scholarly journals Delayed buckling of spherical shells due to viscoelastic knockdown of the critical load

2021 ◽  
Vol 477 (2253) ◽  
pp. 20210253
Author(s):  
Lucia Stein-Montalvo ◽  
Douglas P. Holmes ◽  
Gwennou Coupier
Keyword(s):  
Critical Load ◽  
Material Properties ◽  
Dynamic Pressure ◽  
Elastic Shell ◽  
Applied Pressure ◽  
Delay Period ◽  
Significant Delay ◽  
Spherical Shells ◽  
Viscoelastic Creep ◽  
Shell Buckling

We performed dynamic pressure buckling experiments on defect-seeded spherical shells made of a common silicone elastomer. Unlike in quasi-static experiments, shells buckled at ostensibly subcritical pressures, i.e. below the experimentally determined critical load at which buckling occurs elastically, often following a significant delay period from the time of load application. While emphasizing the close connections to elastic shell buckling, we rely on viscoelasticity to explain our observations. In particular, we demonstrate that the lower critical load may be determined from the material properties, which is rationalized by a simple analogy to elastic spherical shell buckling. We then introduce a model centred on empirical quantities to show that viscoelastic creep deformation lowers the critical load in the same predictable, quantifiable way that a growing defect would in an elastic shell. This allows us to capture how both the deflection at instability and the time delay depend on the applied pressure, material properties and defect geometry. These quantities are straightforward to measure in experiments. Thus, our work not only provides intuition for viscoelastic behaviour from an elastic shell buckling perspective but also offers an accessible pathway to introduce tunable, time-controlled actuation to existing mechanical actuators, e.g. pneumatic grippers.

Optimal Forms of Shallow Shells With Circular Boundary, Part 2: Maximum Buckling Load

1984 ◽  
Vol 51 (3) ◽  
pp. 531-535 ◽  
Author(s):  
R. H. Plaut ◽  
L. W. Johnson
Keyword(s):  
Critical Load ◽  
Elastic Shell ◽  
Material Surface ◽  
Fundamental Vibration ◽  
Uniform Loading ◽  
Concentrated Load ◽  
Shallow Shells ◽  
Simply Supported ◽  
Circular Boundary ◽  
Boundary Part

In Part 1, optimal forms were determined for maximizing the fundamental vibration frequency of a thin, shallow, axisymmetric, elastic shell with given circular boundary. Our objective in this part is to maximize the critical load for buckling under a uniformly distributed load or a concentrated load at the center. Again, the shell form is varied and the material, surface area, and uniform thickness of the shell are specified. Both clamped and simply supported boundary conditions are considered for the case of uniform loading, while one example is presented involving a concentrated load acting on a clamped shell. The optimality condition leads to forms that have zero slope at the boundary if it is clamped. The maximum critical load is sometimes associated with a limit point and sometimes with a bifurcation point. It is often substantially higher than the critical load for the corresponding spherical shell.

Plastic Instabilities in Spherical Vessels for Static and Dynamic Loading

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
T. A. Duffey
Keyword(s):  
Strain Rate ◽  
Strain Rate Sensitivity ◽  
Damage Mechanics ◽  
Dynamic Pressure ◽  
Constitutive Relations ◽  
Rate Sensitivity ◽  
Plastic Collapse ◽  
Instability Condition ◽  
Spherical Shells

Significant changes were made in design limits for pressurized vessels in the 2007 version of the ASME code (Sec. VIII, Div. 3) and 2008 and 2009 Addenda, and these are now a part of the 2010 code. There is now a local damage-mechanics based strain-exhaustion limit, including the well-known global plastic collapse limit. Moreover, Code Case 2564 (Sec. VIII, Div. 3) has recently been approved to address impulsively loaded vessels. It is the purpose of this paper to investigate the plastic collapse limit as it applies to dynamically loaded spherical vessels. Plastic instabilities that could potentially develop in spherical shells under symmetric loading conditions are examined for a variety of plastic constitutive relations. First, literature survey of both static and dynamic instabilities associated with spherical shells is presented. Then, a general plastic instability condition for spherical shells subjected to displacement-controlled and short-duration dynamic pressure loading is given. This instability condition is evaluated for six plastic and viscoplastic constitutive relations. The role of strain rate sensitivity on the instability point is investigated. Conclusions of this work are that there are two fundamental types of instabilities associated with failure of spherical shells. In the case of impulsively loaded vessels, where the pulse duration is short compared with the fundamental period of the structure, one instability type is found not to occur in the absence of static internal pressure. Moreover, it is found that the specific role of strain rate sensitivity on the instability strain depends on the form of the constitutive relation assumed.

