Dr Martin Walker

When poking a thin shell-like structure, like a plastic water bottle, experience shows that an initial axisymmetric dimple forms around the indentation point. The ridge of this dimple, with increasing indentation, eventually buckles into a polygonal shape. The polygon order generally continues to increase with further indentation. In the case of spherical shells, both the underlying axisymmetric deformation and the buckling evolution have been studied in detail. However, little is known about the behaviour of general geometries. In this work we describe the geometrical and mechanical features of the axisymmet-ric ridge that forms in indented general shells of revolution with non-negative Gaussian curvature and the conditions for circumferential buckling of this ridge. We show that, under the assumption of 'mirror buckling' a single unified description of this ridge can be written if the problem is non-dimensionalised using the local slope of the undeformed shell mid-profile at the ridge radial location. However, in dimensional form the ridge properties evolve in quite different ways for different mid-profiles. Focusing on the indentation of shallow shells of revolution with constant Gaussian curvature, we use our theoretical framework to study the properties of the ridge at the circumferential buckling threshold and evaluate the validity of the mirror buckling assumption against a linear stability analysis on the shallow shell equations, showing very good agreement. Our results highlight that circumferential buckling in indented thin shells is controlled by a complex interplay between the geometry and the stress state in the ridge. The results of our study will provide greater insight into the mechanics of thin shells. This could enable indentation to be used as a means to measure the mechanical properties of a wide range of shell geometries or used to design shells with specific mechanical behaviours.

Tubular auxetic structures have wide-ranging applications including medical stents, collapsible energy absorbers, and novel fasteners. To expand development in these areas, and open up new application directions, an expanded range of design and construction methods for auxetic tubes is required. In this study we propose a new method to construct polygonal cross-section auxetic tubes using the principles of origami and kirigami. These tubes exhibit useful global auxetic behaviour under axial extension, despite the individual polygon faces not being auxetic themselves. A flat kirigami sheet cannot be simply folded into a polygonal tube since this creates kinematic incompatibilities along the polygon edges. This is resolved by replacing the edge folds with an origami mechanism consisting of a pair of triangular facets. This approach eliminates the incompatibilities at the edges while maintaining a connection between faces. The proposed edge connection also introduces additional control parameters for the tube kinematics: for example, introducing a kinematic limit on tube extension and enabling non-uniform behaviour along the length of the tube. The rich kinematic behaviour possible with polygonal cross-section kirigami tubes has potential applications ranging from soft robotics to energy-dissipating devices.

The paper examines the composite performance of hybrid steel-timber lightweight floor assemblies incorporating cold-formed steel (CFS) profiles and plywood (PW) flooring panels with varying degrees of shear connection achieved by means of self-drilling screws. Material, push-out, and three-point short-span floor tests with or without web openings were carried out. The results and observations from the tests provide a detailed insight into the inelastic properties and ultimate response of such floor systems. Push-out tests indicate that denser connector arrangements increase connection stiffness, while push-out and short beam tests suggest an optimum connector spacing equal to the beam depth for a balance between structural performance and constructability. The experimental observations indicate that the ultimate condition of the short composite beams was characterized by CFS web crippling under the load application point, followed by a pull-through of the self-drilling screws. Web openings reduced the strength of the floor elements compared to the members with full webs. Complementary numerical studies are undertaken using nonlinear finite element procedures which were validated against the beam tests, offering a detailed insight into the stress levels in the timber, steel, and connectors. Codified procedures for determining the capacity of composite CFS sections are compared with the test results, and guidance for the practical design and construction of such systems is given.

Effective elastic moduli of lattice-based materials are one of the most crucial parameters for the adoption of such artificial microstructures in advanced mechanical and structural systems as per various application-specific demands. In conventional naturally occurring materials, these elastic moduli remain invariant under tensile and compressive normal modes or clock-wise and anti-clock-wise shear modes. Here we introduce programmed domain discontinuities in the cell walls of the unit-cells of lattice metamaterials involving a bi-level microstructural design to achieve non-invariant elastic moduli under tensile and compressive normal modes or clock-wise and anti-clock-wise shear modes. More interestingly, such non-invariance can be realized in the linear small deformation regime and the elastic moduli can be tailored to have higher or lower value in any mode compared to the other depending on the placement and intensity of the discontinuities in a programmable paradigm. We have derived an efficient analytical framework for the effective elastic moduli of lattice materials taking into account the influence of domain discontinuity. The axial and shear deformations at the beam level are considered along with bending deformation in the proposed analytical expressions. The numerical results ascertain that the domain discontinuities, in conjunction with unit cell level geometric parameters, can impact the effective elastic constants significantly under different modes of far-field stresses. It is further revealed that the degree of auxeticity of such lattices can be programmed to have target values (including non-invariance under different modes of deformation) as a function of the intensity and location of domain discontinuity when axial and shear deformations are included at the beam level. Realization of the unusual non-invariant elastic moduli of bi-level architected lattice materials would lead to a range of technologically demanding niche applications where one mode of deformation requires more or less force to deform compared to the opposite mode. Besides being able to perform as a load-bearing component, the proposed metamaterial can be used as an integrated sensor for measuring the level of stress or strain in structures.

The effect of blast loading on civilian structures has received much attention over the past several years. The behavior of architectural glazing is of particular interest owing to the disproportionate amount of damage often associated with the failure of this component in a blast situation. This paper presents the development of a simple yet accurate finite element-based tool for the analysis of architectural glazing subjected to blast loading. This has been achieved through the creation of a user-friendly computer program employing the explicit finite-element method to solve for the displacements and stresses in a pane of glass. Both monolithic and laminated panes have been considered, in single and insulated unit configurations, and employing several types of glass. In all cases, the pane of glass has been modeled as a plate supported by an array of boundary conditions that include spring supports, and two failure criteria are employed. Furthermore, the program is designed to predict the hazard level, given a particular glazing configuration and blast load.

