Deriving Ogden Constitutive Parameters from Biaxial Stretch Testing Data
Deriving Ogden constitutive parameters pairs non-linear biaxial stretch data with Drucker stability constraints to ensure reliable finite element simulations.
Ogden Model
Meaning
A phenomenological hyperelastic material formulation expresses strain energy density directly in terms of principal stretch ratios rather than strain invariants. Utilizing the ogden model captures complex non-linear stress-strain paths and severe strain hardening in rubbers and soft thermoplastic elastomers up to large deformations. The model applies effectively across wide stretch ranges provided accurate multiaxial test data exists for calibration, but exhibits non-physical numerical instability when extrapolated beyond calibrated strain bounds.
Strain Potentials
Summing fractional power terms of principal stretches allows the formulation to match experimental stress curves with extreme flexibility. Calibrating an ogden model requires determining paired shear moduli and non-integer exponent coefficients for each term in the series expansion. Higher N-order terms improve mathematical fitting precision for severe non-linear responses, such as high-stretch rubber vulcanizates or stretch blow moulded PET preforms.
Selecting an order above three risks mathematical oscillation between calibration points, violating Drucker stability conditions in FEA models.
Fit Accuracy
Excellent agreement with empirical curves makes this model preferred for complex rubber spring and seal simulations. Calibration must include planar shear and equibiaxial tension to avoid under-predicting multiaxial stiffness.
Computational Demand
Non-integer exponents require extra CPU processing time to calculate principal stretch powers and derivative matrices. Simulating large industrial meshes with higher-order Ogden terms slows solver throughput significantly.