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“En las profundidades del invierno finalmente aprendí que en mi interior habitaba un verano invencible. ”

Albert Camus


Si bien el concepto de resiliencia orbita alrededor de una idea central, (mantener y/o regresar a un estado de estabilidad nominal tras haber sucumbido una perturbación extraordinaria), existen muchas definiciones periféricas en diversas áreas de estudio y aplicación. A lo largo de esta sección presentaremos las vertientes más significativas de dicho concepto y finalmente demostraremos como todas convergen a una aplicación en el campo de la "desastrología".

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History and Etymology of RESILIENCE

The academical concept of resilience was first introduced at the beginning of the 17th century with a scientific connotation. The concept’s application emphasizes a material´s ability to return to its original shape after being compressed or stretched [6]. Resilience etymology can be traced back to the entourage of the Latin verb “salire” meaning “to jump”, indicating in the overall: “resiliere” – “resiliens”, to jump (-salire) again (re-) [7]. In the English language, the term´s definition can be traced back to 1529: “act of rebounding” [8]. In French, arguably the “lingua franca” of the 17th century, a similar definition can be retrieved. However, the contemporary accepted French definition focuses on the material science context as a first definition, followed by a zoological and a psychological characterization [9, 10, 11]. Linguistically, resilience is a descriptive term which gives the attribute of a given system to return to its original state after being affected by an external factor.

To understand the relationship of the resilience concept and its applicability in the different fields of human knowledge we most first state a structuralist and logical framework which can help us deconstruct the resilience concept into all its components. The following philosophical tools are guidelines which can help us to better understand resilience beyond a word or a definition. But also, its essence, linguistic, practical functionality, context, and applicability.

Signifier and Signified

According to the philosopher Saucier, signs are composed by two parts: a signifier and a signified. The signifier being the representation and the signified is what the signifier is aiming to portray. A sign in this case can be a word with a particular meaning, the signifier would act as the word itself and the signified would be the given meaning or the functionality of such word. [1]

Lacan developed furthermore the idea of Saucier and builds the concept of the “signifying chain”, which refer to the social construct of signs contextualization which can evolve over time. Impaling that the meaning that is given by society to the signifier might change over time. If the societal construct of a concept changes, the word which represent such concept might remain the same. This means that signifieds tend to change as signifiers might remain constant, therefore the signifier represses the signified. Ontologically, words can change their meanings according to the context of a sentence. A sentence can change its context in a given paragraph and subsequently paragraphs can obtain new meanings in the context of a book. The signifying chain described by Lacan shows how signifiers can relate to one another of substitute among themselves, potentially resulting in single signifier with several signifieds. For this work, the signifier of interest is the word “resilience” and its signified is the given definition of this word. [1]

Univocal, Equivocal, and Derivative

In the work Categories by Aristoteles, there is a distinction between 3 different ways in which terms can be used or being named. Not only to differentiate the term of name as its own but also the actual use they have. According to Aristoteles terms can be differentiated as univocal, equivocal and derivatives or analogous. The distinction is important because in many cases when we use language in ways that we don’t realize we are not actually referring to the same thing and we get into arguments with each other. Terms, signs, and names may have a core meaning but often they are equivocal and if we don’t recognize the “equivocity” we can go wrong reasoning about them and we can get into disagreements because we are not actually talking about the same thing. [2]

Univocal words have the same core or in Aristoteles words: “statement of essence” (logos tastes useiess), and the same name. This means that there is a unique significant associated to a unique signifier. Personal names are an example of univocal terms, the combination of name, middle name, and surname (the signifier) is attributed to a single unique human being (the signified).  

Equivocal terms share the same significant, yet the signifier can change; they don’t have the same “statement of essence”. In this case the same word is being used to denote different things. Such terms tend to be clarified in the context they are being used. For example: a “plant” can infer to describe a living being but also can refer to an energy production facility (a power plant). The same signifier can have multiple unrelated signifieds.

Derivative or analogous terms are those which are derivative one from the other. These terms share the same significant and have different signifiers just like the equivocal terms. The main difference between derivative and equivocal terms is that there is a logical attachment or evolution between the words. For example: “health” has several analogous terms all sharing a common significant and a different signifier, yet the signifiers are related to each other by a similar idea or a common origin. In the case of the work, resilience can be initially described as an analogous term. Resilience has a common signifier in all its different applications, and all its definitions (signifieds) can be traced back to a similar common idea. However, they can be drastically different among themselves.

