scholarly journals Design of Hierarchical Architected Lattices for Enhanced Energy Absorption

Materials ◽  
2021 ◽  
Vol 14 (18) ◽  
pp. 5384
Author(s):  
Mohamad Al Nashar ◽  
Alok Sutradhar
Keyword(s):  
Relative Density ◽  
Energy Absorption ◽  
Second Order ◽  
Displacement Curve ◽  
First Order ◽  
Lattice Design ◽  
Fused Deposition ◽  
Wide Range ◽  
Absorption Performance ◽  
Hierarchical Lattices

Hierarchical lattices are structures composed of self-similar or dissimilar architected metamaterials that span multiple length scales. Hierarchical lattices have superior and tunable properties when compared to conventional lattices, and thus, open the door for a wide range of material property manipulation and optimization. Using finite element analysis, we investigate the energy absorption capabilities of 3D hierarchical lattices for various unit cells under low strain rates and loads. In this study, we use fused deposition modeling (FDM) 3D printing to fabricate a dog bone specimen and extract the mechanical properties of thermoplastic polyurethane (TPU) 85A with a hundred percent infill printed along the direction of tensile loading. With the numerical results, we observed that the energy absorption performance of the octet lattice can be enhanced four to five times by introducing a hierarchy in the structure. Conventional energy absorption structures such as foams and lattices have demonstrated their effectiveness and strengths; this research aims at expanding the design domain of energy absorption structures by exploiting 3D hierarchical lattices. The result of introducing a hierarchy to a lattice on the energy absorption performance is investigated by varying the hierarchical order from a first-order octet to a second-order octet. In addition, the effect of relative density on the energy absorption is isolated by creating a comparison between a first-order octet lattice with an equivalent relative density as a second-order octet lattice. The compression behaviors for the second order octet, dodecahedron, and truncated octahedron are studied. The effect of changing the cross-sectional geometry of the lattice members with respect to the energy absorption performance is investigated. Changing the orientation of the second-order cells from 0 to 45 degrees has a considerable impact on the force–displacement curve, providing a 20% increase in energy absorption for the second-order octet. Analytical solutions of the effective elasticity modulus for the first- and second-order octet lattices are compared to validate the simulations. The findings of this paper and the provided understanding will aid future works in lattice design optimization for energy absorption.

Out-of-plane static compression and energy absorption of paper hierarchical corrugation sandwich panels

2021 ◽  
pp. 030932472110085
Author(s):  
Huineng Wang ◽  
Yanfeng Guo ◽  
Yungang Fu ◽  
Dan Li
Keyword(s):  
Yield Strength ◽  
Bearing Capacity ◽  
Energy Absorption ◽  
Sandwich Panel ◽  
Second Order ◽  
Compression Rate ◽  
Static Compression ◽  
First Order ◽  
Out Of Plane ◽  
Analytical Approaches

This study introduces the opinion of the corrugation hierarchy to develop the second-order corrugation paperboard, and explore the deformation characteristics, yield strength, and energy absorbing capacity under out-of-plane static evenly compression loading by experimental and analytical approaches. On the basis of the inclined-straight strut elements of corrugation unit and plastic hinge lines, the yield and crushing strengths of corrugation unit were analyzed. This study shows that as the compressive stress increases, the second-order corrugation core layer is firstly crushed, and the first-order corrugation structures gradually compacted until the failure of entire structure. The corrugation type has an obvious influence on the yield strength of the corrugation sandwich panel, and the yield strength of B-flute corrugation sandwich panel is wholly higher than that of the C-flute structure. At the same compression rate, the flute type has a significant impact on energy absorption, and the C-flute second-order corrugation sandwich panel has better bearing capacity than the B-flute structure. The second-order corrugation sandwich panel has a better bearing capacity than the first-order structure. The static compression rate has little effect on the yield strength and deformation mode. However, with the increase of the static compression rate, the corrugation sandwich panel has a better cushioning energy absorption and material utilization rate.

Multi-objective design optimization of additively manufactured lattice structures for improved energy absorption performance

2021 ◽  
pp. 095440622199554
Author(s):  
Recep M Gorguluarslan
Keyword(s):  
Energy Absorption ◽  
Response Surfaces ◽  
Optimization Process ◽  
Truss Optimization ◽  
Size Optimization ◽  
Lattice Structures ◽  
Multi Objective ◽  
Lattice Design ◽  
Highly Nonlinear ◽  
Absorption Performance

