Deformation Energy
Hyperelastic materials store energy internally when subjected to mechanical deformation without suffering permanent damage. This relationship is described by a strain energy function, which defines the stored energy density as a function of the strain invariants or the principal stretch ratios. The application of this concept is restricted to elastic deformations where no energy is lost as heat or plastic strain.
Mathematical Modeling
Computing the derivative of this energy density function with respect to the strain components yields the stress-strain relations for the material. Different mathematical formulations like the Neo-Hookean or Mooney-Rivlin models are selected depending on the degree of deformation and the material type. These models use material constants that must be determined experimentally through tensile or compressive testing.
This mathematical framework allows engineers to simulate the behavior of complex elastomeric seals and diaphragms.
Material Limitation
Elastomeric materials lose their hyperelastic properties when subjected to extreme temperatures or high rates of strain. Under these harsh conditions, the strain energy function no longer represents the actual behavior of the material, which can lead to simulation errors.
Metrological Validation
Laboratory technicians perform multi-axial testing on material samples to gather the stress-strain data needed to calibrate the function coefficients. This testing involves pulling or compressing the sample while high-resolution cameras track the deformation. If the predicted stress differs from the measured value by more than the specified limit, the model parameters must be adjusted.
This validation process ensures that the simulation accurately predicts the mechanical behavior of the components.
