Strain Energy
Mathematical coefficients are used in finite strain theories to characterize the non-linear stress-strain behavior of rubbery and biological materials. Determining the Ogden material parameters involves fitting multi-term strain energy density functions to experimental test data. This approach describes the response of hyperelastic elastomers under large deformations.
Accurate parameters are essential for predicting seal behavior in complex industrial assemblies.
Hyperelastic Modeling
Material testing must include multiple deformation modes to ensure that the parameter set is mathematically stable. When determining the Ogden material parameters, uniaxial tension, biaxial tension, planar shear, and volumetric compression tests are performed on the polymer. The fitting algorithm optimizes the shear modulus and exponents to match the measured forces.
The resulting model must satisfy the stability criteria across the expected range of deformation.
Metrological Sourcing
Calibration of the hyperelastic test equipment is verified using high-resolution extensometers and load cells to ensure data integrity. Specimen dimensions must be measured with digital calipers before the test starts to avoid strain calculations based on incorrect thickness. Non-contact optical systems are used to measure the strain without applying load to the specimen.
Small variations in sample preparation or curing times can skew the force curve. The parameter report must include the stress-strain curves and the root mean square error of the curve fitting.
Simulation Limit
Polymer degradation and temperature changes limit the applicability of the parameters when the elastomer operates outside of the reference test temperature. High rates of loading introduce viscoelastic effects that cannot be represented by purely hyperelastic coefficients.