Comment on: I-Shih Liu: Constitutive theory of anisotropic rigid heat conductors

In I-Shih Liu's paper \C{1}, the compatibility of anisotropy and material frame indifference of a rigid heat conductor is investigated. For this purpose, the deformation gradient is introduced into the domain of the constitutive mapping. Because of the presupposed rigidity, the deformation gradient is here represented by an orthogonal tensor. The statement, that the usual procedure -- not to introduce the deformation gradient into the state space of rigid heat conductors -- causes isotropy because of the material frame indifference, is misleading.Comment: 8 page

Self-Consistent Screening Approximation for Flexible Membranes: Application to Graphene

Crystalline membranes at finite temperatures have an anomalous behavior of the bending rigidity that makes them more rigid in the long wavelength limit. This issue is particularly relevant for applications of graphene in nano- and micro-electromechanical systems. We calculate numerically the height-height correlation function $G(q)$ of crystalline two-dimensional membranes, determining the renormalized bending rigidity, in the range of wavevectors $q$ from $10^{-7}$ \AA$^{-1}$ till 10 \AA$^{-1}$ in the self-consistent screening approximation (SCSA). For parameters appropriate to graphene, the calculated correlation function agrees reasonably with the results of atomistic Monte Carlo simulations for this material within the range of $q$ from $10^{-2}$ \AA$^{-1}$ till 1 \AA$^{-1}$. In the limit $q\rightarrow 0$ our data for the exponent $\eta$ of the renormalized bending rigidity $\kappa_R(q)\propto q^{-\eta}$ is compatible with the previously known analytical results for the SCSA $\eta\simeq 0.82$. However, this limit appears to be reached only for $q<10^{-5}$ \AA$^{-1}$ whereas at intermediate $q$ the behavior of $G(q)$ cannot be described by a single exponent.Comment: 5 pages, 4 figure

Formability evaluation of double layer circular tube as a device with energy absorption capacity

Recently, earthquakes frequently occur in Japan. It is desired to promote seismic isolation technology of building. It has been found that newly designed composite material filled with low rigidity material to high rigidity material has significant energy absorbing capacity. However, it must have higher energy absorption capacity in order to respond to a large scale earthquake. Therefore, we have proposed an energy absorbing device with a double layer circular tube as a cell. In previous work, it has been shown that hysteresis occurs and absorbs the energy by friction that is generated between the outer layer and the inner layer. It is effective when inside shape of inner layer is defined as floral pattern. In this study, we considered to form the inner layer circular tube by forward and backward extrusion and to assemble with the outer layer circular tube at the same time. After forming, it is necessary to generate hysteresis around the entire circumference of the circular tube. Ideally, the inner layer circular tube is tightened to the outer layer circular tube. In this research, it was aimed to know the contact state between the outer layer and the inner layer after forming. Therefore, the influence of the presence or absence of the outer layer circular tube on formability was investigated. As a result, there was a tendency for large elastic strain to remain at the contact portion between the circular tubes when the outer layer circular tube was set. This means that the outer layer circular tube hinders elastic recovery of the inner layer circular tube. Therefore, it was confirmed that the inner layer circular tube was tightened by the outer layer circular tube. The same result was obtained when the inner shape of the inner layer circular tube was a flower pattern

A Study in the Use of Elastic Materials in Expandable Containment Units

The rigidity of materials in conjunction with the aspect of elasticity has been a concern of modern technologies and construction in recent centuries because of the advantages that expandable storage would bring to the fields of containment units with respect to population growth and space exploration. The world population is currently growing at an exponential rate, and as our population grows, the more important it will become to have containment units that can both contain large volumes of material as well as minuscule amounts of material without wasting space. In order accomplish this, we will need a new type of storage container that utilizes the inherent strengths of both flexibility and rigidity to find a unique balance between the two. The purpose of this study is not to necessarily find the final answer to the question of expandable storage, but to narrow the range of questions that later research will use to finally answer the question, “How will we do it?” In order to research the utility of elastic material in creating storage devices in the same manner as has have described, this study would create an expandable backpack as a scaled-down case study. The backpack utilizes grooved panels made of lightweight, rigid material such as PVC-plastic in conjunction with elastic cloth, made of a mix of nylon and spandex, to create a container that will stand rigid on its own, but also expand in horizontal directions so that it can hold objects larger than its original volume. By creating male and female connectors in the individual panels, the container will be able to stand rigid, but also expand using elastic cloth sandwiched between the halves of each panel. The front and back of the container will be made of two panels, but the sides will be made up of 4 panels, so that expansion is more likely to occur in those directions, as well as lessen the stress on the fabric. In order to create the container, the team sampled multiple ratios of nylon-to-spandex, as well as tested the rigidity of different woods and plastics. Upon deciding on a material, PVC, a prototype was built and tested. The testing process involved filling the container to with varying amounts of weight, such as textbooks and laptops, and having a test subject walk around carrying the objects for varying amounts of time. The study also tested the amount of volume the backpack is able to expand, aiming for between five and ten percent increased volume. While the purpose of this study is not to solve the problem of expandable storage definitively, the concept of elastic cloth between interlocking panels has a high likelihood of being a step in the right direction