Structural resilience theory
Introduction
In resistance of materials, the deformation energy (per unit volume) that can be recovered from a deformed body when the stress that causes the deformation ceases is called resilience of a material. Resilience is equal to the external work done to deform a material to its elastic limit:
For a specimen of linear elastic material subjected to uniform axial tension:[1].
where:.
In simple terms, it is the memory capacity of a material to recover from deformation, resulting from an external stress.
Relationship between resilience and tenacity
It differs from toughness in that it quantifies the amount of energy stored by the material before breaking, while resilience only accounts for the energy stored during elastic deformation. The relationship between resilience and tenacity is generally monotonic increasing; That is, when one material has greater resilience than another, it generally has greater toughness. However, this relationship is not linear.
Toughness corresponds to the area under the curve of a tensile test between zero strain and the strain corresponding to the break limit (when the material breaks).
Resilience is the ability to store energy in the elastic period, and corresponds to the area under the tensile test curve between zero deformation and the limit of elastic proportionality of the material. This means that resilience is the property that represents the ability of a material to recover its shape after undergoing deformation.
Measuring the resilience of a material
The quantification of the resilience of a material is determined by testing by the Izod method or the Charpy pendulum, resulting in a value indicative of the fragility or resistance to shocks of the tested material. A high degree of resilience is characteristic of austenitic steels, steels with a high austenite content. In carbon steels, soft steels (with a lower percentage of carbon content) have greater resilience than hard steels.
For a linear elastic material, resilience can be calculated by the equation:.