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.
Strain Energy Density
Meaning
Stored elastic potential energy per unit volume represents mechanical work done on a deformable body during loading. Quantifying strain energy density provides the scalar potential required to derive Cauchy stress tensors and material stiffness matrices in hyperelastic finite element calculations. The thermodynamic scalar applies strictly to reversible elastic deformations in polymers, elastomers, and flexible membranes, losing physical validity when plastic deformation or viscoelastic heat dissipation occurs.
Potential Functions
Integrating stress over applied strain generates energy curves that characterize material stiffness across multiple stretch regimes. Defining strain energy density through invariant-based functions like Mooney-Rivlin or stretch-based potentials like Ogden enables non-linear stress predictions. Hyperelastic material models calculate local stresses by taking partial derivatives of this energy function with respect to strain invariants or principal stretch ratios.
Failure to capture low-strain and high-strain energy curves accurately causes large errors in thermoforming wall thickness simulations.
FEA Application
Implicit structural solvers evaluate local strain energy values at every element integration point during non-linear stepping. High energy gradients indicate localized stress concentrations, guiding tool modifications to improve part durability.
Energy Dissipation
Cyclic loading introduces Mullins effect softening and hysteresis losses in filled rubber compounds. Constitutive models must incorporate damage parameters when energy potential curves decay during repeated strain cycles.