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.
Hyperelasticity
Meaning
Non-linear mechanical behavior allows materials to undergo severe elastic deformations and return fully to their original shape upon load removal. Mathematical modeling of hyperelasticity uses strain energy density functions to represent non-linear stress-strain relationships in elastomers, rubbers, and softened thermoplastics above glass transition temperatures. The constitutive framework applies to conservative, path-independent elastic deformations up to several hundred percent strain, ceasing to hold when plastic yield, permanent set, or viscoelastic dissipation dominates.
Strain Energy Formulation
Continuum mechanics describes material response by relating strain energy storage directly to deformation invariants or principal stretch ratios. Defining hyperelasticity through strain energy functions enables accurate stress calculations under complex multiaxial loads. Phenomenological models like Mooney-Rivlin or Yeoh capture moderate strains, whereas micro-mechanical models like the Arruda-Boyce eight-chain potential capture strain hardening near physical chain entanglement limits.
Selecting an inappropriate strain energy formulation leads to inaccurate clamping force calculations and wall thickness errors in blown container simulations.
Tooling Design
Mold designers rely on hyperelastic material models to size core pins and ejection mechanisms for elastomeric parts. Precise strain recovery predictions prevent seals from binding inside cavity undercuts during automated demolding sequences.
Incompressibility Assumption
Elastomers maintain nearly constant volume during deformation, exhibiting Poisson ratios close to one half. Bulk modulus values must exceed shear modulus values by orders of magnitude in finite element solver formulations to prevent volumetric locking.