When one applies a force on to a medium the force will introduce a deformation of the medium, and some of the energy will be lost through e.g. friction, or internal dissipation. If this loss of energy can be neglected all the energy will be stored in the medium, and the medium can perform the same amount of work on its surroundings. Such a material is called elastic. Elastic material models are extensively used in engineering, mainly because of the simplicity and the possibility to interpolate and extrapolate.
Even when the relationship between force and deformation is linear, the resolution of the equations involves a large number of calculations. Using knowledge about common materials the theoretical model can be further simplified using one or more of the following:
| Linear elastic material | - | the stress-strain (load-deformation) follows a linear relationship |
| Hyper (or Green) elastic material | - | the deformation work can be expressed as a change in a potential |
| Materials with one symmetry plane. | - | Chrystals with one symmetry plane are called Monocline. |
| Orthotropic materials: | - | An orthotropic material is a material that has two or more orthogonal planes of symmetry, along which material properties are constant and independent of orientation. |
| Isotropic materials: | - | An isotropic material is a material that has the same properties independent of the orientation. |
| Homogenous materials: | - | A homogenous material is a material which has the same material properties througout, i.e. wherever it is tested. A homogenous material does not have to be isotropic. |
The above definitions and idealized material descriptions can be used to simplify the material models used in structural engineering. The following pages will show how the relationship between the stress tensor and strain tensor, i.e. the elasticity tensor, can be simplified using them.