Department of Mathematics Directory

  • Liping Liu
  • Profile Image
  • Professor of Mathematics & Mechanical Aerospace Engineering
  • TTF
  • Faculty, Research
  • Applied Analysis
  • Specialty Area: Mechanics and Mathematics of Materials
  • Click for Website
  • Email:
  • Location:


  • Campus: busch
  • Office hours - 1:

    HLL 516

  • Campus (2): busch
  • Office hours - 2:

    MW 3:15pm 4:45pm

  • Research Interests: Mechanics and Mathematics of Materials
  • Bio:

    Professor of Mathematics, and Mechanical Aerospace Engineering, Rutgers University, New Brunswick, NJ


    1996-2000         Bachelor of Engineering in Mechanics and Engineering Science, July 2000

                               Beijing (or Peking) University, Beijing, China

    2000-2006         Ph.D. in Aerospace Engineering and Mechanics, August 2006

                               University of Minnesota, Twin Cities



    Jul. 2019 - Present               Professor, Department of Mathematics & Department of

                                                 Mechanical Aerospace Engineering, Rutgers University, NJ

    Jul. 2014 - Jul. 2019            Associate Professor, Department of Mathematics & Department of

                                                 Mechanical Aerospace Engineering, Rutgers University, NJ

    Jan. 2012 - Jul. 2014           Assistant Professor, Department of Mathematics & Department of

                                                 Mechanical Aerospace Engineering, Rutgers University, NJ

    Oct. 2008 - Jan. 2012         Assistant Professor, Department of Mechanical Engineering,

                                                 University of Houston, Houston, TX

    Oct. 2006 - Oct. 2008         Postdoctoral Scholar, Division of Engineering and Applied Science,

                                                California Institute of Technology, CA


    • Best Dissertation Award, College of Science and Engineering, University of Minnesota (one awardee per year in the college), 2008

    • Professor of the Year (Teaching Award), American Society of Mechanical Engineering at University of Houston, 2010

    • Young Investigator Program Award, AFOSR, 2012

    • Eshelby Award for Young Faculty, 2014

    • CAREER Award, NSF: CMMI, 2014

    • Young Investigator Medal, Society of Engineering Science, 2015

    • Melville Medal for the best paper, ASME, 2015 (Coauthored with Parnia Mohammadi and Pradeep Sharma)

    • Simons Fellow, Simons Foundation, 2016

    • Chancellor’s Scholar Award, Rutgers University, 2016 

    •  T.J Hughes Young Investigator Award, ASME, 2018

  • Publications:

    Google Scholar Link (Disclaimer:  auto-managed by google, not always manually verified)


    1. A. H. Rahmati and R. Jia and K. Tan and L. Liu and X. Zhao and Q. Deng and P. Sharma. Giant Magnetoelectricity in Soft Materials Using Hard Magnetic Soft Materials Materials Today Physics 100969 (2023)
    2. R. Li and S. Moazzeni and L. Liu and H. Lin Micro and Macroscopic Stress-Strain Relations in Disordered Tessellated Networks, Physical Review Letters 130 188201 (2023)


    1. M Torbati, K Mozaffari, L Liu, P Sharma, Coupling of mechanical deformation and electromagnetic fields in biological cells, Reviews of Modern Physics 94 (2), 025003, 2022
    2. K Mozaffari, L Liu, P Sharma, Theory of soft solid electrolytes: Overall properties of composite electrolytes, effect of deformation and microstructural design for enhanced ionic conductivity, Journal of the Mechanics and Physics of Solids 158, 104621, 2022
    3. N Khodabandehloo, K Mozaffari, L Liu, P Sharma, Micro-Structural Design of Soft Solid Composite Electrolytes with Enhanced Ionic Conductivity, Journal of Applied Mechanics, 1-12, 2022
    4. A. H. Rahmati and L. Liu and P. Sharma, Homogenization of electrets with ellipsoidal microstructure and pathways for designing piezoelectricity in soft materials, Mechanics of Materials 173 104420 (2022)
    5. A. H. Rahmati and R. Jia and K. Tan and X. Zhao and Q. Deng and L. Liu and P. Sharma. Theory of hard magnetic soft materials to create magnetoelectricity, Journal of the Mechanics and Physics of Solids 105136 (2022)


