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.
Biaxial Testing
Meaning
Simultaneous multiaxial mechanical deformation measures material response under balanced or unequal orthogonal tension states. Executing biaxial testing yields stress and strain data along two perpendicular axes to characterize anisotropic behavior or calibrate hyperelastic constitutive models for polymer film processing. The measurement method applies to elastomeric sheets, thermoplastic membranes, and molten preforms undergoing planar tension, but cannot isolate pure shear states without secondary fixture modifications.
Deformation Kinematics
Applied loads along independent axes force polymer chains to align simultaneously in orthogonal directions. Mechanical actuators control strain rates along each axis independently to simulate complex processing modes such as film orientation or container blowing. Equal stretch ratios yield equibiaxial tension, while unconstrained orthogonal expansion allows planar shear fields to develop within the gauge section.
Capturing true stress requires continuous thickness tracking throughout the deformation path because cross-sectional areas shrink rapidly under dual loading vectors.
Datasheet Discrepancy
Tensile modulus values reported on standard resin datasheets originate from uniaxial pull tests that fail to capture multiaxial strain hardening. Biaxial testing reveals higher stiffening slopes at lower stretch ratios than single-axis tension curves predict. Designing thermoforming molds based solely on uniaxial data results in wall thinning underestimation and poor corner detail reproduction.
Specimen Geometry
Flat square films equipped with corner relief slots prevent load concentration along clamping edges. Uniform deformation occurs only within the central zone of the planar specimen.