Resilience

Resilience generally means the ability to recover from (or to resist being affected by) some shock, insult, or disturbance. However, it is used quite differently in different fields.

Psychology
Psychological resilience is a term used in psychology to describe the capacity of people to cope with stress and catastrophe. It is also used to indicate a characteristic of resistance to future negative events.

Industrial and organisational safety
Within the broad domain of industrial safety, the term resilience has come into use to emphasise that safety must be proactive as well as reactive. Whereas conventional risk management approaches are based on hindsight and emphasise error tabulation and calculation of failure probabilities, Resilience Engineering looks for ways to enhance the ability of organisations to create processes that are robust yet flexible, to monitor and revise risk models, and to use resources proactively in the face of disruptions or ongoing production and economic pressures. In Resilience Engineering failures do not stand for a breakdown or malfunctioning of normal system functions, but rather represent the converse of the adaptations necessary to cope with the real world complexity. Individuals and organisations must always adjust their performance to the current conditions; and because resources and time are finite it is inevitable that such adjustments are approximate. Success has been ascribed to the ability of groups, individuals, and organisations to anticipate the changing shape of risk before damage occurs; failure is simply the temporary or permanent absence of that.

Business
In business terms, resilience is the ability of an organization, resource, or structure to sustain the impact of a business interruption and recover and resume its operations to continue to provide minimum services.

Ecology
In ecology, resilience has been defined in two competing fashions that emphasize two different aspects of stability. The consequences of those different aspects for ecological systems were first emphasized by the Canadian ecologist C. S. Holling in order to draw attention to the paradoxes between efficiency on the one hand and persistence on the other, or between constancy and change, or between predictability and unpredictability.

One definition of resilience is the rate at which a system returns to a single steady or cyclic state following a perturbation. This definition of resilience assumes that behavior of a system remains within the stable domain that contains this steady state.

When a system can reorganize, that is shift from one stability domain to another, a more relevant measure of ecosystem dynamics is ecological resilience. It is a measure of the amount of change or disruption that is required to transform a system from being maintained by one set of mutually reinforcing processes and structures to a different set of processes and structures.

The first definition focuses on efficiency, control, constancy. and predictability - all attributes at the core of desires for fail-safe design and optimal performance. The second focuses on persistence, adaptiveness, variability, and unpredictability - all attributes embraced and celebrated by those with an evolutionary or developmental perspective. The latter attributes are at the heart of understanding sustainability.

The first definition, which is more traditional, concentrates on stability near an equilibrium steady-state, where resistance to disturbance and speed of return to the equilibrium are used to measure the property. This type of resilience has been defined as engineering resilience.

The second definition emphasizes conditions far from any steady-states, where instabilities can flip a system into another regime of behavior - i.e. to another stability domain. In this case resilience is measured by the magnitude of disturbance that can be absorbed before the system changes its structure by changing the variables and processes that control behavior. This type of resilience has been defined as ecological resilience.

These two aspects of a system's stability have very different consequences for evaluating, understanding and managing complexity and change. Sustainable relationships between people and nature require an emphasis on ecological resilience, because the interplay between stabilizing and destabilizing properties is at the heart of present issues of development and the environment- global change, biodiversity loss, ecosystem restoration and sustainable development. Emphasis on engineering resilience reinforces the dangerous myth that the variability of natural systems can be effectively controlled, that the consequences are predictable and that sustained production is an attainable and sustainable goal.

The two contrasting aspects of stability- essentially one that focuses on maintaining efficiency of function (engineering resilience) vs. one that focuses on maintaining existence of function (ecological resilience)- are so fundamental that they can become alternative paradigms whose devotees reflect traditions of a discipline or of an attitude more than of a reality of nature.

Materials
In physics and engineering, resilience is defined as the capacity of a material to absorb energy when it is deformed elastically and then, upon unloading to have this energy recovered. It is represented by the area under the curve in the elastic region in the Stress-Strain diagram. Modulus of Resilience, $$U_r$$, can be calculated using the following formula: $$U_r=\frac{\sigma^2}{2\times E}=0.5\sigma_\epsilon=0.5 \sigma\times(\frac{\sigma}{\epsilon})$$