    1. T Yuan, W Yuan, L Liu, JW Shan, Electric-field-controlled diffusion of anisotropic particles: theory and experiment, Journal of Fluid Mechanics 924, 2021
    2. K Tan, X Wen, Q Deng, S Shen, L Liu, P Sharma, Soft rubber as a magnetoelectric material—Generating electricity from the remote action of a magnetic field, Materials Today 43, 8-16, 2021
    3. F. Darbaniyan, K. Mozaffari, L. Liu, P. Sharma, Soft matter mechanics and the mechanisms underpinning the infrared vision of snakes, Matter 4 (1), 241-252, 2021
    4. R Li, C Ibar, Z Zhou, S Moazzeni, AN Norris, KD Irvine, L Liu, H Lin, E2 and gamma distributions in polygonal networks
      Physical Review Research 3 (4), L042001, 2021
    5. Seyedsajad Moazzeni, Yasir Demiryurek, Miao Yu, David I Shreiber, Jeffrey D Zahn, Jerry W Shan, Ramsey A Foty, Liping Liu, Hao Lin, Single-cell mechanical analysis and tension quantification via electrodeformation relaxation, Physical Review E 103 (3), 032409, 2021


    1. X Zhu, Z Qian, X Chen, L Liu, C Sheng, W Gu, Electrohydrodynamics-printed silver nanoparticle flexible pressure sensors with improved gauge factor, IEEE Sensors Journal 21 (5), 5836-5844, 2020


    1. S. Krichen, L. Liu, P. Sharma, “Liquid inclusions in soft materials: capillary effect, mechanical stiffening and enhanced electromechanical response”, Journal of the Mechanics and Physics of Solids, 127, 332-357, 2019.
    2. F. Darbaniyan, K. Dayal, L. Liu, P. Sharma, “Designing soft pyroelectric and electrocaloric materials using electrets”, Soft Matter, 15, 262 – 277, 2019.
    3. Yuan, W., Tutuncuoglu, G., Mohabir, A., Liu, L., Feldman, L. C., Filler, M. A., & Shan, J. (2019). Contactless Electrical and Structural Characterization of Semiconductor Nanowires with Axially Modulated Doping Profiles. Small, 15(15).


    1. L. P. Liu, P. Sharma. Emergent electromechanical coupling of electrets and some exact relations —The effective properties of soft materials with embedded external charges and dipoles. J. Mech. Phys. Solids, 112:1-24, 2018.
    2. M. Yu, A. Mahtabfar, P. Beelen, Y. Demiryurek, D. Shreiber, J. D. Zahn, R. Foty, L.P. Liu, H. Lin. Coherent Timescales and Mechanical Structure of Multi-Cellular Aggregates. Biophysical Journal, 114(3), p652a, 2018 .


    1. W. Wang, L.P. Liu. Solitary waves in two dimensional granular crystals.   Acta Mechanica, 2017, In Press.
    2. H.X. Wang*, L. P. Liu and D. Liu. Equilibrium shapes of a heterogeneous bubble in an electric field: a variational formulation and numerical verifications.   Proceeding A, In press.
    3. S. Shannon, D.  Jia, I. Entersz, P. Beelen, M. Yu*, C. Carcione, J. Carcione, A. Mahtabfar, C. Vaca, M. Weaver, D. Shreiber, J. D. Zahn, L.P. Liu, H. Lin, and R. A. Foty. Inhibition of glioblastoma dispersal by the MEK-inhibitor PD0325901, BMC Cancer, 17:121, 2017.
    4. W. Yuan*, L.P. Liu, and J. Shan. Tunable acoustic attenuation in dilute suspensions of non-spherical magnetic Particles, J. App. Phys. 121, 045110, 2017.
    5. L.P. Liu, M. Yu*, H. Lin and R. Foty. Deformation and relaxation of an incompressible viscoelastic body with surface viscoelasticity.   J. Mech. Phys. Solids, 98:309-329, 2017.
    6. J. Yvonnet, L.P. Liu. A numerical framework for modeling flexoelectricity and Maxwell stress in soft dielectrics at finite strains. Comp. Meth. Appl. Mech. Engr., 313:450-482, 2017.