This paper aims to improve the energy absorption performance of stiffness-optimized lattice structures by utilizing a multi-objective surrogate-based size optimization that considers the additive manufacturing (AM) constraints such as the minimum printable size. A truss optimization is first utilized at the unit cell level under static compressive loads for stiffness maximization and two optimized lattice configurations called the Face-Body Centered Cubic (FBCC) lattice and the Octet Cubic (OC) are obtained. A multi-objective size optimization process is then carried out to improve the energy absorption capabilities of those lattice designs using non-linear compression simulations with Nylon12 material to be fabricated by the Multi Jet Fusion (MJF) AM process. Thin plate spline (TPS) interpolation method is found to produce very high accuracy as the surrogate model to predict the highly nonlinear response surfaces of energy absorption objectives in the optimization. Compared to the lattice designs with uniform strut diameters, by using the optimization process, the maximum energy absorption efficiency ( EAEm) and the crush stress efficiency ( CSE) of the OC lattice design are further improved up to 33% and 37%, respectively. The FBCC lattice design is also found to have superior EAEm performance compared to the existing lattice types considered for fabricating by the MJF process in the literature.

An Energy Method for Certain Second-Order Effects With Application to Torsion of Elastic Bars Under Tension

1980 ◽  
Vol 47 (1) ◽  
pp. 75-81 ◽  
Author(s):  
R. T. Shield
Keyword(s):  
Axial Force ◽  
Strain Energy Function ◽  
Incompressible Material ◽  
Elastic Cylinder ◽  
Second Order ◽  
The Other ◽  
Circular Cylinders ◽  
Order Effects ◽  
First Order ◽  
Wide Range

When a mechanical system has a potential energy, it is a simple matter to show that if the generalized force corresponding to a coordinate p is known to first order in p for a range of the other coordinates of the system, then the other generalized forces can be found immediately to second order in p, without requiring a second-order analysis of the system. By this method the second-order change in the axial force when a finitely extended elastic cylinder is twisted is found from the first-order value of the twisting moment. Numerical results for a realistic form of the strain-energy function for an incompressible material suggest that the second-order expression for the axial force is very accurate for a wide range of twist for circular cylinders of rubber-like materials extended 100 percent or more.

Hierarchical Corrugated Core Sandwich Panel Concepts

2005 ◽  
Vol 74 (2) ◽  
pp. 259-268 ◽  
Author(s):  
Gregory W. Kooistra ◽  
Vikram Deshpande ◽  
Haydn N. G. Wadley
Keyword(s):  
Relative Density ◽  
Second Order ◽  
Elastic Buckling ◽  
Collapse Mechanism ◽  
First Order ◽  
Collapse Mechanisms ◽  
Modes Of Failure ◽  
The Face ◽  
Shear Buckling ◽  
Equivalent Mass

The transverse compression and shear collapse mechanisms of a second order, hierarchical corrugated truss structure have been analyzed. The two competing collapse modes of a first order corrugated truss are elastic buckling or plastic yielding of the truss members. In second order trusses, elastic buckling and yielding of the larger and smaller struts, shear buckling of the larger struts, and wrinkling of the face sheets of the larger struts have been identified as the six competing modes of failure. Analytical expressions for the compressive and shear collapse strengths in each of these modes are derived and used to construct collapse mechanism maps for second order trusses. The maps are useful for selecting the geometries of second order trusses that maximize the collapse strength for a given mass. The optimization reveals that second order trusses made from structural alloys have significantly higher compressive and shear collapse strengths than their equivalent mass first order counterparts for relative densities less than about 5%. A simple sheet metal folding and dip brazing method of fabrication has been used to manufacture a prototype second order truss with a relative density of about 2%. The experimental investigation confirmed the analytical strength predictions of the second order truss, and demonstrate that its strength is about ten times greater than that of a first order truss of the same relative density.

Processing of Color- and Noncolor-Coded Signals in the Gourami Retina. III. Ganglion Cells

1997 ◽  
Vol 78 (4) ◽  
pp. 2034-2047 ◽  
Author(s):  
Hiroko M. Sakai ◽  
Hildred Machuca ◽  
Michael J. Korenberg ◽  
Ken-Ichi Naka
Keyword(s):  
White Noise ◽  
Spike Train ◽  
Ganglion Cells ◽  
Green Light ◽  
Amacrine Cells ◽  
Second Order ◽  
First Order ◽  
Wide Range ◽  
Mean Luminance ◽  
Order Components

