Category Archives: mechanics

On flatness and roughness

Photograph of aircraft carrier in heavy seas for decorative purposes onlyFlatness is a tricky term to define.  Technically, it is the deviation, or lack of deviation, from a plane. However, something that appears flat to human eye often turns out not to be at all flat when looked at closely and measured with a high resolution instrument.  It’s a bit like how the ocean might appear flat and smooth to a passenger sitting comfortably in a window seat of an aeroplane and looking down at the surface of the water below but feels like a roller-coaster to a sailor in a small yacht.  Of course, if the passenger looks at the horizon instead of down at the yacht below then they will realise the surface of the ocean is curved but this is unlikely to be apparent to the sailor who can only see the next line of waves advancing towards them.  Of course, the Earth is not flat and the waves are better described as surface roughness.  Some months ago I wrote about our struggles to build a thin flat metallic plate using additive manufacturing [see ‘If you don’t succeed, try and try again…’ on September 29th, 2021].  At the time, we were building our rectangular plates in landscape orientation and using buttresses to support them during the manufacturing process; however, when we removed the plates from the machine and detached the buttresses they deformed into a dome-shape.  I am pleased to say that our perseverance has paid off and recently we have been much more successful by building our plates orientated in portrait mode, i.e., with the short side of the rectangle horizontal, and using a more sophisticated design of buttresses.  Viewed from the right perspective our recent plates could be considered flat though in reality they deviate from a plane by less than 3% of their in-plane dimensions and also have a surface roughness of several tens of micrometres (that’s the average deviation from the surface).  The funding organisations for our research expect us to publish our results in a peer-reviewed journal that will only accept novel unpublished results so I am not going to say anything more about our flat plates.  Instead let me return to the ocean analogy and try to make you seasick by recalling an earlier career in which I was on duty on the bridge of an aircraft carrier ploughing through seas so rough, or not flat, that waves were breaking over the flight deck and the ship felt like it was still rolling and pitching when we sailed serenely into port some days later.

The current research is funded jointly by the National Science Foundation (NSF) in the USA and the Engineering and Physical Sciences Research Council (EPSRC) in the UK (see Grants on the Web).

Image from https://laststandonzombieisland.com/2015/07/22/warship-wednesday-july-22-2015-the-giant-messenger-god/1977-hms-hermes-r-12-with-her-bows-nearly-out-of-the-water/

Ice bores and what they can tell us

Map of Greenland sheet showing depth of iceAbout forty years ago, I was lucky enough to be involved in organising a scientific expedition to North-East Greenland.  Our basecamp was on the Bersaerkerbrae Glacier in Scoresby Land, which at 72 degrees North is well within the Arctic Circle and forty years ago was only accessible in summer when the snow receded.  We measured ablation rates on the glacier [1], counted muskoxen in the surrounding landscape [2] [see ‘Reasons for publishing scientific papers‘ on April 21st 2021] and drilled boreholes in the ice of the glacier.  We performed mechanical tests on the ice cores obtained from different depths in the glacier and in various locations in order to assess the spatial distribution of the material properties of the ice in the glacier. This is important information for producing accurate simulations of the flow of the glacier, although our research did not extend to modelling the glacier.  We could also have used our ice cores to investigate the climatic history of the region.  The Greenland ice sheet contains an archive record of the climate on Earth for about the last half million years, stored in the snow and trapped air bubbles accumulated over that time period.  If the ice sheet melts then that unique record will be lost forever.

The thumbnail image is a map of the depth of ice in the Greenland ice sheet.  The map is about five years old and has a wide green fringe along the east coast.  Scoresby Land is the penisula to the north of the large fiord in the middle of the east coast.  In 1982, the edge of the ice sheet was about 80 miles from the Bersaerkerbrae Glacier, whereas today it is at least twice that distance because the ice sheet is receding.

References:

[1] Patterson EA, 1984, A mathematical model for perched block formation. Journal of Glaciology. 30(106):296-301.

[2] Patterson EA, 1984, ‘Sightings of Muskoxen in Northern Scoresby Land, Greenland’, Arctic, 37(1): 61-63.

Image: https://upload.wikimedia.org/wikipedia/commons/thumb/b/b5/Greenland_ice_sheet_AMSL_thickness_map-en.svg/2000px-Greenland_ice_sheet_AMSL_thickness_map-en.svg.png

