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.
ABAQUS UHYPER
Meaning
User-defined FORTRAN subroutines define non-standard strain energy potential functions for hyperelastic finite element calculations during complex polymer deformation analyses. Implementing abaqus uhyper allows finite element solvers to calculate stress tensors and material Jacobians from custom invariant or principal stretch formulations when commercial software libraries lack the specific elastomer constitutive equation. The subroutine applies exclusively to isotropic hyperelastic material models undergoing large elastic strains where energy potentials derive strictly from strain invariants or stretch ratios.
Code Integration
Custom constitutive equations enter the finite element solver by supplying analytical expressions for the strain energy density function alongside its partial derivatives. Writing abaqus uhyper requires explicit mathematical formulation of first, second, and third derivatives with respect to strain invariants. Programmers verify that strain energy equals zero at zero strain state to maintain baseline physical reality.
Incorrect coding of partial derivatives causes quadratic convergence failures in Newton-Raphson iterations during non-linear thermal forming or stretch blowing steps.
Computational Cost
Solution stability depends directly upon mathematical smoothness across all expected strain regimes. Unexpected stiffness spikes occur when custom strain energy functions contain asymptotic limits near physical stretch limits. Solving large elastomer meshes using user subroutines increases central processing unit time compared to built-in strain energy potentials.
Derivative Precision
Material Jacobians passed back to the solver control tangent stiffness matrices at each integration point. High numerical precision prevents spurious element distortion during severe localized thinning in blow moulding calculations.