A Study of the Multi-Stability in a Non-Rigid Stacked Miura-Origami Cellular Mechanism

Multi-stable structures have gathered extensive interest because they can provide a broad spectrum of adaptive functions for many engineering systems. Especially, origami sheets with a translational periodicity can be stacked and assembled to form a multi-stable cellular solid, which has emerged as a promising platform to design functional structures. This paper investigates the multi-stability characteristics of a non-rigid stacked Miura-origami mechanism consisting of Miura-ori sheets and accordion-shaped connecting sheets, focusing on the elemental unit cell. A nonlinear mechanical model based on the barhinge approach is established to quantitatively study the unit cell’s multi-stability with intentionally relaxed rigid-folding conditions. Results show that only two stable states are achievable in the unit cell with enforced rigid-folding kinematics. However, if one relaxes the rigid-folding conditions and allows the facet to deform (i.e. non-rigid folding), four stable states are reachable in the unit cell if the crease torsional stiffness of the connecting sheets becomes sufficiently larger than that of the Miura-ori sheets, or the stress-free folding angle deviates away from 0°. A close examination of the potential energy composition of the non-rigid unit cell provides a detailed principle underpinning the multi-stability. By showing the benefits of exploiting facet compliance, this study can become the building blocks for origami-based structures and material systems with a wider variety of novel functionalities.

On Determination of the Effective Thermal Conductivity of a Bundle of Steel Bars Using the Krischer Model and Considering Thermal Radiation

Cellular solid materials are commonly found in industrial applications. By definition, cellular solids are porous materials that are built of distinct cells. One of the groups of such materials contains metal foams. Another group of cellular metals contains bundles of steel bars, which create charges during the heat treatment of the bars. A granular structure connected by the lack of continuity of the solid phase is the main feature that distinguishes bundles from metal foams. The boundaries of the bundle cells are made of adjacent bars, with the internal region taking the form of an air cavity. In this paper, we discuss the possibility of using the Krischer model to determine the effective thermal conductivity of heat-treated bundles of steel bars based on the results of experimental tests and calculations. The model allows the kef coefficient to be precisely determined, although it requires the weighting parameter f to be carefully matched. It is shown that the value of f depends on the bar diameter, while its changes within the examined temperature range (25–800 °C) can be described using a third-degree polynomial. Determining the coefficients of such a polynomial is possible only when the effective thermal conductivity of the considered charge is known. Moreover, we analyze a simplified solution, whereby a constant value of the f coefficient is used for a given bar diameter; however, the kef values obtained thanks to this approach are encumbered with inaccuracy amounting to several dozen percentage points. The obtained results lead to the conclusion that the Krischer model cannot be used for the discussed case.

The natural neighbor radial point interpolation method in the Elasto-Static analysis of Honeycomb-Shaped foams

Cellular solid materials are progressively becoming more predominant in lightweight structural applications as more technologies realize these materials can be improved in terms of performance, quality control, repeatability and production costs, when allied with fast developing manufacturing technologies such as Additive Manufacturing. In parallel, the rapid advances in computational power and the use of new numerical methods, such as Meshless Methods, in addition to the Finite Element Method (FEM) are highly beneficial and allow for more accurate studies of a wide range of topologies associated with the architecture of cellular solid materials. Since these materials are commonly used as the cores of sandwich panels, in this work, two different topologies were designed — conventional honeycombs and re-entrant honeycombs — for 7 different values of relative density, and tested on the linear-elastic domain, in both in-plane directions, using the Natural Neighbor Radial Point Interpolation Method (NNRPIM), a newly developed meshless method, and the Finite Element Method (FEM) for comparison purposes.

