Topological Mechanics

Mechanical properties (stiffness, stress bearing, wave propagation, etc.) protected by topology are highly robust against disorder.  One major research direction in my group is to study mechanical systems with topologically protected features.  We are interested in both fundamental theory and broad applications in topological mechanical metamaterials.

Transformable Topological Mechanical Metamaterials (TTMM)

Mechanical metamaterials that can transform between rubber-like softness and metal-like rigidity at their surface.

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Topological Mechanics in Aperiodic Systems

We are interested in extending the concept of topological states from periodic lattices, which are typically studied in the field, to aperiodic mechanical networks, such as disordered fiber networks and quasicrystalline tilings.

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Stress and Fracturing Control using Topological Mechanics

Taking advantage of topological mechanics, we can program spatial patterns of stress-bearing in materials.

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Soft Matter Physics

Emergence of Rigidity in Disordered Materials

The “softness” of soft matter lies in the fact that these materials are close to mechanical instability, featuring small elastic moduli.  Studying how rigidity emerge and disappear in soft materials is one central focus of soft matter physics.  My group aims at fundamental understanding of rigidity phenomena in soft matter.  We study emergence of rigidity in system way below typical threshold for stable packing, and explore how these materials fail under stress.

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Nonlinear Elasticity of Fiber Networks and Cell Motility in the Extracellular Matrix

Fiber networks exhibit fascinating mechanical properties with huge elastic moduli change as a function of network geometry and strain.  We study criticality of this phenomenon, as well as its implications on how to characterize cell motility in the extracellular matrix, which are disordered fiber networks.

To read more:

  1. Cell motility, contact guidance, and durotaxis
    Jingchen Feng, Herbert Levine, Xiaoming Mao, and Leonard M. Sander,
    Soft Mater 15, 4856,(2019).
  2. Nonlinear elasticity of disordered fiber networks,
    Jingchen Feng, Herbert Levine, Xiaoming Mao, Leonard M. Sander,
    Soft Matter 12, 1419 (2016).
  3. Criticality and isostaticity in fiber networks,
    P. Broedersz, Xiaoming Mao, F.C. MacKintosh and T. C. Lubensky,
    Nature Physics 7, 983 (2011).

Mechanics vs Entropy

How thermal fluctuations affect the stability of a mechanical network remains an open question.  It’s important to the understanding of soft matter with small building blocks as well as recent engineering effort in producing miniaturized machines.  Our group studies fundamental theories of this effect.

To read more:

  1. Folding mechanisms at finite temperature,
    Zeb Rocklin, Vincenzo Vitelli, and Xiaoming Mao,
    arXiv:1802.02704 [cond-mat.soft], (2018).
  2. Finite temperature mechanical instability in disordered lattices,
    Leyou Zhang and Xiaoming Mao
    Physical Review E 93, 022110 (2016).
  3. Mechanical instability at finite temperature,
    Xiaoming Mao, Anton Souslov, Carlos I. Mendoza, and T. C. Lubensky,
    Nature Communications 6, 5968 (2015).

Colloidal and Nanoscale Self Assembly

Self-assembly is an efficient scalable method to obtain materials with novel structures. My group studies fundamental problems of self-assembly, especially mechanical aspects of the problem.

To read more:

  1. Capillary-driven binding of thin triangular prisms at fluid interfaces,
    Joseph A Ferrar, Deshpreet S Bedi, Shangnan Zhou, Peijun Zhu, Xiaoming Mao, Michael J Solomon,
    Soft Matter, Advance Article (2018).
  2. Self-assembly of three-dimensional open structures using patchy colloidal particles,
    Zeb Rocklin and Xiaoming Mao,
    Soft Matter, 10, 7569 (2014).
  3. Entropy favours open colloidal lattices,
    Xiaoming Mao, Qian Chen, and Steve Granick,
    Nature Materials 12, 217(2013).