Systems: Open, Closed, and Isolated

Etymologically, the term system is derived from systema in Latin: “whole concept made of several parts or members” / “composition” The functional evolution of the “system” concept in the recent years might be as complex and chaotic as “resilience”. Philosopher Ludwig Von Bertalanffy postulated in his work General system theory that any section of the universe around us that we can perceive can be described as a system. [3]

To preserve congruence with this work, we can give an ontologically general analogous signified for “system” which can be applied in the rest of this document within a multidisciplinary approach. A system is a functional composition of elements that is encompassed by a boundary delimited by its observer and the purpose of its study. In this ontological overview, a system can adopt a matryoshka or an onion sense of layers in a macro or micro perspective. A system can be the universe itself, a galaxy, a solar system, a planet, a country, an ecosystem, or an individual depending on the observer, the study that is been undertaken and the purpose of such study. [3]

The study of the observer is therefore guided between the relationship of the system and its external environment. In thermodynamics, systems can be categorized into 3 groups (closed, isolated and open) according to the interaction of energy and mass within itself and its surroundings through its boundaries. In the closed systems, there is energy transfer, yet no transfer of mass across the system’s boundary. The pure thermodynamic approach limits this energy transfer to the expressions of heat and work. Energy is a human construct which we can only measure and observe indirectly through its consequences. For this, energy has many forms and can be translated to several expression. Isolated systems do not allow any mass nor energy transfer at all. Open systems allow interaction of mass and energy throughout its boundaries. The thermodynamics approach is univocal to the works of Bertalanffy and other philosophers who developed its system theory such as Maruyama and Maturna. [4]

"Ancestral" RESILIENCE
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History and Etymology of RESILIENCE

In 1973, Canadian ecologist C.S. Holling popularized the resilience concept in an ecological context, defining it as “a measure of persistence of systems and of their ability to absorb change and disturbance and still maintain the same relationships between populations or state variables”. [r…]

Holling accentuates, the complexity and quantity of external variables and factors related to the resilience of a system, as an initial differentiator between an engineering and ecological approaches regarding resilience. This differentiation is fundament on the unpredictability, externality, and the unmanageable number of components and perturbations related to a system. [13]

Holling uses freshwater lakes as an example of a system, or what he calls “self-contained ecosystem”. In his example he shows that even-though there is little interaction within the boundaries of the system (open system), with its exterior, human interaction can modify the behavior of the system, making it change. He implies that the external factors modify a “neutral stability” by dynamically changing the population growth of living beings inside the system due to the availability and shortage of external nutrients related to eutrophication in addition to human extraction of resources (fishing) and chemical modifications due to human activities. These external factors could be considered as external forces to the system imposed by human interaction. What makes the system collapse (extinction of species) is when such external forces surpass the adaptability capacities of the living beings inside the system. Other natural phenomena, external to human conditions, also can create perturbances in the system, yet these are prolonged over time and species can gradually adapt to the new conditions of the system. Holling states that other systems such as terrestrial biomes can follow similar patterns. Finally, he concludes that the stability of the systems within itself is not as relevant as the likelihood of the system to drastically move to a new condition completely alien from the previous one.

We can illustrate such behavior with Texcoco lake in the valley of Mexico City. This system has been under the continuous pressure of human external factors over the last 700 years from the foundation of Tenochtitlan where the Aztecs modified the lake for agricultural purposes creating the “Chinampas”, introducing nutrients to the lake and starting fishing activities. This modified the internal stability of the system, yet it didn’t drastically change the system to a new state, we could therefore say that the system showed resilience towards these external modifiers. The arrival of the Spanish conquistadors shifted the system to a complete new one, as the system was unable to adapt to the external forces. This was due because the Spanish Conquistadors deliberately dried large sections of the lake to expand the city’s infrastructure. In our present day, completely external and predatorial species were introduced to the little remains of the lake, as other were transformed into sewage pipes. The system encounter by the Aztecs in 1325 A.C is completely different from the system in our present day.

We can infer in general terms that systems in ecology are composed by living beings interacting among themselves inside a local environment and depend on specific factors such as nutrients, chemical and physical compositions which define and sustain the inhabitants of such system. Ecological systems can be described as open systems according to the definitions in the previous sections because they are subject to energy and mass exchanges through its boundaries with the surrounding environment and other neighboring systems. Ecological systems are said to be self-organizing, as there is a constant dynamic interaction among its internal components (the inhabitants of the system and the biological, chemical, and physical aspects of the system) which are constantly creating the conditions for the system to work in a certain equilibrium (neutral stability)

Natural and anthropogenic external perturbances can modify the neutral stability of the system (its cyclic operation behavior under a defined operation range). This can cause the system to operate outside its neutral stability, if the system rapidly adapts and goes back to such neutral stability, the system is being stable. If the external factors overwhelm such stability the system will shift to a new potential operational range or a new stability. The ability of the system to avoid such shifts is the resilience of the system. All perturbances and recoveries inside the limits of the neutral stability of a system can be attributed to the stability properties of the system. Exceeding such limits and shifting to another different state for the system is related to resilience.