Dent Imperfections in Shell Buckling: The Role of Geometry, Residual Stress, and Plasticity

2020 ◽  
Vol 88 (3) ◽  
Author(s):  
S. Gerasimidis ◽  
J. W. Hutchinson
Keyword(s):  
Residual Stress ◽  
Residual Stresses ◽  
Middle Surface ◽  
External Pressure ◽  
Second Step ◽  
Elastic Buckling ◽  
Spherical Shells ◽  
Shell Buckling ◽  
Cylindrical Metal

Abstract Departures of the geometry of the middle surface of a thin shell from the perfect shape have long been regarded as the most deleterious imperfections responsible for reducing a shell’s buckling capacity. Here, systematic simulations are conducted for both spherical and cylindrical metal shells whereby, in the first step, dimple-shaped dents are created by indenting a perfect shell into the plastic range. Then, in the second step, buckling of the dented shell is analyzed, under external pressure for the spherical shells and in axial compression for the cylindrical shells. Three distinct buckling analyses are carried out: (1) elastic buckling accounting only for the geometry of the dent, (2) elastic buckling accounting for both dent geometry and residual stresses, and (3) a full elastic–plastic buckling analysis accounting for both the dent geometry and residual stresses. The analyses reveal the relative importance of the geometry and the residual stress associated with the dent, and they also provide a clear indicator of whether plasticity is important in establishing the buckling load of the dented shells.

Delay-Period Activity in Visual, Visuomovement, and Movement Neurons in the Frontal Eye Field

2005 ◽  
Vol 94 (2) ◽  
pp. 1498-1508 ◽  
Author(s):  
Bonnie M. Lawrence ◽  
Robert L. White ◽  
Lawrence H. Snyder
Keyword(s):  
Spatial Information ◽  
Delay Period ◽  
Frontal Eye Field ◽  
Significant Delay ◽  
Related Activity ◽  
Null Direction ◽  
Preferred Direction ◽  
Canonical Neurons ◽  
Eye Field ◽  
Saccade Direction

In the present study, we examined the role of frontal eye field neurons in the maintenance of spatial information in a delayed-saccade paradigm. We found that visual, visuomovement, and movement neurons conveyed roughly equal amounts of spatial information during the delay period. Although there was significant delay-period activity in individual movement neurons, there was no significant delay-period activity in the averaged population of movement neurons. These contradictory results were reconciled by the finding that the population of movement neurons with memory activity consisted of two subclasses of neurons, the combination of which resulted in the cancellation of delay-period activity in the population of movement neurons. One subclass consisted of neurons with significantly greater delay activity in the preferred than in the null direction (“canonical”), whereas the other subclass consisted of neurons with significantly greater delay activity in the null direction than in the preferred direction (“paradoxical”). Preferred direction was defined by the saccade direction that evoked the greatest movement-related activity. Interestingly, the peak saccade-related activity of canonical neurons occurred before the onset of the saccade, whereas the peak saccade-related activity of paradoxical neurons occurred after the onset of the saccade. This suggests that the former, but not the latter, are directly involved in triggering saccades. We speculate that paradoxical neurons provide a mechanism by which spatial information can be maintained in a saccade-generating circuit without prematurely triggering a saccade.

Instability of Cup-Cylinder Compound Shell Under Uniform External Pressure

1995 ◽  
Vol 39 (02) ◽  
pp. 160-165
Author(s):  
Raisuddin Khan ◽  
Wahhaj Uddin
Keyword(s):  
Critical Pressure ◽  
Nonlinear Differential Equations ◽  
External Pressure ◽  
Shells Of Revolution ◽  
Membrane Stress ◽  
Spherical Shells ◽  
Uniform External Pressure ◽  
Shell Buckling ◽  
Compound Shell ◽  
Method Of Solution

