A finite element method based on ABAQUS is employed to examine the correlation between the microstructure and the elastic response of planar Cayley treelike fiber networks. It is found that the elastic modulus of the fiber network decreases drastically with the fiber length, following the power law. The power law of elastic modulus G' vs the correlation length xi obtained from this simulation has an exponent of -1.71, which is close to the exponent of -1.5 for a single-domain network of agar gels. On the other hand, the experimental results from multidomain networks give rise to a power law index of -0.49. The difference between -1.5 and -0.49 can be attributed to the multidomain structure, which weakens the structure of the overall system and therefore suppresses the increase in G'. In addition, when the aspect ratio of the fiber is smaller than 20, the radius of the fiber cross-section has a great impact on the network elasticity, while, when the aspect ratio is larger than 20, it has almost no effect on the elastic property of the network. The stress distribution in the network is uniform due to the symmetrical network structure. This study provides a general understanding of the correlation between microscopic structure and the macroscopic properties of soft functional materials.

In order to investigate the influence of sand particle-size gradation on cyclic and postcyclic shear strength behaviour on sand-geotextile interfaces, a series of monotonic direct shear (MDS), cyclic direct shear (CDS), and postcyclic direct shear (PCDS) tests were performed using a large-scale direct shear apparatus. The influence of cyclic shear history on the direct shear behaviour of the interface was studied. The results indicated that cyclic shear stress degradation occurred at the sand-geotextile interface. Shear volumetric contraction induced by the cyclic direct shear increased with the increase in cycle number. The lowest final contraction value was observed in discontinuously graded sand. In the MDS tests, there were great differences in interface shear strength due to the different particle-size gradations, whereas the differences between shear volumes were negligible. In the PCDS tests, the shear stress-displacement curves exhibited postpeak stress hardening behaviour for different particle-size gradations, and differences in shear volumes were detected. The well-graded sand-geotextile interface had a higher value of shear stiffness and a higher damping ratio relative to the other interfaces. Postcyclic shear stress degradation was observed for the discontinuously graded sand-geotextile interface.

This article studies consensus problem of multi-agent systems under fast switching networks depending on a small parameter 𝜀 > 0. In contrast to the existing methods that are qualitative, we present, for the first time, constructive and quantitative results for finding an upper bound on 𝜀 that preserves the consensus and for designing the consensus protocol that includes the designs of continuous-time controller and of sampled-data controller. We first employ a time-delay approach to periodic averaging for continuous-time control of multi-agent systems under fast switching networks leading to a time-delay model where the delay length is equal to 𝜀. We construct an appropriate Lyapunov functional for finding sufficient stability conditions in the form of linear matrix inequalities (LMIs). The upper bound on 𝜀 that preserves the exponential stability is found from LMIs. Moreover, sufficient conditions on the existence of controller gain are, for the first time, derived for the multi-agent systems under fast switching networks. For the implementation of consensus protocol, we further extend our method to sampled-data consensus of multi-agent systems under fast switching networks where additional Lyapunov functionals are presented to compensate the term due to the sampling. Finally, an example of Caltech multivehicle wireless test bed vehicles is given to illustrate the efficiency of the method.

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