Holling highlights the fact that resilience and stability should be measurable (“If there is a worthwhile distinction between resilience and stability it is important that both be measurable […]”). There is also a suggestion regarding which units these ecological concepts should have. (“There are two components that are important: one that concerns the cyclic behavior and its frequency and amplitude, and one that concerns the configuration of forces […].”). Frequency is related to time, specifically to cycles per second or Hertz in the SI unit system. Amplitude is characteristic of the phenomenon being studied, in the case of ecology and the examples of Holling, it can be related to population numbers of the inhabitant species of a system. Lastly, the driving external forces causing perturbances in the system can be reflected as the potential extinction of the species in the system. Holling emphasizes that the measurement of these variables would require privilege information of a given system, which could be nearly impossible (“But such measures require an immense amount of knowledge of a system, and it is unlikely that we will often have all that is necessary”). Therefore, even though the signified of resilience in ecology implies a quantitative attribute, its limited to a descriptive functionality which can show the behavior of a system from a qualitative focus.  

The ecological resilience definition was taken as a popular approach to include a social human perspective (“Resilience and Stability of Ecological Systems, is still frequently cited today, because it defines the ecological concept of resilience. It has become the touchstone paper for the resilience community, a community of interdisciplinary global change scholars working in policy and science for society”).  The development of resilience in ecology has created a doorway for other disciplines to apply derivative and analogous signifieds in their own fields of study, particularly in the multidisciplinary disaster fields of study.

psychological RESILIENCE

Resilience in psychology can be traced to a potential common source of inspiration alongside its ecological counterpart. The work of Bertalanffy, in 1950 originated some of the fundaments for both signifieds of resilience in psychology and ecology. [3] Yet, its evolution has progressed over the years to our present day. In psychology the system under study is the human mind and the external forces or perturbances could be described as traumatic events. George A. Bonnano, a research pioneer in the field of trauma defines resilience in the context of trauma as “the ability of adults in otherwise normal circumstances who are exposed to an isolated and potentially highly disruptive event, such as the death of a close relation or a violent or life-threatening situation, to maintain relatively stable, healthy levels of psychological and physical functioning” [15]. This recent definition can help us understand the overall concept of the signified of resilience in psychology since it is not divergent from other psychological resilience signifieds. Such as the one graphically represented in figure 1.

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Resilience in psychology can be generally defined as the characteristic of the human mind to overcome adverse events maintaining or restoring an unperturbed level of functionality equivalent to the one prior to the perturbant event. We will see further down this document that similar characteristics and attributes can be found in other resilience signifieds applied to other fields of study. [14,15]

The interesting connotation of this approach is related to the vertical axis of its graphical representation. The human mind being a complex and unique system is subject to philosophical and scientific debate. It is a field we haven’t fully comprehend therefore measuring its functionality can be subject to inconsistencies. Yet, the concept of functionality or “heaty mind” is ever present in the existing literature regarding this subject. This “functionality” can be attributed to the levels of certain chemicals present in the human brain which can be identified in sectors of the population which haven’t been subject to trauma. These subjects can be referred as a control group, therefore creating a “normal functionality condition” under healthy human brains operate. Subjects who have been exposed to traumatic events are compared to the control group to reveal potential gaps or level differences among such chemical substances. This method can also be executed through psychological analysis of subjects to identify patterns and behaviors which can also signal differences among individuals. Even though resilience is theoretically quantifiable, the complexity of the human mind and its variables have prolonged its applicability in a qualitative approach. This is a similar characteristic with the ecological signified which is also descriptive of a phenomenon.

psychological RESILIENCE
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Resilience in economy can be traces back as a qualitative descriptive term colloquially used, yet the work of Adam Rose and his team has materialized a functional approach to define resilience from an economic perspective [22]. This economic approach finds a common link with the ecological resilience given by Holling “These concepts relate to classic definitions in the literature of maintaining function and recovering rapidly by Holling (1973) [13]”.

Contrary to what we could think, defining resilience in economy is not necessarily exclusive nor related to financial assets, but also includes human and material resources in general. Therefore, it is important to generally define logistics as the transport or movement of material assets, human personal, financial resources, and information.

In general terms, a system is economically resilient if its economy can operate and maintain its functionality after an external perturbation. If the local stock of general resources is sufficient to cope with the response, and the recovery during and after a disaster, the system is therefore statically resilient. Moreover, dynamic economic resilience is related to the administration of a potentially constant flows of resources efficiently used for the response and recovery of a disaster. In the overall, economic resilience is related to the logistics and administration of local and external resources and the interdependencies between sectors (depending on if the system is temporarily severed from its environment or not). [16]. It is important to mention that some industries or business might achieve a more significant role during the response and recovery phases of a disaster due to the nature of the resources (products, services) which they provide.

