mech. 81, 011007, 2013.
L. P. Liu and P. Sharma. Flexoelectricity and Thermal Fluctuations of Lipid Bilayer Membranes: Renormalization of Flexoelectric, Dielectric and Elastic Properties, Phy. Rev. E., 87, 032715, 2013.
L. P. Liu and D. Onofrei. Engineering anisotropy to amplify a long wavelength field without a limit, Proc. of Roy. Soc. A, 469, 20130246, 2013.
L. P. Liu and P. Sharma. Giant and universal magneto-electric coupling in soft materials and concomitant ramifications for materials science and biology. Phy. Rev. E., 88, 040601 (Rapid Communication), 2013.
F. Ahmadpoor, Q. Deng, L. P. Liu and P. Sharma.Apparent flexoelectricity in lipid bilayer membranes due to external charge anddipolar distributions. Phy. Rev. E., 88, 050701 (Rapid Communication), 2013.

L.P. Liu. "A continuum theory of thermoelectric bodies and effective properties of thermoelectric composites." International Journal of Engineering Science, 55, 35-53, 2012.
L. P. Liu, Hsin-Yi Kuo. Closed-form solutions to the effective properties of fibrous magnetoelectric composites and their applications. Int. J. Struct. Solids, 49, 3055-3062, 2012.
Y. X. Zhang, L. P. Liu. On diffusion in heterogeneous media. American Journal of Science 312, 1028-1047, 2012.
L. P. Liu. On energy formulations of electrostatics for continuum media. J. Mech. Phys. Solids, In press, 2012.

V. Gavini and L.P. Liu. "A homogenization analysis of the field theoretic approach to the quasi-continuum method." J. Mech. Phys. of Solids, 59, 1536--1551, 2011.
L.P. Liu."Designing magnets with prescribed fields." New Journal of Physics, 13, 033013, 2011.
L.P. Liu. "New optimal microstructures and restrictions on the attainable Hashin-Shtrikman bounds for multiphase composite materials." Phil. Mag. Lett, 91 473-482,2011
L. X. Hu and L. P. Liu and K. Bhattacharya. "Existence of surface waves and band gaps in periodic heterogeneous half-spaces." J. of Elasticity, 107, 65-79, 2011

L.P. Liu. "Hashin-Shtrikman bounds and their attainability for multi-phase composites." Proc. Roy. Soc. A, 466, 3693-3713, 2010
L.P. Liu."Neutral shells and their applications in the design of electromagnetic shields." Proc. Roy. Soc. A, 466, 3659-3677, 2010
L.P. Liu. "Solutions to periodic Eshelby inclusion problem in two dimensions." Mathematics and Mechanics of Solids, 15, 557-590, 2010

L.P. Liu. "Effective conductivities of two-phase composites with a singular phase." J. Appl. Physics. 105, 103503, 2009
L.P. Liu, K. Bhattacharya."Wave propagation in a sandwich structure." Int. J. Solids and Structures, 46, 3290-3300, 2009
L.P. Liu, R.D. James, P.H. Leo. "New extremal inclusions and their applications to two-phase composites." Archive for Rational Mechanics and Analysis, Accepted, 2009

L.P. Liu. "Solutions to the Eshelby conjectures." Proceedings of Royal Society A, 464, 573 – 594, 2008

L.P. Liu, R.D. James, P.H. Leo. "Periodic inclusion-matrix microstructures with constant field inclusions." Metallurgical and Materials Transactions A, 38, 781 – 787, 2007

L.P. Liu, R.D. James, P.H. Leo. "Magnetostrictive composites in the dilute limit." J. Mech. Phys. Solids, 54, 951 – 974, 2006