Continuum mechanics |
---|
Laws
Conservations |
---|
|
Inequalities |
---|
|
|
Solid mechanics
- Deformation
- Elasticity (linear)
- Plasticity
- Hooke's law
- Stress
- Finite strain
- Infinitesimal strain
- Compatibility
- Bending
- Contact mechanics (frictional)
- Material failure theory
- Fracture mechanics
|
Fluid mechanics
Fluids |
---|
- Statics · Dynamics
- Archimedes' principle · Bernoulli's principle
- Navier–Stokes equations
- Poiseuille equation · Pascal's law
- Viscosity (Newtonian · non-Newtonian)
- Buoyancy · Mixing · Pressure
|
Liquids |
---|
- Surface tension
- Capillary action
|
Gases |
---|
- Atmosphere
- Boyle's law
- Charles's law
- Gay-Lussac's law
- Combined gas law
|
Plasma |
---|
|
Rheology
- Viscoelasticity
- Rheometry
- Rheometer
|
Smart fluids |
---|
- Electrorheological
- Magnetorheological
- Ferrofluids
|
|
Scientists
- Bernoulli
- Boyle
- Cauchy
- Charles
- Euler
- Gay-Lussac
- Hooke
- Pascal
- Newton
- Navier
- Stokes
|
|
The polynomial hyperelastic material model is a phenomenological model of rubber elasticity. In this model, the strain energy density function is of the form of a polynomial in the two invariants
of the left Cauchy-Green deformation tensor.
The strain energy density function for the polynomial model is

where
are material constants and
.
For compressible materials, a dependence of volume is added

where

In the limit where
, the polynomial model reduces to the Neo-Hookean solid model. For a compressible Mooney-Rivlin material
and we have