An open system can be subject to an external perturbance which can isolate it and convert it into a close system, severing the logistic flow with its surroundings and neighboring systems. If such system can operate to a certain nominal functionality with the already existing and remaining assets prior to the perturbance, the system is therefore statically resilient. Such systems can be inherent or adaptive. Inherent static resilient systems utilize redundant assets to serve as support such as backup generators, provisions, and supplies stock. Adaptive static resilient systems are those which can improvise novel solutions with the remaining assets prior to the perturbance to maintain or re-stablish a nominal functionality. Static resilience is a characteristic which will maintain the perturbed system partially operating, yet it will not infer in its total recovery. On the other hand, dynamic resilience can set the perturbed system back to its functioning state prior to the disaster/ perturbance. Therefore, static resilience can be considered as an initial characteristic to gain time until logistic lines are established with the external environment of the perturbed system allowing the flow of assets, facilitating the recovery and reconstruction of the affected system. Dynamic resilience can also be interpreted as “investing” since resources are being spent over time to re-stablish productivity in the future [22].

There are 3 ontological levels on which general economic resilience can operate, for the sake of simplicity we will identify them as: “Local” (Individual business, Utilities, households), “Medium” (Markets), and “High” (Regional and national economy). These levels reflect on the boundaries of a system and how it can build resilience. The local resilience enhancers can be exemplified as the inherent static resilient system previously mentioned. Such enhancers tend to be costly since their passivity (redundant assets are not being used under normal circumstances) prevents them from adding to the economic flow or the nominal functionality of the system. The medium enhancers reflect on the general availability (volume) and price of products in general. If a disaster isolates a system, the essential existing assets will increase their price since now the volume is virtually limited and the demand, in the best case remains constant yet if we consider human irrationality, it can increase leading to shortages of products and price increments. The medium level is potentially an indicator of an abnormal behavior in a system. The High level reflects on regional and national policies to economically cope with a disaster. Considering the system to be an entire country, if a perturbance is significant enough to englobe a large portion of the system, external intervention might be needed to handle with the disaster. This can be exemplified with the 2010 earthquake in Haiti, where international intervention was needed to cope with the situation [22].    

A key aspect to resilience in the economic field is the difference between stocks and flows. Stocks are related to material, infrastructure, and property damage. Flows can relate to transaction or movement of assets which have been severed after a disaster. This implies that stocks are punctual in time while flows are continuous. During a disaster most of the infrastructure and material assets is jeopardize and/or destroyed in a punctual time, causing a punctual quantifiable lost estimate of material things. Moreover, the flows are affected until the logistics lines are restored, this means that there is a continuous financial affectation related to all transactions which have stopped (Lost economic activity) [22].

A study conducted by Adam Rose and his team at the University of southern California, has revealed that the economic looses driven by the halt of economic flows where 4 times greater than the value of lost property after the world trade center terrorist attack in New York.

An initial measurement of economic resilience was proposed as the total avoided losses (stock + flows) divided by the maximum potential total losses in the system. The units of such measurement are given in FIAT USD and since the units are shared by the numerator and denominator, the result is dimensionless and can be interpreted as a percentage. This initial metric example was used to exemplify the resilience of a system if relocation of business would have been done instantaneously after the terrorist attack. The relocation of business would have prevented the flow losses and would have saved the resilience % of the total economical looses due to this perturbance in the system [22].

Economic resilience can be complemented with computational modeling, yet econometrics rely on large data bases with critical information which generally are created with the experience over the year of which data is critical to express the reality of a phenomenon. Unfortunately, econometrics have been applied to disasters until the recent decades, which means that such data bases are still in a building process and their predictability is not reliable yet.

The involvement of a temporal axis in a characteristic diagram to portray resilience is common factor between ecological and economic signifieds of resilience.

In the same line of thought as the ecological resilience, most indexes authors agree that there is no miraculous solution to stablish which factors are more relevant than others, “There is no one-size-fits-all approach to deriving weights, and the method of choice will depend on the particular problem at hand. [16]”. This has created a vast debate and extensive literature on how to measure the functionality of a system, and what variables should be considered.

