Hyper-dual number-based numerical differentiation of eigensystems

DOI10.1016/j.cma.2021.114452OpenAlexW4206309943MaRDI QIDQ2072712

Yusuke Imoto, Masaki Fujikawa, Naoto Mitsume, Masato Tanaka

Publication date: 26 January 2022

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2021.114452

zbMATH Keywords

eigenvalueseigenvectorsnumerical differentiationhyper-dual numbershyperelastic-plastic materialsincremental variational formulation

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Numerical differentiation (65D25) Multilinear algebra, tensor calculus (15A69) Generalities, axiomatics, foundations of continuum mechanics of solids (74A99)

Related Items (1)

A return mapping algorithm based on the hyper dual step derivative approximation for elastoplastic models

Uses Software

• ABAQUS

Cites Work

• Robust numerical calculation of tangent moduli at finite strains based on complex-step derivative approximation and its application to localization analysis
• Automatic implementation of finite strain anisotropic hyperelastic models using hyper-dual numbers
• Complex step derivative approximation of consistent tangent operators for viscoelasticity based on fractional calculus
• Numerical computation of algorithmic (consistent) tangent moduli in large-strain computational inelasticity
• Eigenvalue computation in the 20th century
• A highly accurate 1st- and 2nd-order differentiation scheme for hyperelastic material models based on hyper-dual numbers
• Hyperelastic materials behavior modeling using consistent strain energy density functions
• Error estimation and adaptive meshing in strongly nonlinear dynamic problems
• The variational formulation of viscoplastic constitutive updates
• Multiple bifurcation paths visualized by a computational asymptotic stability theory
• Computational two-mode asymptotic bifurcation theory combined with hyper dual numbers and applied to plate/shell buckling
• Hill-top branching: its asymptotically expanded and visually solved bifurcation equations
• Implementation of incremental variational formulations based on the numerical calculation of derivatives using hyper dual numbers
• Analysis of material instabilities in inelastic solids by incremental energy minimization and relaxation methods: evolving deformation microstructures in finite plasticity
• Fundamental theorem of matrix representations of hyper-dual numbers for computing higher-order derivatives
• Differentiation Formulas for Analytic Functions
• Elastic-Plastic Deformation at Finite Strains
• Large deformation isotropic elasticity – on the correlation of theory and experiment for incompressible rubberlike solids

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