Instability of compound cup-end cylindrical shells under uniform external pressure is studied. Nonlinear differential equations governing the large axisymmetric deformations of shells of revolution which ensure the unique states of lowest potential energy of the shells under a given pressure are solved. The method of solution is multisegment integration, developed by Kalnins and Lestingi, for predicting the mode of buckling and the critical pressure of these compound shells. Results show that, when simple cylindrical and spherical shells which develop the same membrane stress under pressure are used as a compound cup-end cylindrical shell, buckling takes place in the cylinder portion, near the cup-cylinder junction, at loads a few times higher than the buckling load of conventional dome-cylinder shells.

scholarly journals Digital image correlation-based point-wise inverse characterization of heterogeneous material properties of gallbladder in vitro

2014 ◽  
Vol 470 (2167) ◽  
pp. 20140152 ◽  
Author(s):  
Katia Genovese ◽  
Luciana Casaletto ◽  
Jay D. Humphrey ◽  
Jia Lu
Keyword(s):  
Mechanical Properties ◽  
Extracellular Matrix ◽  
Material Properties ◽  
Soft Tissues ◽  
Applied Pressure ◽  
Heterogeneous Material ◽  
Image Correlation ◽  
Surface Geometry ◽  
Stress Strain ◽  
Full Field

Continuing advances in mechanobiology reveal more and more that many cell types, especially those responsible for establishing, maintaining, remodelling or repairing extracellular matrix, are extremely sensitive to their local mechanical environment. Indeed, it appears that they fashion the extracellular matrix so as to promote a ‘mechanical homeostasis’. A natural corollary, therefore, is that cells will try to offset complexities in geometry and applied loads with heterogeneous material properties in order to render their local environment mechanobiologically favourable. There is a pressing need, therefore, for hybrid experimental–computational methods in biomechanics that can quantify such heterogeneities. In this paper, we present an approach that combines experimental information on full-field surface geometry and deformations with a membrane-based point-wise inverse method to infer full-field mechanical properties for soft tissues that exhibit nonlinear behaviours under finite deformations. To illustrate the potential utility of this new approach, we present the first quantification of regional mechanical properties of an excised but intact gallbladder, a thin-walled, sac-like organ that plays a fundamental role in normal digestion. The gallbladder was inflated to a maximum local stretch of 120% in eight pressure increments; at each pressure pause, the entire three-dimensional surface was optically extracted, and from which the surface strains were computed. Wall stresses in each state were predicted from the deformed geometry and the applied pressure using an inverse elastostatic method. The elastic properties of the gallbladder tissue were then characterized locally using point-wise stress–strain data. The gallbladder was found to be highly heterogeneous, with drastically different stiffness between the hepatic and the serosal sides. The identified material model was validated through forward finite-element analysis; both the configurations and the local stress–strain patterns were well reproduced.

scholarly journals Reprogrammable Braille on an elastic shell

2018 ◽  
Vol 115 (29) ◽  
pp. 7509-7514 ◽  
Author(s):  
Jun Young Chung ◽  
Ashkan Vaziri ◽  
L. Mahadevan
Keyword(s):  
Elastic Shell ◽  
Small Scale ◽  
Minimal Realization ◽  
Programmable Matter ◽  
Governing Equations ◽  
Spherical Shells ◽  
Scale Separation ◽  
Low Dimensional ◽  
Geometrical Scale ◽  
At Will

We describe a minimal realization of reversibly programmable matter in the form of a featureless smooth elastic plate that has the capacity to store information in a Braille-like format as a sequence of stable discrete dimples. Simple experiments with cylindrical and spherical shells show that we can control the number, location, and the temporal order of these dimples, which can be written and erased at will. Theoretical analysis of the governing equations in a specialized setting and numerical simulations of the complete equations allow us to characterize the phase diagram for the formation of these localized elastic states, elastic bits (e-bits), consistent with our observations. Given that the inherent bistability and hysteresis in these low-dimensional systems arise exclusively due to the geometrical-scale separation, independent of material properties or absolute scale, our results might serve as alternate approaches to small-scale mechanical memories.