BRIC (Baseline Resilience Indicators for Communities) is an example of vulnerability indicators which can portray the functionality of a system and its potential affectations during a disaster. This approach is an attempting to create consensus on which variables should be considered to determine the functionality of a system. The BRIC was developed for the United States by Dr Susan Cutter and her colleagues. It composed by six resilience subdomains and a hierarchical approach to the index construction. This approach has proven to be functional in the identification of ricks prior to a disaster based on data gathered from previous disasters and even though the BRIC index is used as a structural guide. Each index considers local endemic variables related to the coping capacity of each local community. Since not every variable can be considered, the indexes serve only as a rough guide to approximate the behavior of real phenomena Yet, a relevant factor common to all indexes is the infrastructure related to healthcare [17]. A common critic towards such indicators is the lack of theoretical base, evidence, and selection of critical variables. This might be related to the novelty of this field of study and the already mentioned lack of experience in composition of data bases. Such factors would change how the system’s nominal functionality and affectation is measured, in figure 2 it would refer to the vertical axis. Adam Rose proposes economical output as the indicator to measure such functional states, yet other indicators such as BRIC have been proposed. There is no global consensus regarding the vertical axis, yet the horizontal axis is not only universal in economic resilience but a common factor among other fields of resilience application. In the disaster context, the economical approach emphasizes the resources are necessary for the accomplishment of any task [18, 19]. This perspective is directly refuted by others who state that community resilience and “time banks” are more relevant than the financial aspect [20, 21].  Yet, both opinions find consensus in supporting the local economy of the affected human system and avoiding creating economic dependance on external aid.

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In figure 2 we can observe in the vertical axis the performance/ functionality of an economic system defined by its economic output. In the horizontal axis, time is represented. The nominal operation functionality of the system is interpreted by the line between points A and B. In point B, the system is subject to an external perturbance, and its economic output is drastically affected (the system is underperforming). From points D to G we can observe several paths which the system can follow, each describing a different recovery behavior. Here we can also observe the differences between the representations of static and dynamic resilience.


Stress-strain diagrams

To understand the role of resilience in sciences and engineering, we must first define stress and strain, two fundamental aspects related to this definition.

Stress is a quantity that describes the distribution of internal forces within a body caused in opposition to an external force acting over that that same body. A body for example can be a sample cylinder of any given material (steel, wood, stone, rubber, bone, etc.), yet it can also represent an entire structure, or anything composed by a tangible solid material shaped in any possible geometry. For this section, Let’s define a “system” as any tangible individual or group of solid elements/bodies of any given material. Stress is a measurement of the internal force per unit area (force over area), which makes this concept definable in SI unit systems (Newtons per meter square or Pascals) or in imperial unit system (pounds per square inch). There are sever types of stress depending on how external forces are interacting with the system. If an external force acts axially in relation to the sample cylinder, the stress will be defined as normal. Normal stress can be calculated as the applied external force divided by the cross-sectional area of the sample cylinder. We can observe that if the area of the sample cylinder tends to be infinite then the normal stress will tend to be 0, and if the external force tends to be infinite, the normal stress will tend to be infinite. This means that the greater the area the lesser the stress if the force is kept constant. In opposition, the greater the force the greater the stress, if the area is kept constant. Any system can fail if the stress within it exceeds the strength of the material. [24]

Strain is a quantity that describes the deformation that occurs within a system. The acting external forces will create quantifiable deformations in a system. The normal strain within the sample cylinder will created deformation which can be calculated as the change in length of the cylinder (ΔL) divided by the original length of the cylinder. Strain as itself is a measurable non-dimensional quantity composed by two measurable dimensional quantities. Strain is often expressed as a percentage. [24]

The relationship between stress and strain can be represented by a stress-strain diagram figure 3. Every material has its unique stress-strain diagram. This diagram can be obtained by performing tensile tests. A tensile test is performed by applying a known force to a system (sample cylinder for example) of known geometry. The stress and strain are measured as the known force is gradually incremented. The system will deform over time as the external known force is increased. This will create 2 major zones and 3 critical points characteristic for all known materials. If the material is ductile like a rubber band or most metals, the first zone of the diagram will have a linear behavior. Which means that in this zone, the strain is proportional to the applied stress. Yet, most materials can adopt a linear proximation. In this initial zone, deformations are fully reversable. This means that if the external force is removed the system will return to its original geometry without deformations. Engineers call this zone of the diagram: the elastic region. The linear correlation between stress and strain is defined by Hooke´s law. The ratio between stress and strain represents the Young´s modulus or modulus of elasticity, and it can be calculated as the gradient of the slope in the elastic zone. The Young´s modulus is unique for each material known to humanity and it defines how stiff the material can be. The greater the Young´s modulus the stiffer the material is, which means the temporary elastic deformations will be smaller for any given applied external force. In the opposite circumstance, if the Young´s modulus is small the temporary elastic deformations will be greater.

