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Resilience is the property of a material to absorb energy when it is deformed elastically
Elasticity (physics)
In physics, elasticity is the physical property of a material that returns to its original shape after the stress that made it deform or distort is removed. The relative amount of deformation is called the strain....

 and then, upon unloading to have this energy recovered. In other words, it is the maximum energy per unit volume that can be elastically stored. It is represented by the area (integral) under the curve in the elastic region (the initial, linear portion) of the stress-strain curve
Stress-strain curve
During tensile testing of a material sample, the stress–strain curve is a graphical representation of the relationship between stress, derived from measuring the load applied on the sample, and strain, derived from measuring the deformation of the sample, i.e. elongation, compression, or distortion...

; this quantity is also known as the elastic potential energy of a material.

The modulus of resilience is defined as the energy that can be absorbed per unit volume without creating a permanent distortion. It can be calculated by integrating the stress-strain curve from zero to the elastic limit and dividing by the original volume of the specimen.

Modulus of resilience, , can be calculated using the following formula: , where is yield stress, is Young's modulus
Young's modulus
Young's modulus is a measure of the stiffness of an elastic material and is a quantity used to characterize materials. It is defined as the ratio of the uniaxial stress over the uniaxial strain in the range of stress in which Hooke's Law holds. In solid mechanics, the slope of the stress-strain...

, and is the strain
Strain (materials science)
In continuum mechanics, the infinitesimal strain theory, sometimes called small deformation theory, small displacement theory, or small displacement-gradient theory, deals with infinitesimal deformations of a continuum body...

 at the yield stress.

An example of a biomaterial
A biomaterial is any matter, surface, or construct that interacts with biological systems. The development of biomaterials, as a science, is about fifty years old. The study of biomaterials is called biomaterials science. It has experienced steady and strong growth over its history, with many...

 which has a high resilience is articular cartilage
Cartilage is a flexible connective tissue found in many areas in the bodies of humans and other animals, including the joints between bones, the rib cage, the ear, the nose, the elbow, the knee, the ankle, the bronchial tubes and the intervertebral discs...

, the substance lining the ends of bone
Bones are rigid organs that constitute part of the endoskeleton of vertebrates. They support, and protect the various organs of the body, produce red and white blood cells and store minerals. Bone tissue is a type of dense connective tissue...

s in articulating joints such as the knee
The knee joint joins the thigh with the leg and consists of two articulations: one between the fibula and tibia, and one between the femur and patella. It is the largest joint in the human body and is very complicated. The knee is a mobile trocho-ginglymus , which permits flexion and extension as...

 and hip.

It might be different from rebound resilience, which is used for instance in relation with foam
-Definition:A foam is a substance that is formed by trapping gas in a liquid or solid in a divided form, i.e. by forming gas regions inside liquid regions, leading to different kinds of dispersed media...


The maximum energy which can be stored in a body up to elastic limit is called proof resilience.