The art form of kirigami has recently attracted interest from engineers and scientists for generating complex three-dimensional structures from flat sheet-like materials. When thin metal sheets are used, the deformation can become plastic and localized, allowing for permanent intricate shapes to be formed. In this study, the illustrative case of an annular plate under diametral tension is considered, and it is shown that the deformed shape can be considered as a spatial mechanism of localized plastic yield lines connected to largely undeformed regions. This technique provides useful information for the design of novel permanently deployable structures.

We investigate the bistable behaviour of folded thin strips bent along their central crease. Making use of a simple Gauss mapping, we describe the kinematics of a hinge and facet model, which forms a discrete version of the bistable creased strip. The Gauss mapping technique is then generalised for an arbitrary number of hinge lines, which become the generators of a developable surface as the number becomes large. Predictions made for both the discrete model and the creased strip match experimental results well. This study will contribute to the understanding of shell damage mechanisms; bistable creased strips may also be used in novel multistable systems. •Gauss mapping approach is used to describe the kinematics of a hinge and facet model of a bistable creased strip.•The approach is generalised for an arbitrary number of hinge lines approaching the generators of a developable surface.•Bistability is maintained when a hole is introduced removing the stress singularity.•Predictions are compared to experiment showing good agreement.

Folded structures are often idealized as a series of rigid faces connected by creases acting as revolute hinges. However, real folded structures can deform between creases. An example of particular interest is a disk decorated by multiple radial creases. Such disks are bistable, snapping between a "natural" and "inverted" shape. We investigate the mechanical behavior of these creased disks and propose a new analytical approach to describe their mechanics. Detailed experiments are performed which show that, when indented at the center, a localized dimple forms, precluding the conical shape assumed in previous studies. As the indentation depth increases this dimple expands radially until reaching the disk edge when it snaps to the inverted shape, which has a conical form. We develop an analytical model which approximates each face as a series of rigid facets connected by hinges that can both rotate and stretch. Energy expressions are derived relating hinge rotation and stretching to compatible shell deformations of the facets and equilibrium enforced by minimizing the total strain energy. By increasing the number of facets, the mechanics of the continuum shell is approached asymptotically. The analysis shows that membrane stretching of the faces is required when a conical form of deformation is enforced. However, in the limit of zero thickness, the forming and propagation of a localized dimple is inextensional. This new approach relates the kinematic analysis of rigid origami to the mechanics of thin shells, offering an efficient method to predict the behavior of folded structures.

Explosions generate overpressures that can cause irreparable damage to structures. For many buildings, especially critical infrastructure, continued operation after an explosive attack is essential. The use of energy-dissipating methods will enable the protection of a structure and occupants from a blast and permit the timely repair and re-occupation of the building after an event. The concept behind the system presented is the creation of panels that can be used as cladding for structures. The panels are connected to the main structure using energy-dissipating component assemblies around the panel edge. When subjected to a blast load the panels transfer the blast pressure through the assemblies, thereby reducing the forces transmitted to the underlying structure. After an event, the panels and energy-dissipating component assemblies can be replaced quickly and easily, allowing the building to be reoccupied in a short time after an attack. This study focuses on the characterization of energy-dissipating component assemblies using static and dynamic laboratory testing. A predictive theory, supported by a single degree of freedom model, is developed and a general evaluation method proposed. Further laboratory testing expands the characterization of behaviour of the assemblies through experiments, with a blast generator in tension tests and in simulated blast panel tests. The time histories developed from tension tests are then compared to examine the effect of loading rate. The investigations on blast panels also include a comparison with predictions to determine whether the latter can describe the global behaviour of the system. Lastly, the response of the energy-dissipating component assemblies is evaluated in full-scale field blast tests on cladding panels.

Many structures in Nature and Engineering are dominated by the influence of folds. A very narrow fold is a crease, which may be treated with infinitesimal width for a relatively simple geometry; commensurately, it operates as a singular hinge line with torsional elastic properties. However, real creases have a finite width and thus continuous structural properties. We therefore consider the influence of the crease geometry on the large-displacement flexural behaviour of a thin creased strip. First, we model the crease as a shallow cylindrical segment connected to initially flat side panels. We develop a theoretical model of their coupled flexural behaviour and, by adjusting the relative panel size, we capture responses from a nearly singular crease up to a full tape-spring. Precise experiments show good agreement compared to predictions.

Following on Part I of this work series on local kirigami mechanics, we present a study of a discretely creased mechanism as a model to investigate the mechanics of the basic geometric building block of kirigami - the e-cone. We consider an annular disk with a single radial slit discritised by a series of radial creases connecting kinematically flat rigid panels. The creases allow both relative rotation and separation between panels, capturing both bending and stretching deformations. Admissible equilibrium congurations are obtained by penalising these deformations using elastic springs with stiffnesses derived from compatible continuum plate deformations. This provides a tool to study both inextensible and extensible e-cone congurations due to opening of the slit and rotation of its lips. This creased model hence offers the possibility to study the e-cone away from its isometric limit, i.e., for plates with finite thickness, and explore the full range of post-buckling (far-from-threshold) behaviour as well as initial buckling (near-threshold) instability. Our local approach provides a fundamental understanding of kirigami phenomenology, underpinned by a proper theoretical approach to geometry and mechanics.