The second zone of the diagram starts at the point where the external forces surpass the elastic properties of the material, this is the yield point. From this point forward any deformation to the sample piece will be permanent. This is the plastic zone. If the external force surpasses the plastic properties of the material, then we will reach the fracture point. At this point the sample cylinder has failed and is broken into 2 pieces. [24]

Normal stress calculation and Young´s modulus identification can allow engineers to predict when a system will fail, therefore stress and strain quantification is fundamental for designing any system. Through experimentation and observation, engineers and scientist have determined the behavior of most materials known to humanity. One fundamental aspect of material sciences focuses on finding new materials composites and combinations to define the stress limits they can withstand. [24]

True stress-strain diagrams

A remarkable aspect of stress-strain diagrams if the difference between “approximated” and “true” diagrams. The stress-strain diagrams described above refer to an approximation of reality, yet this method is commonly implemented for general design in engineering. The reason of this is the resemblance of both the reality and approximation, figure […]. True diagrams are defined by true stress and true strain. True diagrams consider the change of dimensions and geometry of the system (sample cylinder) throughout the duration of the test. This only affects the diagram in the plastic zone, and therefore the elastic “true” zone is identical to the approximation [23].

Resilience definition

Resilience is a quantitative value defined as the total energy in the elastic zone (the area under the curve in the stress-strain diagram in the elastic zone) which can be stored in a system subject to an external force. Materials with high resilience are implemented in tasks which cannot allow plastic deformations. In sciences and engineering, the observable consequences of energy are quantifiable in both the SI unit system and the imperial unit system. If we use the SI units for this example, resilience would be Joules per cubic meter. Engineers attributed this quantifiable phenomenon (signified) to the word resilience (signifier). This mathematical tool has been implemented since the industrial revolution, yet in the recent decades, its definition has not been rigorously approached, or has been decontextualized, outside the engineering applications (naval, aerospace, civil, architectural, mechanical, industrial, mechatronics, material sciences) and certain branches of science.

Failure theory

For ductile materials failure is commonly considered to take place at the beginning of the plastic deformation while it occurs at fracture for brittle materials. This difference can mark one of the main the differences between brittle and ductile systems. The concepts showed above have been described under uniaxial tensile conditions. In reality, systems are subject to 3 dimensional external forces and a variety of additional factor which can work as catalyzer for failure. This multi factorial reality complicates the study and predictability of the system’s behavior. There is no universal failure theory in engineering, but a set of different approaches and methos which can be applied according to the circumstantial conditions of the system (Coulomb-Mohr, Rankine, Modified Mohr are methods suited to solve brittle failures. Gurson, Hill, Tresca, Von Mises, Hosford are methods appropriate for ductile failures). Such methods are complementary among themselves and have proven to work well according to the circumstances of the system. Nevertheless, these methods are based on the principles described above. The main difference lies in the type of stresses and strains and their mathematical interpretations. Systems can achieve overwhelming complexities, In the attempt to understand their behavior, they can produce mathematical analysis exceeding the capacities of the human mind. [24]

For this reason, engineers rely on Finite Element Analysis (FEM), to calculate multi axial external forces and external additional factors affecting a system. FEM is a computer assisted method which subdivides a system into smaller categories (discretization) and applies the mathematical tools described above to the subsystems individually. This computational tool has taken engineering to a new horizon and has facilitated the identification of critical points and the predictability of failure in complex systems.