Sakai, Hiroko M., Hildred Machuca, Michael J. Korenberg, and Ken-Ichi Naka. Processing of color- and noncolor-coded signals in the gourami retina. III. Ganglion cells. J. Neurophysiol. 78: 2034–2047, 1997. The dynamics of intracellular responses from ganglion cells, as well as that of spike discharges, were studied with the stimulus regimens and analytic procedures identical to those used to study the dynamics of the responses from horizontal and amacrine cells ( Sakai et al. 1997a , b ). The stimuli used were large fields of red and green light given as a pulsatile input or modulation about a mean luminance by a white-noise signal. Spike discharges evoked by a white-noise stimulus were analyzed in exactly the same manner as that used for analysis of analog responses. The canonical nature of kernels allowed us to correlate the first- and second-order components in a spike train with those of the intracellular responses from horizontal, amacrine, and ganglion cells. Both red and green stimuli given alone in darkness produced noncolor-coded responses from all ganglion cells. In the case of some cells, steady red illumination changed the polarity or waveform of the response to green light. Color-coded ganglions responded only to simultaneous color contrast. Nonlinearities recovered from intracellular responses, and spike discharges were similar to those found in responses from amacrine cells and were of two types, one characteristic of the C amacrine cells and the other characteristic of the N amacrine cells. The first-order kernels of most ganglion cells could be divided into two basic types, biphasic and triphasic. The combination of kernels of these two basic types with different polarities can produce a wide range of responses. Addition of two types of second-order nonlinearity could render color coding in this relatively simple retina as an extremely complex process. Color information appeared to be represented by the polarity, as well as the waveform, of the first-order kernel. The response dynamics is a means of transmission of color-coded information. Second-order components carry information about changes around a mean luminance regardless of the color of an input. Some spike discharges produced a well-defined cross-kernel between red and green inputs to show that a particular time sequence of red and green stimuli was detected by the retinal neuron network. The similarity between signatures of second-order kernels for both amacrine and ganglion cells indicates that signals undergo a minimal transformation in the temporal domain when they are transmitted from amacrine to ganglion cells and then transformed into a spike train. Under our experimental conditions, a single spike train carried simultaneously information about red and green inputs, as well as about linear and nonlinear components. In addition, the spike train also carries a cross-talk component. A spike train is a carrier of multiple signals. Conversely, many types of information in a stimulus are independently encoded into a spike train.

scholarly journals The direction-selective contrast response of area 18 neurons is different for first- and second-order motion

2005 ◽  
Vol 22 (1) ◽  
pp. 87-99 ◽  
Author(s):  
TIMOTHY LEDGEWAY ◽  
CHANG'AN ZHAN ◽  
AARON P. JOHNSON ◽  
YUNING SONG ◽  
CURTIS L. BAKER
Keyword(s):  
Cortical Neurons ◽  
Sine Wave ◽  
Direction Selectivity ◽  
Second Order ◽  
Response Functions ◽  
Characteristic Analysis ◽  
Area 18 ◽  
First Order ◽  
Wide Range ◽  
Contrast Response

Cortical neurons selective for the direction of motion often exhibit some limited response to motion in their nonpreferred directions. Here we examine the dependence of neuronal direction selectivity on stimulus contrast, both for first-order (luminance-modulated, sine-wave grating) and second-order (contrast-modulated envelope) stimuli. We measured responses from single neurons in area 18 of cat visual cortex to both kinds of moving stimuli over a wide range of contrasts (1.25–80%). Direction-selective contrast response functions (CRFs) were calculated as the preferred-minus-null difference in average firing frequency as a function of contrast. We also applied receiver operating characteristic analysis to our CRF data to obtain neurometric functions characterizing the potential ability of each neuron to discriminate motion direction at each contrast level tested. CRFs for sine-wave gratings were usually monotonic; however, a substantial minority of neurons (35%) exhibited nonmonotonic CRFs (such that the degree of direction selectivity decreased with increasing contrast). The underlying preferred and nonpreferred direction CRFs were diverse, often having different shapes in a given neuron. Neurometric functions for direction discrimination showed a similar degree of heterogeneity, including instances of nonmonotonicity. For contrast-modulated stimuli, however, CRFs for either carrier or envelope contrast were always monotonic. In a given neuron, neurometric thresholds were typically much higher for second- than for first-order stimuli. These results demonstrate that the degree of a cell's direction selectivity depends on the contrast at which it is measured, and therefore is not a characteristic parameter of a neuron. In general, contrast response functions for first-order stimuli were very heterogeneous in shape and sensitivity, while those for second-order stimuli showed less sensitivity and were quite stereotyped in shape.

Nonlinear Analysis of Visual Evoked Potentials Elicited by Color Stimulation

1997 ◽  
Vol 36 (04/05) ◽  
pp. 315-318 ◽  
Author(s):  
K. Momose ◽  
K. Komiya ◽  
A. Uchiyama
Keyword(s):  
Visual System ◽  
Evoked Potentials ◽  
Visual Evoked Potentials ◽  
Normal Subjects ◽  
Second Order ◽  
First Order ◽  
The Relationship ◽  
Perceived Color ◽  
Second Order Nonlinearity ◽  
Visual Evoked

Abstract:The relationship between chromatically modulated stimuli and visual evoked potentials (VEPs) was considered. VEPs of normal subjects elicited by chromatically modulated stimuli were measured under several color adaptations, and their binary kernels were estimated. Up to the second-order, binary kernels obtained from VEPs were so characteristic that the VEP-chromatic modulation system showed second-order nonlinearity. First-order binary kernels depended on the color of the stimulus and adaptation, whereas second-order kernels showed almost no difference. This result indicates that the waveforms of first-order binary kernels reflect perceived color (hue). This supports the suggestion that kernels of VEPs include color responses, and could be used as a probe with which to examine the color visual system.

