Nonlinear Dynamics of Spherical Shells Buckling under Step Pressure

This is the author accepted manuscript. The final version is available from The Royal Society via the DOI in this record.Dynamic buckling is addressed for complete elastic spherical shells subject to a rapidly applied step in external pressure. Insights from the perspective of nonlinear dynamics reveal essential mathematical features of the buckling phenomena. To capture the strong buckling imperfection-sensitivity, initial geometric imperfections in the form of an axisymmetric dimple at each pole are introduced. Dynamic buckling under the step pressure is related to the quasi-static buckling pressure. Both loadings produce catastrophic collapse of the shell for conditions in which the pressure is prescribed. Damping plays an important role in dynamic buckling because of the time-dependent nonlinear interaction among modes, particularly the interaction between the spherically symmetric 'breathing' mode and the buckling mode. In this paper we argue that the precise frequency dependence of the damping does not matter as most of the damping happens at a single frequency (the breathing frequency). In general, there is not a unique step pressure threshold separating responses associated with buckling from those that do not buckle. Instead there exists a cascade of buckling thresholds, dependent on the damping and level of imperfection, separating pressures for which buckling occurs from those for which it does not occur. For shells with small and moderately small imperfections the dynamic step buckling pressure can be substantially below the quasi-static buckling pressure

Buckling Thresholds for Pre-loaded Spherical Shells Subject to Localized Blasts

This is the author accepted manuscript. the final version is available from ASME via the DOI in this recordThis paper investigates the robustness against localized impacts of elastic spherical shells pre-loaded under uniform external pressure. We subjected a pre-loaded spherical shell that is clamped at its equator to axisymmetric blast-like impacts applied to its polar region. The resulting axisymmetric dynamic response is computed for increasing amplitudes of the blast. Both perfect shells and shells with axisymmetric geometric imperfections are analyzed. The impact energy threshold causing buckling is identified and compared with the energy barrier that exists between the buckled and un-buckled static equilibrium states of the energy landscape associated with the pre-loaded pressure. The extent to which the impact energy of the threshold blast exceeds the energy barrier depends on the details of its shape and width. Targeted blasts that approximately replicate the size and shape of the energy barrier buckling mode defined in the paper have an energy threshold that is only modestly larger than the energy barrier. An extensive study is carried out for more realistic Gaussian-shaped blasts revealing that the buckling threshold energy for these blasts is typically in the range of at least ten to forty percent above the energy barrier, depending on the pressure pre-load and the blast width. The energy discrepancy between the buckling threshold and energy barrier is due to elastic waves spreading outward from the impact and dissipation associated with the numerical integration scheme. Buckling is confined to the vicinity of the pole such that, if the shell is not shallow, the buckling thresholds are not strongly dependent on the location of the clamping boundary, as illustrated for a shell clamped half way between the pole and the equator.Engineering and Physical Sciences Research Council (EPSRC

A Unified Mathematical Modelling and Simulation for Cathodic Blistering Mechanism incorporating diffusion and fracture mechanics concepts

A novel mathematical model has been developed to understand the mechanism of blister initiation and propagation. The model employs a two-part theoretical approach encompassing the debondment of a coating film from the substrate, coupled with the design components incorporating diffusion and fracture mechanics, where the latter is derived from equi-biaxial tensile loading. Integrating the two components, a comprehensive mathematical design for the propagation of blister boundaries based on specific toughness functions and mode adjustment parameters has been developed. This approach provided a reliable and efficient prediction method for blister growth rate and mechanisms. The model provided a foundation for holistic design based on diffusion and mechanic components to enable better understanding of the debondment of thin elastic films bonded to a metallic substrate

Modeling the anchoring and performance of downhole equipment using an extended Gurson model