Additional factors to resilience

The resilience of a system not only depends on the properties of the material but also on the geometry of the system. Changing the geometry of a system can highly influence its area moment of inertia. The area moment of inertia of a system or second moment of area, is a quantifiable property which reflects how the area of a cross-section is distributed relative to a particular axis. This measures how much resistance the cross-section has to deformation. If a system has a high second moment of area it will be more resilient. Another factor, which tends to be underestimated is weather. Temperature humidity and climatological conditions such as salinity can drastically affect the behavior of a material and a system, therefore its resilience. In 1912 the Titanic experienced a catastrophic failure in the mechanical integrity of its hull. This was due because steel behaves as a brittle material (it is not resilient) when the ambient temperature is below 0. The Titanic disaster was not due to an Ice-berg, as it is commonly believed, but to bad design. In the following decades, the forensic analysis of this disaster marked a new era of more rigorous designing regulations. At the time of the Titanic design, engineers where convinced that all test and regulations where sufficient to build a safe ship [25]. A similar example can be observed with the space shuttle Challenger in 1986. In contrast with the Titanic, several engineers noticed a potential risk with the operational temperature of the O-rings and their brittle behavior under low temperatures. This disaster could have been avoided if the administrative personal of NASA would have listened to the engineering team [26]. An estimate of 90% mechanical failures which have resulted in disasters are attributed to fatigue failure. Fatigue failure is due to propagation of cracks inside a system. These cracks tend to be formed in the surface of a system or in stress concentrators (specific geometries of a systems where stressed tend to be concentrated upon the interaction of an external force with the system). If the application of the external force is periodic or ever present in the system, such cracks will increase their dimensions, inevitably leading to fracture. Fatigue is a fundamental component which influences greatly the resilience of a system. If a system is poorly designed, or has no supervision nor maintenance, its resilience will gradually diminish over time. Fatigue failure is dangerous because the systems can be operational even though they are about to fail. This means that the risk of a disaster due to fatigue is imperceptible and gradually increasing as the resilience weakness over time. If unattended, this leads to a fulminant and instantaneous fracture resulting in disaster. Disasters in engineering are not attributed to a single characteristic, but to a combination of factors. Fatigue can be caused or accelerated by temperature and climatological circumstances and even poorly designed systems. Bridge collapses are significant examples of this combination of factors. In 2018 the Majerhat Bridge in the city of Kolkata, India collapsed. This 50 years old bridge was showing signs of corrosion and cracks created by the weather (fatigue catalyzer) and constant use (external forces). Even though the bridge was design to ensure the transit of pedestrians and vehicles in a daily basis (the bridge was resilient under expected external forces), the climatological conditions where not fully considered. In addition, commuters and local police were aware of the deterioration of the bridge, yet no maintenance was given. The combination of these factors accumulated over time diminishing the resilience of the bridge until the system was not able to undertake more energy without plastic deformations, leading to its collapse. This disaster was preventable if the proper measures had been taken [27].

Design protocols and safety factors

Even though resilience is a quantifiable and measurable property, it is not initially employed for designing systems, its use has a descriptive and/or comparative approach. If a system is resilient, it is a consequence of its design, or the material employed on its elaboration. During the designing and/or prototyping phases of a project, resilience can be used to compare the viability, safety, and functionality of a system over another. Engineers use safety factor calculations to design any sort of system. Each industry and government have laws and regulations on how to calculate and apply such safety factors.

These properties are fundamental to prevent accidents and disasters in the human everyday life. Any system such as: tools, transportation systems, vehicles, energy producing facilities, houses, streets, and electro domestics among many more, have been designed rigorously using the mathematical tools described above. This shows that the proven mathematical functionality of a concept (signifier) is of extreme value, and not something we should easily tamper with. Resilience is a working mathematical tool which has been used to avoid disasters ever since the world shifted to industrialization.

The design of a system is guided by the predictability of its failure. Most systems, especially those who can potentially harm life if they malfunction, are strictly designed to avoid failure. Unfortunately, in the inertia of capitalism criticized by Baudrillard and Hebert Marcuse, some systems are designed to deliberate fail after a period and force the consumer to buy new replacements. This engineering - economical strategy was evidenced after lightbulbs manufactures around the world agreed to lower the quality of their lightbulbs and standardize a failing time (life span). This means that failing points, characteristics and times can be predictable.

Univocity of resilience in other fields of application

Engineering could be considered as a bridge linking mathematics and physics with tangible and functional human applications. Most engineering aspects are based on the abstract tools provided by mathematicians and physicists. Ontologically, mathematics is the lingua franca of all sciences, and physics might be considered as mathematics applied to the human experience with its environment (the universe). Furthermore, the concepts previously presented extend not only for engineering yet for other branches of sciences as well.

In biomedical engineering and medicine, the system in question can be the skeleton or the muscles. And the resilience of such systems can be determined using the same methods and tests described above. The resilience of a bone will change accordingly to its health and age, this will affect the porosity in the bone which will influence its Young´s modulus and its second moment of area. Making an unhealthy and/or older bone be less resilient than a healthy and/or younger one. Therefore, elder people are more propense to fractures than young kids. In geophysics resilience is not measurable directly in many cases.

Geophysicists and geologists use indirect methods such as atomic force acoustic microscopy, among others, to measure the properties and concepts described above. The understanding of the resilience of the ground is fundamental to avoid building households and infrastructure in risk zones. This can also extend to the understanding of volcanos and the generating models to predict eruptions. In Mexico City, the combine efforts of Civil Protection and the academical sector, have culminated in the creation of an accelerographic and seismic alert system network. This network can warn the civilian population of an upcoming earthquake whiting a minute, so people can find refuge or evacuate buildings. The reason such network can work is related in part to the resilience and other mathematical tools described above.

This multidisciplinary common ground could tell us that resilience is a univocal sign in the engineering and certain scientific branches related to the tangible human experience with the world.