    1. H. Agrawala*, L.P. Liu, P. Sharma. Revisiting the curvature-mediated interactions between proteins in biological membranes.   Soft Matter, 12(43):8907-8918, 2016.
    2. H. Agrawala*, M. Zeliskoa, L.P. Liu, P. Sharma. Rigid proteins and softening of biological membranes---with application to HIC-induced cell membrane softening (12pg). Scientific Report, 6: 25412. 2016.
    3. L.P. Liu and N. Lu. Variational formulations, instabilities and critical loadings of space curved beams (13pg). Int. J. Solid. Struc., 87:48-60, 2016.
    4. X.B. Li*, L.P. Liu and P. Sharma. A New Type of Maxwell Stress in Soft Materials due to Quantum Mechanical-Elasticity Coupling (14pg), J. Mech. Phys. Solids, 87, 115–129, 2016.


    1. X.B. Li*, L.P. Liu and P. Sharma. Geometrically nonlinear deformation and the emergent behavior of polarons in soft matter (6pg, Communication). Soft Matter, 11, 8042-8047, 2015.
    2. L.X. Hu* and L. P. Liu.  From atomistics to continuum: effects of a free surface and determination of surface elasticity properties (10pg). Mechanics of Materials, 90, 202-211, 2015.
    3. F. Ahmadpoor, L. P. Liu and P. Sharma. Thermal fluctuations and the minimum electrical field that can be detected by a biological membrane (13 pg). J. Mech. Phys. Solid, 78,110-122,2015.
    4. Z. Alameh*, Q. Deng*, L. P. Liu and P. Sharma. Using electrets to design concurrent magnetoelectricity and piezoelectricity in soft materials (7pg). Journal of Material Research, 30:93-100, 2015


    1. L. P. Liu. Feasibility of Large-scale power plants based on thermoelectric effects. New Journal of Physics, 16, 123019, 2014
    2. Q. Deng*, L. P. Liu and P. Sharma. Flexoelectricity in Soft and Biological Materials (18pg), J. Mech. Phys. Solids, 62, 209-227, 2014.
    3. L. P. Liu. Inhomogeneities of minimum field concentration (8pg). Mechanics of Materials, 75, 95-102, 2014.
    4. L.  X. Hu* and L. P. Liu. Interfacial waves with surface elasticity (6pg). J. Appl. Mech, 81, 081007, 2014.
    5. Q. Deng*, L. P. Liu and P. Sharma. Electrets in soft materials: nonlinearity, size effects, and giant electromechanical coupling (7 pg). Phy. Rev. E, 90, 012603, 2014.
    6. L. P. Liu. A differential approach to microstructure-dependent bounds for multiphase heterogeneous media (8pg). Acta Mechanica, 225, 1245-1266, 2014.
    7. Y. Hanlumyuang, L.P. Liu and P. Sharma. Revisiting the entropic force between fluctuating biological membranes? (8pg)  J. Mech. Phys. Solids, 63, 179-186, 2014.
    8. L. P. Liu. An energy formulation of continuum magneto-electro-elastics with applications (30pg), J. Mech. Phys. Solids, 63:451-480, 2014.


    1. F. Ahmadpoor, Q. Deng, L. P. Liu and P. Sharma. Apparent flexoelectricity in lipid bilayer membranes due to external charge and dipolar distributions (5pg). Phy. Rev. E., 88, 050701 (Rapid Communication), 2013.
    2. L. P. Liu and P. Sharma. Giant and universal magneto-electric coupling in soft materials and concomitant ramifications for materials science and biology (5pg).  Phy. Rev. E., 88, 040601 (Rapid Communication), 2013.
    3. L. P. Liu and D. Onofrei. Engineering anisotropy to amplify a long wavelength field without a limit (15pg), Proc. of Roy. Soc. A, 469, 20130246, 2013.
    4. L. P. Liu and P. Sharma. Flexoelectricity and Thermal Fluctuations of Lipid Bilayer Membranes: Renormalization of Flexoelectric, Dielectric and Elastic Properties (8pg), Phy. Rev. E., 87, 032715, 2013.
    5. P. Mohammadi*, L. P. Liu, Pradeep Sharma. A Theory of Flexoelectric Membranes and Effective Properties of Heterogeneous Membranes, ASME J. Appl. Mech. 81(11 pg), 011007, 2013.
    6. L. P. Liu. On energy formulations of electrostatics for continuum media (23pg).  J.  Mech. Phys. Solids 61, 968-990, 2013
    7. L. P. Liu. Polynomial eigenstress inducing polynomial strain of the same degree in an ellipsoidal inclusion and its applications (13pg), Mechanics and Mathematics of Solids 18, 168-180, 2013.
    8. P. Mohammadi*, 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.


