# Linear elastic materials¶

Linear elastic materials are the materials which obey Hooke’s law i.e. the relationship between the stress and strain is linear, represented as:

where, ‘E’ is the Young’s modulus of the material, ‘\(\sigma\)‘ and ‘\(\epsilon\)‘ are the stress and strain respectively.

These materials also deform elastically through out the analysis, which means that they will return back to their initial state upon unloading, irrespective of the deformation. In the vast majority of simulations involving linear elastic materials, we are dealing with an isotropic material that does not have any directional sensitivity. To describe such a material, only three independent material parameters are required:

For most of the structural analysis involving metals such as steel and aluminum, if the stresses are below yield strength, linear elastic material model shall be used. However, this model is incapable of truly describing the material behaviour, if the objective of the analysis is to study plasticity. In that case, use *Plastic material* model for the analysis. Additionally, there are also materials such as rubbers and elastomers for which relationship between stress and strain are non linear while deforming elastically. For such materials, *Hyperelastic material* model is the most appropriate choice.