material science A material is a substance or mixture of substances that constitutes an object. Materials can be pure or impure, living or non-living matter. Materials can be classified on the basis of their physical and chemical properties, or on their geol ...

, resilience is the ability of a material to absorb energy when it is deformed elastically, and release that energy upon unloading. Proof resilience is defined as the maximum energy that can be absorbed up to the elastic limit, without creating a permanent distortion. The modulus of resilience is defined as the maximum 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. In uniaxial tension, under the assumptions of linear elasticity, :

U_= \frac = \frac

where ''Ur'' is the modulus of resilience, ''σy'' is the yield strength, ''εy'' is the yield strain, and ''E'' is the

Young's modulus Young's modulus (or the Young modulus) is a mechanical property of solid materials that measures the tensile or compressive stiffness when the force is applied lengthwise. It is the modulus of elasticity for tension or axial compression. Youn ...

. This analysis is not valid for non-linear elastic materials like rubber, for which the approach of area under the curve until elastic limit must be used.

Unit of resilience

Modulus of resilience (''U''_r) is measured in a unit of

joule The joule ( , or ; symbol: J) is the unit of energy in the International System of Units (SI). In terms of SI base units, one joule corresponds to one kilogram- metre squared per second squared One joule is equal to the amount of work d ...

per cubic meter (J·m⁻³) in the SI system, ''i.e.'' elastical deformation energy per surface of test specimen (merely for gauge-length part). Like the unit of tensile

toughness In materials science and metallurgy, toughness is the ability of a material to absorb energy and plastically deform without fracturing.Pa × % = (N·m⁻²)·(unitless) :''U''_r N·m·m⁻³ :''U''_r J·m⁻³

Unit of resilience

See also