Linear elastic material models follow the linearity and elasticity assumptions.
Linearity Assumption
The induced response is directly proportional to the applied loads. For example, if you double the magnitude of loads, the model's response (displacements, strains, and stresses) will double. You can make the linearity assumption if the following conditions are satisfied:
- The highest stress is in the linear range of the stress-strain curve characterized by a straight line starting from the origin. As the stress increases, materials demonstrate nonlinear behavior above a certain stress level. This assumption asserts that the stress should be below this level. Some materials, like rubber, demonstrate a nonlinear stress-strain relationship even for low stresses.
- The maximum displacement is considerably smaller than the characteristic dimension of the model. For example, the maximum displacement of a plate must be considerably smaller than its thickness and the maximum displacement of a beam must be considerably smaller than the smallest dimension of its cross-section.
Elasticity Assumption
The loads do not cause any permanent deformation. In other words, the model is assumed to be perfectly elastic. A perfectly elastic model returns to its original shape when the loads are removed.