Nano biomechanical engineering of agent delivery to cells

figure 1 from [1] with text explanationWhile many of us are being jabbed in the arm to deliver an agent that stimulates our immune system to recognize the coronavirus SARS-CoV-2 as a threat and destroy it, my research group has been working, in collaboration with colleagues at the European Commission Joint Research Centre, on the dynamics of nanoparticles [1] [see ‘Size matters‘ on October 23rd, 2019] which could be used as carriers for the targeted delivery of therapeutic, diagnostic and imaging agents in the human body [2].  The use of nanoparticles to mechanically stimulate stem cells to activate signalling pathways and modulate their differentiation also has some potential [3]. In studies of the efficacy of nanoparticles in these biomedical applications, the concentration of nanoparticles interacting with the cell is a primary factor influencing both the positive and negative effects.  Such studies often involve exposing a monolayer of cultured cells adhered to the bottom of container to a dose of nanoparticles and monitoring the response over a period of time.  Often, the nominal concentration of the nanoparticles in biological medium supporting the cells is reported and used as the basis for determining the dose-response relationships.  However, we have shown that this approach is inaccurate and leads to misleading results because the nanoparticles in solution are subject to sedimentation due to gravity, Brownian motion [see ‘Slow moving nanoparticles‘ on December 13th, 2017] and inter-particle forces [see ‘ Going against the flow‘ on February 3rd, 2021] which affect their transport within the medium [see graphic] and the resultant concentration adjacent to the monolayer of cells.  Our experimental results using the optical method of caustics [see ‘Holes in fluids‘ on October 22nd, 2014] have shown that nanoparticle size, colloidal stability and solution temperature influence the distribution of nanoparticles in solution.  For particles larger than 60 nm in diameter (about one thousandth of the diameter of a human hair) the nominal dose differs significantly from the dose experienced by the cells.  We have developed and tested a theoretical model that accurately describes the settling dynamics and concentration profile of nanoparticles in solution which can be used to design in vitro experiments and compute dose-response relationships.

References

[1] Giorgi F, Macko P, Curran JM, Whelan M, Worth A & Patterson EA. 2021 Settling dynamics of nanoparticles in simple and biological media. Royal Society Open Science, 8:210068.

[2] Daraee H, Eatemadi A, Abbasi E, Aval SF, Kouhi M, & Akbarzadeh A. 2016 Application of gold nanoparticles in biomedical and drug delivery. Artif. Cells Nanomed. Biotechnol. 44, 410–422. (doi:10.3109/21691401.2014.955107)

[3] Wei M, Li S, & Le W. 2017 Nanomaterials modulate stem cell differentiation: biological
interaction and underlying mechanisms. J. Nanobiotechnol. 15, 75. (doi:10.1186/s12951-
017-0310-5)

Jigsaw puzzling without a picture

A350 XWB passes Maximum Wing Bending test

A350 XWB passes Maximum Wing Bending test

Research sometimes feels like putting together a jigsaw puzzle without the picture or being sure you have all of the pieces.  The pieces we are trying to fit together at the moment are (i) image decomposition of strain fields [see ‘Recognising strain’ on October 28th 2015] that allows fields containing millions of data values to be represented by a feature vector with only tens of elements which is useful for comparing maps or fields of predictions from a computational model with measurements made in the real-world; (ii) evaluation of the variation in measurement uncertainty over a field of view of measured displacements or strains in a large structure [see ‘Industrial uncertainty’ on December 12th 2018] which provides information about the quality of the measurements; and (iii) a probabilistic validation metric that provides a measure of how well predictions from a computational model represent measurements made in the real world [see ‘Million to one’ on November 21st 2018].  We have found some of the missing pieces of the jigsaw, for example we have established how to represent the distribution of measurement uncertainty in the feature vector domain [see ‘From strain measurements to assessing El Niño events’ on March 17th 2021] so that it can be used to assess the significance of differences between measurements and predictions represented by their feature vectors – this connects (i) and (ii) together.  Very recently we have demonstrated a generic technique for performing image decomposition of irregularly shaped fields of data or data fields with holes [see Christian et al, 2021] which extends the applicability of our method for comparing measurements and predictions to real-world objects rather than idealised shapes.  This allows (i) to be used in industrial applications but we still have to work out how to connect this to the probabilistic metric in (iii) while also incorporating spatially-varying uncertainty.  These techniques can be used in a wide range of applications, as demonstrated in our recent work on El Niño events [see Alexiadis et al, 2021], because, by treating all fields of data as images, the techniques are agnostic about the source and format of the data.  However, at the moment, our main focus is on their application to ground tests on aircraft structures as part of the Smarter Testing project in collaboration with Airbus, Centre for Modelling & Simulation, Dassault Systèmes, GOM UK Ltd, and the National Physical Laboratory with funding from the Aerospace Technology Institute.  Together we are working towards digital continuity across virtual and physical testing of aircraft structures to provide live data fusion and enable condition-led inspections, test control and validation of computational models.  We anticipate these advances will reduce time and costs for physical tests and accelerate the development of new designs of aircraft that will contribute to global sustainability targets (the aerospace industry has committed to reduce CO2 emissions to 50% of 2005 levels by 2050).  The Smarter Testing project has an ambitious goal which reveals that our pieces of the jigsaw puzzle belong to a small section of a much larger one.

For more on the Smarter Testing project see:

https://www.aerospacetestinginternational.com/news/structural-testing/smarter-testing-research-program-to-link-virtual-and-physical-aerospace-testing.html

https://www.aerospacetestinginternational.com/opinion/how-integrating-the-virtual-and-physical-will-make-aerospace-testing-and-certification-smarter.html

References

Alexiadis A, Ferson S, Patterson EA. Transformation of measurement uncertainties into low-dimensional feature vector space. Royal Society open science. 8(3):201086, 2021.

Christian WJ, Dean AD, Dvurecenska K, Middleton CA, Patterson EA. Comparing full-field data from structural components with complicated geometries. Royal Society open science. 8(9):210916, 2021.

Image: http://www.airbus.com/galleries/photo-gallery