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.
Planar Stretch
Meaning
Pure shear deformation in thin wide sheet materials maintains zero strain along one planar axis while stretching along the orthogonal axis. Inducing planar stretch isolates intermediate stress states essential for calibrating hyperelastic material models used in thermoforming and blow moulding simulations. The deformation mode applies specifically to thin membranes, elastomeric films, and preform wall elements undergoing wide-strip extension where lateral contraction is mechanically constrained.
State Kinematics
Width constraints force thinning along the sheet thickness direction to preserve material volume during axial extension. Achieving planar stretch requires test specimens with a high width-to-length aspect ratio, typically exceeding ten to one, preventing edge contraction near central measurement zones. Material elements experience multi-axial stress despite single-axis jaw displacement, generating transverse tensile forces that hold sample width constant.
Inaccurate width clamping allows edge necking, converting true planar extension into non-uniform uniaxial tension.
Constitutive Role
Pure shear equivalent loading provides data points positioned between simple uniaxial tension and balanced equibiaxial extension on the strain invariant plane. Hyperelastic models calibrated without planar data fail to predict side-wall thinning during vacuum thermoforming.
Test Execution
Custom wide-grip fixtures maintain uniform lateral restraint across broad polymer sheets. Standard tensile clamps permit lateral contraction and introduce severe measurement errors.