Elastic
Elastic is an adjective describing the property of returning to an original shape after deformation. It may also refer to:- [[Elasticity (physics)]], the measure of an object's or material's resistance to permanent deformation (see [[#Scientific and Technical Meanings|Scientific and Technical Meanings]])
- [[Price elasticity of demand]] and [[Price elasticity of supply]], concepts in economics measuring responsiveness to price changes (see [[#Economic Concepts|Economic Concepts]])
- A flexible fabric or band used in clothing and other products (see [[#Everyday and Industrial Uses|Everyday and Industrial Uses]])
- [[Elastic N.V.]], a multinational technology company specializing in search and analytics software (see [[#Proper Names and Brands|Proper Names and Brands]])
Scientific and Technical Meanings
Elasticity in Physics
Elasticity in physics refers to the property of a material that allows it to undergo deformation under applied stress and subsequently return to its original shape and size once the stress is removed, distinguishing it from plastic deformation where permanent changes occur. This reversible behavior is fundamental to understanding how solids respond to mechanical forces, enabling applications in structures and devices that require resilience. The concept assumes small deformations where the material's response remains linear, a key assumption in classical elasticity theory.[2] A foundational principle is Hooke's law, which states that the restoring force F exerted by an elastic object, such as a spring, is directly proportional to the displacement x from its equilibrium position and acts in the opposite direction:F = -k x
where k is the spring constant, a measure of the object's stiffness. This law derives from the assumption of linear elasticity, where strain is proportional to stress within the elastic regime, allowing the force-displacement relationship to be modeled as a straight line on a graph. For continuous materials, Hooke's law generalizes to relate stress and strain tensors, but the simple form applies to uniaxial deformations like stretching.[3] Stress \sigma is defined as the force F per unit cross-sectional area A:
\sigma = \frac{F}{A}
while strain \epsilon quantifies the relative deformation as the change in length \Delta L divided by the original length L:
\epsilon = \frac{\Delta L}{L}
Young's modulus E, a material-specific constant, relates them in tension or compression via E = \frac{\sigma}{\epsilon}, indicating stiffness; higher values mean less deformation under the same stress. Poisson's ratio \nu describes lateral contraction during axial extension:
\nu = -\frac{\epsilon_{\text{lateral}}}{\epsilon_{\text{axial}}}
with typical values around 0.3 for metals, reflecting the material's incompressibility. Elastic potential energy stored during deformation, for a spring, is given by
U = \frac{1}{2} k x^2
representing the work done to deform the object, which is recoverable upon release. These behaviors hold up to the elastic limit, the maximum stress beyond which deformation becomes permanent, often coinciding with the yield point where nonlinearity begins and plastic flow initiates.[4][2][5][6][7][8][9]