In oil and gas (O&G) exploration the well casing, in the form of a long steel tube, maintains the opening of the drilled well hole. Mechanical equipment is often inserted into the well for the purpose of well monitoring, pressure control and various operations. This downhole equipment may be mechanically connected to the pipe casing by the outward radial motion of anchoring teeth such that the inner wall casing is indented. The connection between the tool and the casing must support significant mechanical loads in the longitudinal (axial) direction of the casing, i.e. transverse to the direction of indentation, while minimizing the indentation depth in order to preserve the stiffness and strength of the casing. Consequently, a determination of the ultimate strength of the connection is of critical importance. Failure of this connection involves intense shear of the inner wall of the casing, akin to a machining operation. The critical load for axial slip can be determined experimentally or numerically (or by combination of both). In this study, detailed simulations are performed using the shear-extended GTN (Gurson-Tvergaard-Needleman) model. The choice of model is motivated by the need to accurately the extensive plastic deformation associated with indentation as well as shear-dominated ductile failure on a sub-millimeter scale. The shear-extended GTN model requires a careful calibration of the model parameters by an accurate measurement of the material response. Accordingly, the casing steel was characterized by appropriate measurements under a range of stress states. The calibrated model was used to investigate an idealized two-dimensional representation of the anchoring problem, with a focus on the effect of indentation depth upon connection strength. Both the indentation of the casing inner wall by the anchoring teeth and the subsequent shear of the casing wall were simulated in detail to determine the load required to initiate and progress slip of the anchoring teeth. The results of these analyses show that the connection strength increases linearly with increasing indentation depth

Probing shells against buckling: a non-destructive technique for laboratory testing

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.This paper addresses testing of compressed structures, such as shells, that exhibit catastrophic buckling and notorious imperfection sensitivity. The central concept is the probing of a loaded structural specimen by a controlled lateral displacement to gain quantitative insight into its buckling behaviour and to measure the energy barrier against buckling. This can provide design information about a structure's stiffness and robustness against buckling in terms of energy and force landscapes. Developments in this area are relatively new but have proceeded rapidly with encouraging progress. Recent experimental tests on uniformly compressed spherical shells, and axially loaded cylinders, show excellent agreement with theoretical solutions. The probing technique could be a valuable experimental procedure for testing prototype structures, but before it can be used a range of potential problems must be examined and solved. The probing response is highly nonlinear and a variety of complications can occur. Here, we make a careful assessment of unexpected limit points and bifurcations, that could accompany probing, causing complications and possibly even collapse of a test specimen. First, a limit point in the probe displacement (associated with a cusp instability and fold) can result in dynamic buckling as probing progresses, as demonstrated in the buckling of a spherical shell under volume control. Second, various types of bifurcations which can occur on the probing path which result in the probing response becoming unstable are also discussed. To overcome these problems, we outline the extra controls over the entire structure that may be needed to stabilize the response

Mechanical theory of the film-on-substrate-foil structure : curvature and overlay alignment in amorphous silicon thin-film devices fabricated on free-standing foil substrates

Flexible electronics will have inorganic devices grown at elevated temperatures on free-standing foil substrates. The thermal contraction mismatch between the substrate and the deposited device films, and the built-in stresses in these films, cause curving and a change in the in-plane dimensions of the workpiece. This change causes misalignment between the device layers. The thinner and more compliant the substrate, the larger the curvature and the misalignment. We model this situation with the theory of a bimetallic strip, which suggests that the misalignment can be minimized by tailoring the built-in stress introduced during film growth. Amorphous silicon thin-film transistors (a-Si:H TFTs) fabricated on stainless steel or polyimide (PI) (Kapton E®) foils need tensile built-in stress to compensate for the differential thermal contraction between the silicon films and the substrate. Experiments show that by varying the built-in stress in just one device layer, the gate silicon nitride (SiNx), one can reduce the misalignment between the source/drain and the gate levels from ∼400 parts-per-million to ∼100 parts-per-million

Smartphone Apps for Food Purchase Choices: Scoping Review of Designs, Opportunities, and Challenges