Imaginings

2017 ◽  
Vol 9 (3) ◽  
pp. 17-30
Author(s):  
Kelly James Clark
Keyword(s):  
Religious Tradition ◽  
Second Order ◽  
Fine Tuning ◽  
Intellectual Humility ◽  
First Order ◽  
Natural Processes ◽  
Empirically Supported ◽  
Group Violence ◽  
The World ◽  
The Universe

In Branden Thornhill-Miller and Peter Millican’s challenging and provocative essay, we hear a considerably longer, more scholarly and less melodic rendition of John Lennon’s catchy tune—without religion, or at least without first-order supernaturalisms (the kinds of religion we find in the world), there’d be significantly less intra-group violence. First-order supernaturalist beliefs, as defined by Thornhill-Miller and Peter Millican (hereafter M&M), are “beliefs that claim unique authority for some particular religious tradition in preference to all others” (3). According to M&M, first-order supernaturalist beliefs are exclusivist, dogmatic, empirically unsupported, and irrational. Moreover, again according to M&M, we have perfectly natural explanations of the causes that underlie such beliefs (they seem to conceive of such natural explanations as debunking explanations). They then make a case for second-order supernaturalism, “which maintains that the universe in general, and the religious sensitivities of humanity in particular, have been formed by supernatural powers working through natural processes” (3). Second-order supernaturalism is a kind of theism, more closely akin to deism than, say, Christianity or Buddhism. It is, as such, universal (according to contemporary psychology of religion), empirically supported (according to philosophy in the form of the Fine-Tuning Argument), and beneficial (and so justified pragmatically). With respect to its pragmatic value, second-order supernaturalism, according to M&M, gets the good(s) of religion (cooperation, trust, etc) without its bad(s) (conflict and violence). Second-order supernaturalism is thus rational (and possibly true) and inconducive to violence. In this paper, I will examine just one small but important part of M&M’s argument: the claim that (first-order) religion is a primary motivator of violence and that its elimination would eliminate or curtail a great deal of violence in the world. Imagine, they say, no religion, too.Janusz Salamon offers a friendly extension or clarification of M&M’s second-order theism, one that I think, with emendations, has promise. He argues that the core of first-order religions, the belief that Ultimate Reality is the Ultimate Good (agatheism), is rational (agreeing that their particular claims are not) and, if widely conceded and endorsed by adherents of first-order religions, would reduce conflict in the world.While I favor the virtue of intellectual humility endorsed in both papers, I will argue contra M&M that (a) belief in first-order religion is not a primary motivator of conflict and violence (and so eliminating first-order religion won’t reduce violence). Second, partly contra Salamon, who I think is half right (but not half wrong), I will argue that (b) the religious resources for compassion can and should come from within both the particular (often exclusivist) and the universal (agatheistic) aspects of religious beliefs. Finally, I will argue that (c) both are guilty, as I am, of the philosopher’s obsession with belief. 

Evidence for general base catalysis by protic solvents in a kinetic study of alcoholyses and hydrolyses of 1-(phenoxycarbonyl)pyridinium ions under both solvolytic and non-solvolytic conditions

2009 ◽  
Vol 74 (1) ◽  
pp. 43-55 ◽  
Author(s):  
Dennis N. Kevill ◽  
Byoung-Chun Park ◽  
Jin Burm Kyong
Keyword(s):  
Second Order ◽  
Base Catalysis ◽  
Substitution Reactions ◽  
Third Order ◽  
Methoxy Derivative ◽  
First Order ◽  
General Base ◽  
Protic Solvents ◽  
Kinetics Of ◽  
Pyridinium Ions

The kinetics of nucleophilic substitution reactions of 1-(phenoxycarbonyl)pyridinium ions, prepared with the essentially non-nucleophilic/non-basic fluoroborate as the counterion, have been studied using up to 1.60 M methanol in acetonitrile as solvent and under solvolytic conditions in 2,2,2-trifluoroethan-1-ol (TFE) and its mixtures with water. Under the non- solvolytic conditions, the parent and three pyridine-ring-substituted derivatives were studied. Both second-order (first-order in methanol) and third-order (second-order in methanol) kinetic contributions were observed. In the solvolysis studies, since solvent ionizing power values were almost constant over the range of aqueous TFE studied, a Grunwald–Winstein equation treatment of the specific rates of solvolysis for the parent and the 4-methoxy derivative could be carried out in terms of variations in solvent nucleophilicity, and an appreciable sensitivity to changes in solvent nucleophilicity was found.

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