Multiscale Modelling and Mechanical Anisotropy of Periodic Cellular Solids with Rigid-Jointed Truss-Like Microscopic Architecture

This paper investigates the macroscopic anisotropic behavior of periodic cellular solids with rigid-jointed microscopic truss-like architecture. A theoretical matrix-based procedure is presented to calculate the homogenized stiffness and strength properties of the material which is validated experimentally. The procedure consists of four main steps, namely, (i) using classical structural analysis to determine the stiffness properties of a lattice unit cell, (ii) employing the Bloch’s theorem to generate the irreducible representation of the infinite lattice, (iii) resorting to the Cauchy–Born Hypothesis to express the microscopic nodal forces and deformations in terms of a homogeneous macroscopic strain field applied to the lattice, and (iv) employing the Hill–Mandel homogenization principle to obtain the macro-stiffness properties of the lattice topologies. The presented model is used to investigate the anisotropic mechanical behavior of 13 2D periodic cellular solids. The results are documented in three set of charts that show (i) the change of the Young and Shear moduli of the material with respect to their relative density; (ii) the contribution of the bending stiffness of microscopic cell elements to the homogenized macroscopic stiffness of the material; and (iii) polar diagrams of the change of the elastic moduli of the cellular solid in response to direction of macroscopic loading. The three set of charts can be used for design purposes in assemblies involving the honeycomb structures as it may help in selecting the best lattice topology for a given functional stiffness and strength requirement. The theoretical model was experimentally validated by means of tensile tests performed in additively manufactured Lattice Material (LM) specimens, achieving good agreement between the results. It was observed that the model of rigid-joined LM (RJLM) predicts the homogenized mechanical properties of the LM with higher accuracy compared to those predicted by pin-jointed models.

Effect of the Operational Conditions in the Characteristics of Ceramic Foams Obtained from Quartz and Sodium Silicate

Ceramic foams were fabricated without using melting pots through the direct foaming of compacted powder mixtures of commercial quartz (SiO2) with fluxing agents (Na2CO3 and CaO) and a foaming agent (Na2SiO3·5H2O) at a relatively low temperature range (850−870 °C). The effects of the pressing pressure of the powders, the foaming time, foaming temperature, and mixture content were evaluated. The obtained cellular solid materials presented an acceptable volumetric expansion at a pressing pressure of 4 t. The materials only presented porosity at a minimum temperature of 850 °C and at a minimum time of 30 min. All the foamed samples showed an acceptable symmetric expansion and non-appreciable fissures. The study of the mixture content through the statistical software MODDE® shows that the porosity of the samples was principally affected by the Na2SiO3 content and the foaming temperature. The samples obtained at the optimum controlling factors proposed by this statistical software presented an apparent density, porosity, and mechanical strength of 1.09 ± 0.03 g/cm3, 56.01% ± 1.12%, and 3.90 ± 0.16 MPa, respectively. Glass and ceramics foams such as those obtained in this work become attractive as insulation materials in applications where high temperatures occur due to their higher melting points.

Drooping of Gerbera flower heads: mechanical and structural studies of a well-known phenomenon

Gerbera , one of the most loved cut flowers, is (in)famous for the drooping of its flower heads under dehydration. This effect has been quantified by analysing both fully turgescent and wilting peduncles of Gerbera jamesonii ‘Nuance’. Wilting peduncles display pronounced bending in the region directly below the inflorescence after 24 h of dehydration, while the rest of the peduncle remains upright. Using anatomical measurements and three-point bending tests, we have analysed whether this phenomenon is caused by mechanical and/or geometrical alterations. We have found that both the flexural rigidity and the axial second moment of area are significantly decreased in the apical part of wilting peduncles, whereas the bending elastic modulus shows no significant change. Moreover, cross-sections of wilting peduncles ovalize significantly more than those of turgescent peduncles and exhibit considerable shrinkage of the parenchyma, taking up the majority of the cross-sectional area. Generally, the drooping of wilting Gerbera flowers can be regarded as a temporary instability of a rod-shaped cellular solid caused by anatomical differences (tissue arrangement, existence or the absence of a pith cavity) and geometrical changes (the decrease of axial second moment of area, cross-sectional ovalization, shrinkage of tissues) between the apical and basal regions of their peduncles.