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In the past ten years, the group members of Solid Mechanics Division have got great achievements in the elasticity theory at nanoscale, the constitutive laws and failure behavior of functional materials, and the computational mechanics methods for materials and structures.

Impacts: Over the past five years, more than 30 scientific and engineering research projects have been finished, including several projects supported by the State Key Program, the Major Research plan of the National Natural Science Foundation of China, and the National Basic Research Program (973 Program) of China. Over 200 peer-reviewed articles have been published on international journals, including Nature Comm., PNAS, PRL, JMPS, APL, Adv Appl Mech, Acta Mater, Adv Mater, etc. It has been widely cited by researchers. Eight papers become hot papers of the journals, and two papers have become highly cited papers, each cited more than 170 times (SCI). The works had been granted with the Second Prize of National Natural Science Award (2010). The researchers have been invited to give more than 40 plenary lectures, keynote lectures, and invited lectures at international conferences/IUTAM symposia.
a) Mechanics theory of complex materials
(1) Eshelby formalism and micromechanical framework for nanocomposites. We established the non-classical Eshelby formalism for nano-inclusions by including the surface stress effect. The most salient feature different from the classical formalism is that the elastic fields become nonuniform in the inclusion/inhomogeneity and are size-dependent, whereas the classical ones are uniform and size-independent. We developed the fundamental framework of micromechanical procedure to account for the interface stress effect for predicting the effective elastic moduli of heterogeneous materials containing nano inhomogeneities. It is shown that the effective bulk and shear moduli depend on the ratios of the intrinsic length scales of the surface elasticity to the characteristic length of the nano metre feature in the material. Based on the above micromechanical framework and experiment, we found that Hierarchical, multilayered cell walls reinforced by recycled silk cocoons enhance the structural integrity of honeybee combs.

Figure 2.1 Hierarchical structure of one-year-old honeycomb at macro-, micro- and nanoscales. (Zhang et al., Proc. National Acad. Sci. USA, 107, 9502, 2010).
(2) Theory of surface stress and wetting transition for complex solid surfaces. We investigated the bending of cantilevers with rough surfaces, and showed that the sensitivity of the cantilever sensor can be tuned by surface structuring. In some cases, the sign of the bending curvature may be inverted. Therefore, the work suggests a correction to the classical Stoney formula, and provides a tool for intentionally tuning the cantilever sensitivity. We examined in situ liquid-air interfaces on a submerged surface patterned with cylindrical micropores by confocal experiments, and showed that a metastable state dynamically involves, leading the wetting transition from a Cassie-Baxter to Wenzel state. A diffusion-based model was proposed and the prediction agrees well with the experiment results.

Figure 2.2 Left: Images of various wetting states taken by confocal microscopy. Right: Comparison between theoretical and experimental results (Lv et al., Physical Review Letters, 112, 196101, 2014.)
(3) Realization of nanofluidic control by nanoporous materials. We showed for aqueous electrolyte imbibition in nanoporous gold that the fluid flow can be reversibly switched on and off through electric potential control of the solid–liquid interfacial tension, that is, we can accelerate the imbibition front, stop it, and have it proceed at will. Our findings demonstrate that the high electric conductivity along with the pathways for fluid/ionic transport render nanoporous gold a versatile, accurately controllable electrocapillary pump and flow sensor for minute amounts of liquids with exceptionally low operating voltages.

Figure 2.3 Schematic of experiment setup (setup) and electric-switchable control of imbibition in nanoporoud gold (Left) (Xue et al., Nature Communications 5:4237 DOI:10.1038/ncomms5237, 2014).
(4) Mechanics theory of heterogeneous films and its application. We presented the solutions of temperature and stresses in a film/substrate structure under a local thermal load on the film surface. Then, we proposed and fabricated a novel graphene coated CAFM tip for the electrical characterization of nanostructured materials. Our graphene coated tips are shown to be extremely stable and resistant even under high currents and frictions, leading to longer device lifetime, and the tips can also protect the material under test from interaction with the tip varnish, which could lead to false imagining.


Figure 2.4 Schematic of an a) as-received, and (b) graphene-coated, commercially available Pt–Ir varnished tip. c) EDS analysis of both as-received (red line) and graphene-coated (black line) tips (Lanza et al., Advanced Materials 25, 1440, 2014).
b)  Constitutive laws and failure behavior of functional materials
(1) The constitutive theory of ferroelectric materials. We conducted a series of constitutive experiments on ferroelectric materials under coupled electromechanical loading. Based on the experiments results, we proposed a united macro/micro-scopic constitutive model for ferroelectrics, which had been recognized as one of the three ferroelectric constitutive models in the world. We further proposed the concept of constrained domain switching and built a microscopic model for polycrystalline ferroelectrics, which can well reproduce the Taylor’s rule of plasticity.
(2) Reliability study of ferroelectric materials. We systematically investigated the fracture, fatigue and mechanical depolarization behavior of ferroelectrics under electric and/or mechanical loading. We proposed a Paris Law for ferroelectric fatigue crack propagation which is analogical to the case in structural materials.
(3) Tunable pseudoelasticity in ferroelectrics and ferromagnetics. Pseudoelasticity is common in shape memory alloys but rarely seen in ferroelectrics and ferromagnetics. We realized pseudoelasticity in both ferroelectrics and ferromagnetics under electromechanical or magnetomechanical loading. The pseudoelasticity can be tunable by applied electric (magnetic) field. This work had been cited by a Perspective paper on Science 2013.


Fig 2.5. The principle of revealing superelasticity in a poled tetragonal ferroelectric crystal via reversible 90o domain switching under electromechanical loading. (Li et al, Applied Physics Letters, 102, 092905, 2013)
c) Computational mechanics methods for materials and structures
(1)  We developed both 2-D and 3-D discrete element method (DEM) and proposed the failure criterion for the continuum mechanics problems. We also developed high-precision formulism and realized the united computations on gas, liquid and solids, which cannot be solved by the commercial software.
(2)  We systematically studied multi-scale computational mechanics methods for electromechanical coupled problems and built a computational platform for these problems. We also use these computational methods to study the multifunctional materials and structures with light weight, high strength, thermal insulation, etc.
Address: Mechanics Building, Peking University, Beijing, China Zip: 100871 Phone: +86-10-62753257 Fax: +86-10-62753257 Email: mes@mech.pku.edu.cn