Order reduction in computational inelasticity: Why it happens and how to overcome it-The ODE-case of viscoelasticity

DOI10.1002/nme.3144zbMath1242.74187OpenAlexW2081189461MaRDI QIDQ2894789

Charlotte Kuhn, Bernhard Eidel

Publication date: 2 July 2012

Published in: International Journal for Numerical Methods in Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/nme.3144

zbMATH Keywords

finite element methodtime integrationviscoelasticityorder reductioninelasticityKutta methodsimplicit Runge

Mathematics Subject Classification ID

Finite element methods applied to problems in solid mechanics (74S05) Finite difference methods applied to problems in solid mechanics (74S20) Nonlinear constitutive equations for materials with memory (74D10)

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Analytical and numerical treatment of electro-thermo-mechanical coupling ⋮ Benchmark solution of the dynamic response of a spherical shell at finite strain ⋮ Finite strain viscoelasticity: how to consistently couple discretizations in time and space on quadrature-point level for full order \(p\geq 2\) and a considerable speed-up ⋮ An explicit solution for implicit time stepping in multiplicative finite strain viscoelasticity ⋮ Anisotropic finite strain viscoelasticity based on the Sidoroff multiplicative decomposition and logarithmic strains ⋮ A continuum and computational framework for viscoelastodynamics. I: Finite deformation linear models ⋮ Efficient implicit integration for finite-strain viscoplasticity with a nested multiplicative split

Cites Work

• Finite element analysis of viscoelastic structures using Rosenbrock-type methods
• Second-order accurate integration algorithms for von-Mises plasticity with a nonlinear kinematic hardening mechanism
• A theory of finite viscoelasticity and numerical aspects
• Computation in finite-strain viscoelasticity: finite elements based on the interpretation as differential-algebraic equations
• Formulation and implementation of three-dimensional viscoelasticity at small and finite strains
• Discussion of finite deformation viscoelasticity laws with reference to torsion loading
• Runge-Kutta methods in elastoplasticity
• The numerical solution of differential-algebraic systems by Runge-Kutta methods
• High-order time integration applied to metal powder plasticity
• A remark on the application of the Newton-Raphson method in nonlinear finite element analysis
• A BDF2 integration method with step size control for elasto-plasticity
• Remarks on the interpretation of current non‐linear finite element analyses as differential–algebraic equations
• Accuracy and stability of integration algorithms for elastoplastic constitutive relations
• Non-linear B-stability and symmetry preserving return mapping algorithms for plasticity and viscoplasticity
• Diagonally Implicit Runge–Kutta Methods for Stiff O.D.E.’s
• On the application of multi‐step integration methods to infinitesimal elastoplasticity
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