Comparison of models for finite plasticity: A numerical study

@article{Neff2003ComparisonOM,
  title={Comparison of models for finite plasticity: A numerical study
},
  author={Patrizio Neff and Christian Wieners},
  journal={Computing and Visualization in Science},
  year={2003},
  volume={6},
  pages={23-35}
}
  • P. Neff, C. Wieners
  • Published 1 June 2003
  • Mathematics
  • Computing and Visualization in Science
Abstract.We introduce a general framework for the numerical approximation of finite multiplicative plasticity. The method is based on a fully implicit discretization in time which results in an iteratively evaluated stress response; the arising nonlinear problem is then solved by a Newton method where the linear subproblems are solved with a parallel multigrid method. The procedure is applied to models with different elastic free energy functionals and a plastic flow rule of von Mises type. In… 
Numerical approximation of incremental infinitesimal gradient plasticity
We investigate a representative model of continuum infinitesimal gradient plasticity. The formulation is an extension of classical rate‐independent infinitesimal plasticity based on the additive
Rate-independent elastoplasticity at finite strains and its numerical approximation
Gradient plasticity at large strains with kinematic hardening is analyzed as quasistatic rate-independent evolution. The energy functional with a frame-indifferent polyconvex energy density and the
Some Results Concerning the Mathematical Treatment of Finite Plasticity
The initial-boundary value problems arising in the context of finite elasto-plasticity models relying on the multiplicative split F = Fe F p are investigated. First, we present such a model based on
Mixed least squares finite element methods based on inverse stress-strain relations in hyperelasticity
Reliable simulation techniques for the description of elastic deformation processes in solid mechanics are nowadays of great importance. A reasonable model should take nonlinear kinematics and a
Iterative solvers within sequences of large linear systems in non‐linear structural mechanics
This article treats the computation of discretized constitutive models of evolutionary‐type (like models of viscoelasticity, plasticity, and viscoplasticity) with quasi‐static finite elements using
Local existence and uniqueness for quasistatic finite plasticity with grain boundary relaxation
This paper is concerned with a phenomenological model of initially isotropic finite-strain multiplicative elasto-plasticity for polycrystals with grain boundary relaxation (Neff, Cont. Mech. Thermo.,
Finite multiplicative plasticity for small elastic strains with linear balance equations and grain boundary relaxation
This paper is concerned with the formulation of a phenomenological model of finite elasto-plasticity valid for small elastic strains for initially isotropic polycrystalline material. As a basic we
A First-Order System Least Squares Method for Hyperelasticity
TLDR
It is proved that the first-order least squares residual constitutes an upper bound for the error measured in a suitable norm, provided that the finite element approximation is sufficiently close.
An Adaptive Least-Squares Mixed Finite Element Method for Elasto-Plasticity
TLDR
The nonlinear least-squares functional is shown to constitute an a posteriori error estimator on which an adaptive refinement strategy may be based and Computational results for a benchmark problem of elasto-plasticity under plane strain conditions are presented.
Existence Theory for Finite-Strain Crystal Plasticity with Gradient Regularization
We provide a global existence result for the time-continuous elastoplasticity problem using the energetic formulation. The deformation gradient is decomposed multiplicatively into an elastic part and
...
...

References

SHOWING 1-10 OF 28 REFERENCES
Multigrid methods for Prandtl-Reuss plasticity
  • C. Wieners
  • Computer Science
    Numer. Linear Algebra Appl.
  • 1999
TLDR
An interface is explained which separates the pointwise evaluation of the elastoplastic material law and the global solution of the momentum balance equation and a detailed numerical investigation of a benchmark example of perfect plasticity and isotropic hardening is presented.
Local existence and uniqueness for quasistatic finite plasticity with grain boundary relaxation
This paper is concerned with a phenomenological model of initially isotropic finite-strain multiplicative elasto-plasticity for polycrystals with grain boundary relaxation (Neff, Cont. Mech. Thermo.,
Finite multiplicative plasticity for small elastic strains with linear balance equations and grain boundary relaxation
This paper is concerned with the formulation of a phenomenological model of finite elasto-plasticity valid for small elastic strains for initially isotropic polycrystalline material. As a basic we
Non–convex potentials and microstructures in finite–strain plasticity
  • C. Carstensen, K. Hackl, A. Mielke
  • Mathematics
    Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
  • 2001
A mathematical model for a finite–strain elastoplastic evolution problem is proposed in which one time–step of an implicit time–discretization leads to generally non–convex minimization problems. The
On microstructures occuring in a model of finite‐strain elastoplasticity involving a single slip—system
Starting from a novel variational principle the flow theory of elastoplasticity can be formulated as a minimization problem with respect to the total deformation and the update of the plastic
Efficient Elasto-Plastic Simulation
TLDR
This paper describes a method for the construction of radial return algorithms to the plasticity models discussed in Alber and shows that the algorithms in Simo-Hughes can be derived by this method in a systematic way.
...
...