Robust and efficient implementation of finite strain generalized continuum models for material failure: analytical, numerical, and automatic differentiation with hyper-dual numbers

Cites Work

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Robust numerical calculation of tangent moduli at finite strains based on complex-step derivative approximation and its application to localization analysis
Constitutive equations for micropolar hyper-elastic materials
One-sided finite-difference approximations suitable for use with Richardson extrapolation
Complex step derivative approximation of consistent tangent operators for viscoelasticity based on fractional calculus
Geometrie der Dynamen. Die Zusammensetzung von Kräften und verwandte Gegenstände der Geometrie.
Preliminary sketch of biquaternons.
Numerical differentiation for local and global tangent operators in computational plasticity
A comparison of different methods for calculating tangent-stiffness matrices in a massively parallel computational peridynamics code
A highly accurate 1st- and 2nd-order differentiation scheme for hyperelastic material models based on hyper-dual numbers
An excursion into large rotations
Variational updates for thermomechanically coupled gradient-enhanced elastoplasticity -- implementation based on hyper-dual numbers
Numerical calculation of thermo-mechanical problems at large strains based on complex step derivative approximation of tangent stiffness matrices
Implementation of incremental variational formulations based on the numerical calculation of derivatives using hyper dual numbers
Using Multicomplex Variables for Automatic Computation of High-Order Derivatives
An overview of the Trilinos project
GRADIENT ENHANCED DAMAGE FOR QUASI-BRITTLE MATERIALS
Using Complex Variables to Estimate Derivatives of Real Functions
On compressible versions of the incompressible neo-Hookean material
Cosserat Continuum Mechanics
The complex-step derivative approximation
Consistent tangent matrices for substepping schemes