# Elasticity (physics)

**elasticityelasticelasticity theoryelastic bodyelasticallyelastic propertiesinelasticelastic constantselastic materialelastic solid**

In physics, elasticity (from Greek ἐλαστός "ductible") is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed.wikipedia

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### Hooke's law

**spring constantforce constantelasticity tensor**

If the material is isotropic, the linearized stress–strain relationship is called Hooke's law, which is often presumed to apply up to the elastic limit for most metals or crystalline materials whereas nonlinear elasticity is generally required to model large deformations of rubbery materials even in the elastic range. For small strains, the measure of stress that is used is the Cauchy stress while the measure of strain that is used is the infinitesimal strain tensor; the resulting (predicted) material behavior is termed linear elasticity, which (for isotropic media) is called the generalized Hooke's law.

Hooke's equation holds (to some extent) in many other situations where an elastic body is deformed, such as wind blowing on a tall building, and a musician plucking a string of a guitar.

### Plasticity (physics)

**plasticityplasticplastic deformation**

For even higher stresses, materials exhibit plastic behavior, that is, they deform irreversibly and do not return to their original shape after stress is no longer applied.

In engineering, the transition from elastic behavior to plastic behavior is called yield.

### Elastomer

**elasticelastomerselastomeric**

For rubber-like materials such as elastomers, the slope of the stress–strain curve increases with stress, meaning that rubbers progressively become more difficult to stretch, while for most metals, the gradient decreases at very high stresses, meaning that they progressively become easier to stretch.

An elastomer is a polymer with viscoelasticity (i.e., both viscosity and elasticity) and has very weak intermolecular forces, generally low Young's modulus and high failure strain compared with other materials.

### Shearing (physics)

**shearingshearshear deformation**

For instance, Young's modulus applies to extension/compression of a body, whereas the shear modulus applies to its shear.

Often, the verb shearing refers more specifically to a mechanical process that causes a plastic shear strain in a material, rather than causing a merely elastic one.

### Viscoelasticity

**viscoelasticvisco-elasticVisco-elasticity**

Elasticity is not exhibited only by solids; non-Newtonian fluids, such as viscoelastic fluids, will also exhibit elasticity in certain conditions quantified by the Deborah number.

Viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation.

### Viscosity

**viscouskinematic viscositydynamic viscosity**

Under larger strains, or strains applied for longer periods of time, these fluids may start to flow like a viscous liquid.

Stresses which can be attributed to the deformation of a material from some rest state are called elastic stresses.

### Elastic modulus

**modulus of elasticityelastic modulimodulus**

There are various elastic moduli, such as Young's modulus, the shear modulus, and the bulk modulus, all of which are measures of the inherent elastic properties of a material as a resistance to deformation under an applied load.

### Spring (device)

**springspringsspring-loaded**

As noted above, for small deformations, most elastic materials such as springs exhibit linear elasticity and can be described by a linear relation between the stress and strain.

A spring is an elastic object that stores mechanical energy.

### Hypoelastic material

**hypoelastic**

Cauchy elastic materials and hypoelastic materials are models that extend Hooke's law to allow for the possibility of large rotations, large distortions, and intrinsic or induced anisotropy. The elastic behavior of objects that undergo finite deformations has been described using a number of models, such as Cauchy elastic material models, Hypoelastic material models, and Hyperelastic material models.

In continuum mechanics, a hypoelastic material is an elastic material that has a constitutive model independent of finite strain measures except in the linearized case.

### Tensor

**tensorsorderclassical treatment of tensors**

Although the general proportionality constant between stress and strain in three dimensions is a 4th-order tensor called stiffness, systems that exhibit symmetry, such as a one-dimensional rod, can often be reduced to applications of Hooke's law.

Tensors are important in physics because they provide a concise mathematical framework for formulating and solving physics problems in areas such as mechanics (stress, elasticity, fluid mechanics, moment of inertia, ...), electrodynamics (electromagnetic tensor, Maxwell tensor, permittivity, magnetic susceptibility, ...), or general relativity (stress–energy tensor, curvature tensor, ... ) and others.

### Hyperelastic material

**hyperelastichyperelasticityhyperelastic material models**

The elastic behavior of objects that undergo finite deformations has been described using a number of models, such as Cauchy elastic material models, Hypoelastic material models, and Hyperelastic material models.

