Is rubber hyper elastic?
The most common example of this kind of material is rubber, whose stress-strain relationship can be defined as non-linearly elastic, isotropic and incompressible. Hyperelasticity provides a means of modeling the stress–strain behavior of such materials.
What is incompressible material?
When a material is incompressible, the volume remains the same or change in volume is zero, when a body undergoes deformation.
What does incompressible material mean?
Incompressible fluids and solids will not change in volume if a pressure is applied. If the density changes have negligible effects on the solution, the fluid is called incompressible and the changes in density are ignored. Solid matter is rigid, has a fixed shape, and is incompressible.
What is the difference between strain energy and strain energy density?
Strain energy is defined as the energy stored in a body due to deformation. The strain energy per unit volume is known as strain energy density and the area under the stress-strain curve towards the point of deformation.
What is Mooney-Rivlin model?
The Mooney–Rivlin model is a special case of the generalized Rivlin model (also called polynomial hyperelastic model) which has the form are material constants related to the volumetric response. For a compressible Mooney–Rivlin material
Is the Mooney–Rivlin model of tensile deformation flawed?
However, this interpretation is flawed. Rivlin and Saunders 9 have pointed out that the agreement between experimental tensile data and equation (22) is somewhat fortuitous. The Mooney–Rivlin model obtained by fitting tensile data is quite inadequate in other modes of deformation, especially compression. 9
What is the strain energy density function for an incompressible Mooney Rivlin material?
The strain energy density function for an incompressible Mooney–Rivlin material is . For an incompressible material, . The Mooney–Rivlin model is a special case of the generalized Rivlin model (also called polynomial hyperelastic model) which has the form are material constants related to the volumetric response.
Why develop Mooney-Rivlin equations?
Developing Mooney-Rivlin equations for these special cases appears to be a very popular thing to do. There are a couple reasons for this. First, the deformation modes are (relatively) easily accomplished in lab tests, at least the uniaxial tension case is.