Background: Smartphone apps can aid consumers in making healthier and more sustainable food purchases. However, there is still a limited understanding of the different app design approaches and their impact on food purchase choices. An overview of existing food purchase choice apps and an understanding of common challenges can help speed up effective future developments.Objective: We examined the academic literature on food purchase choice apps and provided an overview of the design characteristics, opportunities, and challenges for effective implementation. Thus, we contribute to an understanding of how technologies can effectively improve food purchase choice behavior and provide recommendations for future design efforts.Methods: Following the PRISMA-ScR (Preferred Reporting Items for Systematic Reviews and Meta-Analyses extension for Scoping Reviews) guidelines, we considered peer-reviewed literature on food purchase choice apps within IEEE Xplore, PubMed, Scopus, and ScienceDirect. We inductively coded and summarized design characteristics. Opportunities and challenges were addressed from both quantitative and qualitative perspectives. From the quantitative perspective, we coded and summarized outcomes of comparative evaluation trials. From the qualitative perspective, we performed a qualitative content analysis of commonly discussed opportunities and challenges.Results: We retrieved 55 articles, identified 46 unique apps, and grouped them into 5 distinct app types. Each app type supports a specific purchase choice stage and shares a common functional design. Most apps support the product selection stage (selection apps; 27/46, 59%), commonly by scanning the barcode and displaying a nutritional rating. In total, 73% (8/11) of the evaluation trials reported significant findings and indicated the potential of food purchase choice apps to support behavior change. However, relatively few evaluations covered the selection app type, and these studies showed mixed results. We found a common opportunity in apps contributing to learning (knowledge gain), whereas infrequent engagement presents a common challenge. The latter was associated with perceived burden of use, trust, and performance as well as with learning. In addition, there were technical challenges in establishing comprehensive product information databases or achieving performance accuracy with advanced identification methods such as image recognition.Conclusions: Our findings suggest that designs of food purchase choice apps do not encourage repeated use or long-term adoption, compromising the effectiveness of behavior change through nudging. However, we found that smartphone apps can enhance learning, which plays an important role in behavior change. Compared with nudging as a mechanism for behavior change, this mechanism is less dependent on continued use. We argue that designs that optimize for learning within each interaction have a better chance of achieving behavior change. This review concludes with design recommendations, suggesting that food purchase choice app designers anticipate the possibility of early abandonment as part of their design process and design apps that optimize the learning experience

Inboard and outboard radial electric field wells in the H- and I-mode pedestal of Alcator C-Mod and poloidal variations of impurity temperature

We present inboard (HFS) and outboard (LFS) radial electric field (E[subscript r]) and impurity temperature (T[subscript z]) measurements in the I-mode and H-mode pedestal of Alcator C-Mod. These measurements reveal strong Er wells at the HFS and the LFS midplane in both regimes and clear pedestals in T[subscript z], which are of similar shape and height for the HFS and LFS. While the H-mode E[subscript r] well has a radially symmetric structure, the E[subscript r] well in I-mode is asymmetric, with a stronger ExB shear layer at the outer edge of the E[subscript r] well, near the separatrix. Comparison of HFS and LFS profiles indicates that impurity temperature and plasma potential are not simultaneously flux functions. Uncertainties in radial alignment after mapping HFS measurements along flux surfaces to the LFS do not, however, allow direct determination as to which quantity varies poloidally and to what extent. Radially aligning HFS and LFS measurements based on the T[subscript z] profiles would result in substantial inboard-outboard variations of plasma potential and electron density. Aligning HFS and LFS E[subscript r] wells instead also approximately aligns the impurity poloidal flow profiles, while resulting in a LFS impurity temperature exceeding the HFS values in the region of steepest gradients by up to 70%. Considerations based on a simplified form of total parallel momentum balance and estimates of parallel and perpendicular heat transport time scales seem to favor an approximate alignment of the E[subscript r] wells and a substantial poloidal asymmetry in impurity temperature.United States. Dept. of Energy (Cooperative Agreement DE-FC02-99ER54512)Swiss National Science Foundatio

Multiple-length-scale elastic instability mimics parametric resonance of nonlinear oscillators

Spatially confined rigid membranes reorganize their morphology in response to the imposed constraints. A crumpled elastic sheet presents a complex pattern of random folds focusing the deformation energy while compressing a membrane resting on a soft foundation creates a regular pattern of sinusoidal wrinkles with a broad distribution of energy. Here, we study the energy distribution for highly confined membranes and show the emergence of a new morphological instability triggered by a period-doubling bifurcation. A periodic self-organized focalization of the deformation energy is observed provided an up-down symmetry breaking, induced by the intrinsic nonlinearity of the elasticity equations, occurs. The physical model, exhibiting an analogy with parametric resonance in nonlinear oscillator, is a new theoretical toolkit to understand the morphology of various confined systems, such as coated materials or living tissues, e.g., wrinkled skin, internal structure of lungs, internal elastica of an artery, brain convolutions or formation of fingerprints. Moreover, it opens the way to new kind of microfabrication design of multiperiodic or chaotic (aperiodic) surface topography via self-organization.Comment: Submitted for publicatio

Optimisation of Interface Roughness and Coating Thickness to Maximise Coating-Substrate Adhesion - A Failure Prediction and Reliability Assessment Modelling

This paper addresses a novel modelling technique which is based on a multidisciplinary approach to predict the coating-substrate adhesion. It proposes new equations governing coating debondment that combines material science concepts with and solid mechanics concepts. The effects of two parameters i.e. interface roughness λ and coating thickness h on coating-substrate adhesion has been analysed. The reliability of newly developed technique has been validated by comparison with the experimental results