田中 展

A very low-frequency mode supported within an auxetic structure is presented. We propose a constrained periodic framework with corner-to-corner and edge-to-edge sharing of tetrahedra and develop a kinematic model incorporating two types of linear springs to calculate the momentum term under infinitesimal transformations. The modal analysis shows that the microstructure with its two degrees of freedom has both low- and high-frequency modes under auxetic transformations. The low-frequency mode approaches zero frequency when the corresponding spring constant tends to zero. With regard to coupled eigenmodes, the stress–strain relationship of the uniaxial forced vibration covers a wide range. When excited, a very slow motion is clearly observed along with a structural expansion for almost zero values of the linear elastic modulus.

<p>In this study, based on the Orowan equation and the principle of Bergstrom dislocation evolution, the plastic mechanical response of single crystalline micropillars is investigated by considering dislocation evolution. According to the single-arm source model, a physically revised Peirce-Asaro-Needleman (PAN) hardening model is proposed that can describe size-dependent hardening flow. The dislocation evolution parameters greatly affect the size-dependent plastic behavior of the single crystalline micropillars. Linking to the crystal plasticity finite element (CPFE) method, a physical plastic constitutive model with the framework of the CPFE method is proposed to solve the size-dependent boundary value problem. Compared with the results based on the original PAN hardening model, the proposed constitutive model can provide mechanical responses in different sizes, depending on the shear strain in each slip plane. If the non-friction condition between the rigid punch and the top surface of the pillar under uniaxial compression is considered, the results show that the shear band of the pillar mainly results from shear deformation on the slip plane with the maximum Schmid factor. Otherwise, the actual shear band deformation of the micropillars is complicated and combined with the other slip planes, that is, a multislip system. The results also indicate that friction affects size-dependent hardening.</p>

The friction of filled rubber on a rough surface is mainly determined by the rubber viscoelasticity and the surface property of multiple-scale asperities that can be represented by the power spectral density of the surface profile (i.e., power spectrum of surface roughness). This paper investigates a prediction model of rubber friction on dry and wet surfaces with large roughness under lightly squeezing, and finds a high stationary friction coefficient that depends on sliding speed. To this end, we demonstrated friction testing at low velocities with carbon-black-filled rubber and a hard substrate having self-affine surface roughness. From the experiment results, we estimated the hysteresis friction coefficient related to energy dissipation resulting from cyclic deformations of the viscoelastic rubber by applying the theory developed by Persson [(J. Chem. Phys. 115, 3840 (2001)]. We discussed the additional factor, an adhesion force, which also increases the friction coefficient. We concluded that the hysteresis loss of rubber viscoelastic deformation contributes most of the friction force, accounting for the nonlinear viscoelastic behavior of filled rubber, and that the operative surface wavelength extends to the order of micrometers.

Cellular solids with internal microstructures enable the reduction in some environmental loads because of their lightweight bodies, and deliver unique elastic, electromagnetic and thermal properties. In particular, their large deformability without topological change is one of their most interesting solid properties. In this study, we propose a bar-and-joint framework assembled with a basic unit of motion structure, which has eightfold rotational symmetry (MS-8). The MS-8 is made of tetragons, arranged in a concentric fashion, which are transformed into either one of two different aligned patterns of square cells according to the coordinated rotations of the inside squares. Square cells are extremely anisotropic, which is why the stiffness of the MS-8 changes dramatically in the transformation process. Thus, the MS-8 exhibits bi-stiffness according to the two different motions. Taking advantage of the bi-stiffness property, the possibilities of deformation behaviours for repetitive structures of MS-8s are discussed.

Spatial structures as being observed in cellular solids behave a wide variety of elastic deformation. In particular, some types of bending-dominated structures might produce the potential deformation mechanics exerted by the rotational manners of flexible joints. In this paper, we propose some of two-dimensional microstructures constructed of four-coordinate flexible joints and elbowed beam members, and conduct the numerical analyses and uniaxial tensile tests, using the really manufactured frameworks, for evaluating the Poisson's ratios of the proposed structures. The elastic properties obtained by the real model, which cover the considerable ranges of Poisson's raios dependent on joint flexibilities, correspond well to those by numerical results. In addtion, the out-of-plane deformation of a certain rigidly jointed structure is newly found from the present experiment.

In this paper, we propose a finite displacement modeling technique based on the total Lagrangian formulation for the structural analysis of two-dimensional (2D) framed structures connected by flexible joints. Our proposed model consists of beam segments with three-node elements and flexible joints with multi-rotational nodes, which have higher rotational degrees of freedom for deformation compared with those of a classical continuum beam model. Therefore, the category of this model can be regarded as a piecewise C¹ continuum beam model with rotational discontinuity on the joints. The objective of this study is to understand both the buckling modes and the post-buckling behaviors, which are key issues to understanding the integrity of the framed structures. Large elastic deformation simulations of the proposed model reveal that a 2D repetitive structure with finite square grids has biaxial symmetry buckling as a higher-order mode under uniaxial compression and has redundant post-buckling deformability, which rigid-jointed structures might not have.