A hyperelastic or green elastic material is a type of constitutive model for ideally elastic material for which the stress–strain relationship derives from a strain energy density function.

### Stress–strain curve

**Stress-strain curvestress and strainstress–strain**

The elasticity of materials is described by a stress–strain curve, which shows the relation between stress (the average restorative internal force per unit area) and strain (the relative deformation).

Typical brittle materials like glass do not show any plastic deformation but fail while the deformation is elastic.

### Rubber elasticity

**rubbersElasticity of rubberentropic elasticity**

For rubbers and other polymers, elasticity is caused by the stretching of polymer chains when forces are applied.

### Constitutive equation

**constitutive relationconstitutive equationsconstitutive model**

A hypoelastic material can be rigorously defined as one that is modeled using a constitutive equation satisfying the following two criteria:

### Infinitesimal strain theory

**strain tensorstraininfinitesimal strain tensor**

For small strains, the measure of stress that is used is the Cauchy stress while the measure of strain that is used is the infinitesimal strain tensor; the resulting (predicted) material behavior is termed linear elasticity, which (for isotropic media) is called the generalized Hooke's law.

The infinitesimal strain theory is commonly adopted in civil and mechanical engineering for the stress analysis of structures built from relatively stiff elastic materials like concrete and steel, since a common goal in the design of such structures is to minimize their deformation under typical loads.

### Anisotropy

**anisotropicanisotropiesanisotropically**

Cauchy elastic materials and hypoelastic materials are models that extend Hooke's law to allow for the possibility of large rotations, large distortions, and intrinsic or induced anisotropy.

This alignment leads to a directional variation of elasticity wavespeed.

### Fracture mechanics

**crack propagationmicrofracturefracture**

This theory is also the basis of much of fracture mechanics.

It applies the physics of stress and strain behavior of materials, in particular the theories of elasticity and plasticity, to the microscopic crystallographic defects found in real materials in order to predict the macroscopic mechanical behavior of those bodies.

### Robert Hooke

**HookeDr Robert HookeHooke, Robert**

A geometry-dependent version of the idea was first formulated by Robert Hooke in 1675 as a Latin anagram, "ceiiinosssttuv".

In 1660, Hooke discovered the law of elasticity which bears his name and which describes the linear variation of tension with extension in an elastic spring.

### Deformation (engineering)

**deformationplastic deformationelastic deformation**

The elasticity of materials is described by a stress–strain curve, which shows the relation between stress (the average restorative internal force per unit area) and strain (the relative deformation). Solid objects will deform when adequate forces are applied to them.

### Strain energy density function

**strain energy function**

Hyperelastic materials (also called Green elastic materials) are conservative models that are derived from a strain energy density function (W).

For an isotropic hyperelastic material, the function relates the energy stored in an elastic material, and thus the stress–strain relationship, only to the three strain (elongation) components, thus disregarding the deformation history, heat dissipation, stress relaxation etc.

### Linear elasticity

**elastic waveselastic wavelinear elastic**

For small strains, the measure of stress that is used is the Cauchy stress while the measure of strain that is used is the infinitesimal strain tensor; the resulting (predicted) material behavior is termed linear elasticity, which (for isotropic media) is called the generalized Hooke's law.

### Elastography

**Tactile imagingtransient elastographyacoustic radiation force impulse imaging**

Elastography is a medical imaging modality that maps the elastic properties and stiffness of soft tissue.

### Pseudoelasticity

**superelasticitysuperelasticsuper elastic**

Pseudoelasticity, sometimes called superelasticity, is an elastic (reversible) response to an applied stress, caused by a phase transformation between the austenitic and martensitic phases of a crystal.

### Stress (mechanics)

**stressstressestensile stress**

The elasticity of materials is described by a stress–strain curve, which shows the relation between stress (the average restorative internal force per unit area) and strain (the relative deformation).

Stress analysis for elastic structures is based on the theory of elasticity and infinitesimal strain theory.

### Resilience (materials science)

**resiliencemodulus of resilienceresiliency**

In material science, resilience is the ability of a material to absorb energy when it is deformed elastically, and release that energy upon unloading.