Tag Archives: stress

Psychological entropy increased by ineffectual leaders

Decorative image of a flowerYou might have wondered why I used ‘entropy’, and ‘psychological entropy’ in particular, as examples in my post on drowning in information a couple of weeks ago [‘We are drowning in information while starving for wisdom‘ on January 20th, 2021].  It was not random.  I spent some of the Christmas break catching up on my reading pile of interesting looking scientific papers and one on psychological entropy stimulated my thinking.  Psychological entropy is the concept that our brains are self-organising systems in a continual dialogue with the environment which leads to the emergence of a relatively small number of stable low-entropy states.  These states could be considered to be assemblies of neurons or patterns of thoughts, perhaps a mindset.  When we are presented with a new situation or problem to solve for which the current assembly or mindset is unsuitable then we start to generate new ideas by generating more and different assemblies of neurons in our brains.  Our responses become unpredictable as the level of entropy in our minds increases until we identify a new approach that deals effectively with the new situation and we add it to our list of available low-entropy stable states.  If the external environment is constantly changing then our brains are likely to be constantly churning through high entropy states which leads to anxiety and psychological stress.  Effective leaders can help us cope with changing environments by providing us with a narrative that our brains can use as a blueprint for developing the appropriate low-entropy state.  Raising psychological entropy by the right amount is conducive to creativity in the arts, science and leadership but too much leads to mental breakdown.


Hirsh JB, Mar RA, Peterson JB. Psychological entropy: A framework for understanding uncertainty-related anxiety. Psychological review. 2012 Apr;119(2):304

Handscombe RD & Patterson EA, The Entropy Vector: connecting science and business, Singapore: World Scientific Press, 2004.

Potential dynamic buckling in hypersonic vehicle skin

The skin of an aircraft is supported on the inside by a network, or mesh, of ribs and stringers running approximately at right angles to one another; so that the skin is effectively a series of rectangular plates supported around their edges.   In hypersonic flight, above five times the speed of sound, these rectangular plates are subject to vibration and to high temperatures that vary spatially and with time.  The combined vibratory and thermal loading causes the plates to buckle out of plane which has two possible detrimental consequences: first, it causes the formation of fatigue cracks leading to catastrophic failure; and, second, it might influence the formation of the boundary layer in the flow over the skin of the aircraft and affect the aerodynamics of the aircraft.  In my laboratory, we have built a test-rig that allows us to subject rectangular plates to random mechanical vibrations up to 1000Hz and, at the same time, to temperature distributions upto 1000K that vary in time and space.  Earlier this year, we published an article in which we showed, by experiment, that an edge-reinforced rectangular plate behaved as a dynamic system in response to thermal loading.  In other words, when a constant temperature distribution is applied, the shape of the plate varies with time until an equilibrium state is achieved.  In addition, we found that the post-buckled shape of the plate is not proportional to the energy supplied but dependent on the in-plane temperature distribution.  Probably, both of these observed behaviours are a result of differential thermal expansion of the plate and its reinforcements.

The image shows point-wise temperature and displacement measurements (centre) at the centre and edge of a reinforced plate (top) subject to a localised strip of heating over time as shown by the temperature distributions (bottom).

This is the fourth in a series of posts on recent work published by my research group.  The others are: ‘Salt increases nanoparticle diffusion‘ on April 22nd, 2020; ‘Spatio-temporal damage maps for composite materials‘ on May 6th, 2020; and, ‘Thinking out of the box leads to digital image correlation through space‘ on June 24th, 2020.


Santos Silva AC, Lambros J, Garner DM & Patterson EA, Dynamic response of a thermally stressed plate with reinforced edges, Experimental Mechanics, 60:81-92, 2020.

Spatio-temporal damage maps for composite materials

Earlier this year, my group published a new technique for illustrating the development of damage as a function of both space and time in materials during testing in a laboratory.  The information is presented in a damage-time map and shows where and when damage appears in the material.  The maps are based on the concept that damage represents a change in the structure of the material and, hence, produces changes in the load paths or stress distribution in the material.  We can use any of a number of optical techniques to measure strain, which is directly related to stress, across the surface of the material; and then look for changes in the strain distribution in real-time.  Wherever a permanent change is seen to occur there must also be permanent deformation or damage. We use image decomposition techniques that we developed some time ago [see ‘Recognizing strain‘ on October 28th, 2018], to identify the changes. Our damage-time maps remove the need for skilled operators to spend large amounts of time reviewing data and making subjective decisions.  They also allow a large amount of information to be presented in a single image which makes detailed comparisons with computer predictions easier and more readily quantifiable that, in turn, supports the validation of computational models [see ‘Model validation‘ on September 18th, 2012].