    1. Y. X. Zhang and L. P. Liu. On diffusion in heterogeneous media (20pg). American Journal of Science, 312, 1028-1047, 2012.
    2. L. P. Liu, Hsin-Yi Kuo.  Closed-form solutions to the effective properties of fibrous magnetoelectric composites and their applications (8pg). Int.  J.  Struct. Solids, 49, 3055-3062, 2012.
    3. L. P. Liu. A continuum theory of thermoelectric bodies and effective properties of thermoelectric composites (19pg). Int.  J.  Eng. Sci. 55, 35-53, 2012.


    1. L. X. Hu*, L. P. Liu, K. Bhattacharya. Existence of surface waves and band gaps in periodic heterogeneous half-spaces (15pg). J Elasticity, 107, 65-79, 2011.
    2. L. P. Liu. Designing magnets with prescribed fields (11 pg).  New Journal of Physics, 13, 033013, 2011.
    3. L. P. Liu. New optimal microstructures and restrictions on the attainable Hashin-Shtrikman bounds for multiphase composite materials. (9 pg) Phil. Mag. Lett. 91, 473, 2011.
    4. Vikram Gavini and L. P. Liu. An analysis of the field theoretic approach to quasi-continuum method (16pg).  J. Mech. Phys. Solids. 59, 1536-1551, 2011.


    1. L. P. Liu. Neutral shells and their applications in the design of electromagnetic shields (19pg). Proceedings of Royal Society A. 466 (2124) 3659-3677, 2010.
    2. L.P. Liu. Hashin-Shtrikman bounds and their attainability for multiphase composites (21pg). Proceedings of Royal Society A. 466 (2124) 3693-3713, 2010.
    3. L.P. Liu. Solutions to periodic Eshelby inclusion problems (34pg).  Mechanics and Mathematics of Solids. 15: 557-590, 2010.


    1. L.P. Liu and K. Bhattacharya. Wave propagation in a sandwich structure. (11pg) Int. J. Solids and Structures, 46: 3290-3300, 2009
    2. L.P. Liu. Effective conductivities of two-phase composites with a singular phase (9pg). J. Appl. Phys. 105, 103503, 2009.

    2008 and before

    1. L.P. Liu. Solutions to the Eshelby conjectures (22pg).  Proceedings of Royal Society A, 464 (2091): 573-594, 2008.
    2. L.P. Liu, R.D. James, and P.H. Leo. Periodic inclusion-matrix microstructures with constant field inclusions (7pg). Met.  Mater. Trans. A, 38:781—787, 2007.
    3. L.P. Liu, R.D. James, and P.H. Leo. Magnetostrictive composites in the dilute limit (24pg).  J. Mech. Phys. Solids, 54 (5): 951--974, 2006.
  • Mailing Address:

    110 Frelinghuysen Rd., Piscataway, NJ 08854-8019

  • Research Description:

    Our research group at Rutgers University focus on mechanics and materials --- multiscale-multiphysics analysis and modeling, optimal design of multiphase and multifunctional composites, and theoretical and computational material science.

    Research topics we are interested ininclude:

    Optimal bounds and optimal microstructures for multiphase composites

    Eshelby inclusion problems

    Predictive modeling of multifunctional composites

    Dynamic modeling of heterogeneous structures/media

    Variational inequalities and their applications in designs

    Superconductive composites and modeling

    Surface energy and elasticity

    Thermoelectric materials, modeling, design and energy harvesting

    Continuum theory for multiferroic materials

    Multiscale analysis: homogenization theory and theories for lower dimensional bodies

  • Talks:

    1.  Optimal bounds and optimal microstructures for multiphase composites

  • Grad Student Mentees:
    • Lixin Hu, Ph.D., graduated in 2015
    • Hanxiong Wang, Ph.D., graduated in 2019
    • Wuhan Yuan, Ph.D., graduated in 2019
  • Resource sk12:

    1. The Elements of Algebra I

    2. The Elements of Geometry I