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.
Stretch Ratio
Meaning
Deformed length divided by initial gauge length quantifies finite extensional strain in polymer processing and hyperelastic material testing. Expressing deformation as a stretch ratio provides the fundamental kinematic variable used to calculate strain invariants and principal stresses in non-linear elastic analysis. The non-dimensional metric applies to large-strain elastic regime calculations, where simple linear engineering strain fails to account for geometric non-linearities and volumetric conservation.
Kinematic Calculation
Value of unity represents an undeformed material state, while values greater than one indicate extension and values less than one signify compression. Computing the stretch ratio along principal material axes allows continuum mechanics solvers to track volume change and shear distortion. In biaxial film stretching, principal stretch ratios govern the degree of molecular orientation and strain hardening achieved by the polymer sheet.
Neglecting continuous thickness tracking during high stretch elongation leads to false true-stress calculations in constitutive data fitting.
Constitutive Input
Hyperelastic material formulations like the Ogden or Arruda-Boyce models take principal stretch values as direct inputs. Mathematical potential functions compute strain energy density directly from these stretch values to output accurate stress tensors.
Processing Limit
Exceeding ultimate stretch limits causes molecular chain scission and tearing in semi-crystalline polymer sheets. Process windows must hold deformation below rupture stretch ratios across all thermoforming plug assist steps.