The structural integrity of composite materials is an on-going area of research because we only have a limited understanding of these materials.  It is easy to design structures using materials that have a uniform or homogeneous structure and mechanical properties which do not vary with orientation, i.e. isotropic properties.  For simple components, an engineer can predict the stresses and likely failure modes using the laws of physics, a pencil and paper plus perhaps a calculator.  However, when materials contain fibres embedded in a matrix, such as carbon-fibres in an epoxy resin, then the analysis of structural behaviour becomes much more difficult due to the interaction between the fibres and with the matrix.  Of course, these interactions are also what make these composite materials interesting because they allow less material to be used to achieve the same performance as homogeneous isotropic materials.  There are very many ways of arranging fibres in a matrix as well as many different types of fibres and matrix; and, engineers do not understand most of their interactions nor the mechanisms that lead to failure.

The image shows, on the left, the maximum principal strain in a composite specimen loaded longitudinally in tension to just before failure; and, on the right, the corresponding damage-time map indicating when and where damage developing during the tension loading.


Christian WJR, Dvurecenska K, Amjad K, Pierce J, Przybyla C & Patterson EA, Real-time quantification of damage in structural materials during mechanical testing, Royal Society Open Science, 7:191407, 2020.

Massive engineering

Last month I was at the Photomechanics 2018 conference in Toulouse in France.  Photomechanics is the science of using photons to measure deformation and displacements in anything, from biological cells to whole engineering structures, such as bridges or powerstations [see for example: ‘Counting photons to measure stress‘ posted on November 18th, 2015].  I am interested in the challenges created by the extremes of scale and environmental conditions; although on this occasion we presented our research on addressing the challenges of industrial applications, in the EU projects INSTRUCTIVE [see ‘Instructive update‘ on October 4th, 2017] and MOTIVATE [see ‘Brave New World‘ posted on January 10th, 2018].

It was a small conference without parallel sessions and the organisers were more imaginative than usual in providing us with opportunities for interaction.  At the end of first day of talks, we went on a guided walking tour of old Toulouse.  At the end of second day, we went to the Toulouse Aerospace Museum and had the chance to go onboard Concorde.

I stayed an extra day for an organised tour of the Airbus A380 assembly line.  Only the engine pylons are made in Toulouse.  The rest of the 575-seater plane is manufactured around Europe and arrives in monthly road convoys after travelling by sea to local ports.  The cockpit, centre, tail sections of the double-deck fuselage travel separately on specially-made trucks with each 45m long wing section following on its own transporter.  It takes about a month to assemble these massive sections.  This is engineering on a huge scale performed with laser precision (laser systems are used to align the sections).  The engines are also manufactured elsewhere and transported to Toulouse to be hung on the wings.  The maximum diameter of the Rolls-Royce Trent 900 engines, being attached to the plane we saw, is approximately same as the fuselage diameter of an A320 airplane.

Once the A380 is assembled and its systems tested, then it is flown to another Airbus factory in Germany to be painted and for the cabin to be fitted out to the customer’s specification.  In total, 11 Airbus factories in France, Germany, Spain and the United Kingdom are involved in producing the A380; this does not include the extensive supply chain supporting these factories.  As I toured the assembly line and our guide assailed us with facts and figures about the scale of the operation, I was thinking about why the nuclear power industry across Europe could not collaborate on this scale to produce affordable, identical power stations.  Airbus originated from a political decision in the 1970s to create a globally-competitive European aerospace industry that led to a collaboration between national manufacturers which evolved into the Airbus company.  One vision for fusion energy is a globally dispersed manufacturing venture that would evolve from the consortium that is currently building the ITER experiment and planning the DEMO plant.  However, there does not appear to be any hint that the nuclear fission industry is likely to follow the example of the European aerospace industry to create a globally-competitive industry producing massive pieces of engineering within a strictly regulated environment.

There was no photography allowed at Airbus so today’s photograph is of Basilique Notre-Dame de la Daurade in Toulouse.