Thin Film Polymer Stress Measurement Using Piezoresistive Anisotropically Etched Pressure Sensors

1996 ◽  
Vol 436 ◽  
Author(s):  
G. Bitko ◽  
R. Harries ◽  
J. Matldn ◽  
A. C. McNeil ◽  
D. J. Monk ◽  
...  
Keyword(s):  
Thin Film ◽  
Thermal Stress ◽  
High Temperature ◽  
Material Properties ◽  
Applied Pressure ◽  
Pressure Sensors ◽  
Offset Voltage ◽  
High Temperature Storage ◽  
Linear Expression ◽  
Temperature Storage

AbstractSilicon bulk micromachined piezoresistive pressure sensors are very sensitive to applied stresses: that is, applied pressure and/or packaging-related stresses. Device encapsulation has been observed to affect the electrical output of the pressure sensor significantly. The magnitude of the zero applied pressure output voltage (i.e., the offset voltage) that can be attributed to a thin film encapsulant is proportional to the magnitude of the roomtemperature thermal stress of that film. Parylene C coatings have been used as encapsulants in this work. Finite element and analytical modeling techniques were used to evaluate the effect of material property variation on the offset of a pressure sensor. A simple, linear expression of offset as a function of a material property parametric group, that includes: parylene thickness, parylene biaxial modulus, parylene CTE, silicon thickness, and annealing temperature; has been established. Experimental analysis of parylene coated pressure sensors and parylene coated silicon and gallium arsenide wafers was performed to confirm the resulting model. Known variations in parylene material properties caused by processing (i.e., uncontrolled deposition, annealing, and high temperature storage) have been used as an experimental vehicle for this purpose. An empirical relationship between offset voltage on parylene coated devices and room-temperature thermal stress on parylene coated wafers that have been exposed to the same processing is a linear expression with a similar slope to the modeling results. Furthermore, stress measurements from parylene coated silicon wafers and parylene coated gallium arsenide wafers have been used to estimate the parylene biaxial modulus (approximately 5000 MPa) and the parylene CTE (approximately 50 ppm/°C) independently. These material properties were observed to shift following parylene annealing and high temperature storage exposure experiments in a manner that is consistent with the established model.

scholarly journals Buckling of epithelium growing under spherical confinement

2019 ◽  
Author(s):  
Anastasiya Trushko ◽  
Ilaria Di Meglio ◽  
Aziza Merzouki ◽  
Carles Blanch-Mercader ◽  
Shada Abuhattum ◽  
...  
Keyword(s):  
Elastic Modulus ◽  
Stress Field ◽  
Elastic Deformation ◽  
Material Properties ◽  
Three Dimensional ◽  
Spherical Shells ◽  
Compressive Stresses ◽  
Inner Surface ◽  
Shape Changes

SummaryMany organs, such as the gut or the spine are formed through folding of an epithelium. This change in shape is usually attributed to tissue heterogeneities, for example, local apical contraction. In contrast, compressive stresses have been proposed to fold a homogeneous epithelium by buckling. While buckling is an appealing mechanism, demonstrating that it underlies folding requires to measure the stress field and the material properties of the tissue, which is currently inaccessible in vivo. Here we show that monolayers of identical cells proliferating on the inner surface of elastic spherical shells can spontaneously fold. By measuring the elastic deformation of the shell, we infer the forces acting within the monolayer and its elastic modulus. Using analytical and numerical theories linking forces to shape, we find that buckling quantitatively accounts for the shape changes of our monolayers. Our study shows that forces arising from epithelium growth in three-dimensional confinement are sufficient to drive folding by buckling.

Distributed Piezoelectric Neurons and Muscles for Shell Continua

1991 ◽  
Author(s):  
H. S. Tzou
Keyword(s):  
Closed Loop ◽  
Broad Class ◽  
Elastic Shell ◽  
Closed Loop System ◽  
State Equations ◽  
Spherical Shells ◽  
System Parameters ◽  
Zero Curvature ◽  
Piezoelectric Layers ◽  
System Equations

Abstract Conventional shell continua are passive, which do not possess any sensation and action/reaction capabilities. In this paper, distributed piezoelectric layers coupled with conventional elastic shell distributed systems are used as distributed “neurons” (sensors) and “muscles” (actuators) for structural monitoring and actuation of shells. New theories on distributed “neural” sensation and actuation of shells are developed based on a generic shell continuum coupled with piezoelectric neurons and muscles. Open and closed loop system dynamic equations are also derived. The system equations are further transferred to state equations. The derived theories can be directly simplified to a broad class of geometries, cylindrical shells, spherical shells, conical shels, zero-curvature shells (i.e., plates: rectangular, circular, etc.), beams, etc. Applications of the theories to a cylindrical shell using four system parameters, two Lame’s parameters and two radii of curvature, are demonstrated.

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