Non-linear materials fall into several categories including plastically deforming materials, temperature or time-dependent material properties and hyper-elastic (rubber-like) materials.


Plasticity involves straining a material past its yield point so that the structure does not return to its original shape when the load is released. Some basic examples of plasticity include the bending of points on staples and the crushing of aluminum cans. There are a multitude of material plasticity models that are chosen based on the material characteristics, load curve and level of deformation expected. Each of these models requires a specialized solution strategy.

Material Properties

Most materials experience a change in properties depending on their operational requirements. Metals can soften at high temperatures and become very brittle in the cold. A ceramic spindle may be able to carry thousands of pounds of static load, but fail when subjected to the slightest impact load. A plastic bolt tightened to its proof torque may stress relieve over time due to creep, thus releasing its clamping load. Analysis of these effects requires the inclusion of non-linear material properties within the analysis model.


Hyperelastic materials are a class of materials that can undergo very large elastic deformations. These materials are also characterized as being nearly incompressible which does not allow for the use of standard material relationships. Instead, specialized models such as the Mooney-Rivlin or Ogden models are used with model constants derived from material test data.

PMI has the experience to analyze a wide variety of non-linear material effects. Due to our varied experience, we are familiar with references that publish approximate values for non-linear properties. We can also assist you in preparing tests to determine material properties specific for your application.