A novel growing field of resilience application is found in computer sciences. There are several definitions attributed to this field each one of them related to a specific sector or problem in computer science. The 3 general ideas behind resilience in computer science are related to energy, time, and redundancy. Software micro-operations can be interpreted in the use of energy over time, an inefficient system would achieve a task using an unnecessary amount of energy in a long period of time. Contrary to these efficient systems utilize little energy and time to achieve the same task. Moreover, computational systems are constantly vulnerable and subject to hazards. External factor can create perturbances in such systems which can reflect of the efficiency of the system and/or its integrity. Resilience in this context is related to capacity of a system to overcome external perturbances through redundant efficient subsystems and/or defense mechanisms. External agents acting on a system with purposes different than what the system was envisioned for, should have limited ways of affecting the behavior of the system. Resilience can be measured as the percentage of time that the system can perform the job it was envisioned to execute. [28,29,30,31]

Comparison with ecological resilience

Engineering systems undergoes several development stages before they can be implemented in everyday life. The TRL (Technology readiness level) scale shows the maturity of a system and the conditions on which its performance is measured. Holling’s initial criticism towards the applicability of quantitative methods in ecological systems would perfectly apply if the system in question is being subject to controlled conditions in a close environment (any system from TRL1 to TRL6). Yet, no system past TRL9 will be subject to such controlled conditions. Fully developed systems are normally operating in open environment subject to unpredictability, randomness, and overwhelming variables. Understanding the limitation highlighted by Holling, engineers develop their designs under boundary conditions based on critical operational points in combination with security factors. The worst possible scenario (plus a security factor) and the best possible scenario will determine the operation range of the system. In addition to this approach, engineers tend to neglect the transient stated of a phenomenon, primarily considering the initial state and the final state of the evolution of the phenomenon. The evolution of phenomenon’s can be subdivided in several sub-initial and sub-final states, using mathematical models such as Bayesian methods and stochastic differential equations. Reducing a system’s operation to boundary conditions can drastically simplify its complex. This method can translate a general complex behavior to simple dominant fundamental values. These values govern the behavior of the phenomenon and can generally be interpreted as SI (International System of Units) base units such as: seconds, meters, kilograms, Ampere, Kelvin, mole, candela. The risk of a system’s failure (disaster) is increased when the external conditions can exceed the operation range of the system. This can be caused by overwhelming forces not considered nor expected in the initial design or poor designs not considering such external forces. Using this techniques humanity has been able to safely send and operate functional crafts in other planets with alien hazardous, unpredictable and overwhelming environments.

Holling descriptions of ecological systems behavior could be parallelized with the behavior of engineering systems: “[…] natural systems have a high capacity to absorb change without dramatically altering.” From an engineering approach this can be referring to the elasticity elastic zone in the stress-strain diagram. “[…] resilient character has its limits, and when limits are passed […] the system rapidly changes to another condition.” In the same context, this sentence can be interpreted as the transition between elastic and plastic zones. Or even further, to the “necking” in the true stress-strain diagrams.

“[…] stability, which represent the ability of a system to return to an equilibrium state after a temporary disturbance; the more rapidly it returns and the less it fluctuates, the more stable it would be.” This statement from Holling could be interpreted as ductility in the stress-strain diagram

According to some researchers, resilience in engineering can better describe a homogeneous system. For example, in material sciences, it can describe the behavior of a homogeneous material (with a constant density and/ or constant molecular composition) subject to an external force or stress. Ecological resilience is used to describe nonhomogeneous and more complex (with more variables) systems. […] [R29, R1]

Yet, such systems are initially defined by Holling as closed (“I started with self-contained closed systems […]”) even though he mentions the external interaction with human activity (“This alteration towards eutrophication seems to have been initiated by the construction of the Via Cassia about 171 BC, which caused a subtle change in the hydrographic regime”) which implies the openness of the system.


Resilience related to seismic events has been further developed within a qualitative method. This approach is related to the performance of a system over a lapse of time. Such systems could be represented as services related to the infrastructure of a community. They perform on a certain capacity during nominal operational conditions, yet their performance can be served and diminish when affected by an external factor such a disaster originated by a seismic event. Moreover, these systems can also represent the economic, cultural, and social aspects of a community. It is important to mention that the literature related to resilience in the seismic context emphasizes in the analysis of essential systems during the response of a disaster. The concepts of robustness and redundancy and resourcefulness are correlated to the seismic resilience approach. If a system is in alignment with such additional concepts, it is more likely to be resilient. [R2]

PhD Michel Bruneau was the first to introduce a performance resilience related diagram on which a given system is said to operate at its 100% capacity prior to a catastrophic event. After the disaster occurs such system will be impacted, and its operational percentage capacity will diminish proportionally to the magnitude of the disaster. During the recovery phase of the disaster the system will re-establish its operational capacity on a given time. The least time it takes to recover to more resilient the system is. 

Engineering Resilience

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