• Corpus ID: 236772750

On static and evolutionary homogenization in crystal plasticity for stratified composites

@inproceedings{Davoli2021OnSA,
  title={On static and evolutionary homogenization in crystal plasticity for stratified composites},
  author={Elisa Davoli and Carolin Kreisbeck},
  year={2021}
}
The starting point for this work is a static macroscopic model for a high-contrast layered material in single-slip finite crystal plasticity, identified in [Christowiak & Kreisbeck, Calc. Var. PDE (2017)] as a homogenization limit via Γ-convergence. First, we analyze the minimizers of this limit model, addressing the question of uniqueness and deriving necessary conditions. In particular, it turns out that at least one of the defining quantities of an energetically optimal deformation, namely… 

Figures from this paper

A homogenization result in finite plasticity and its application to high-contrast media
. We carry out a variational study for integral functionals that model the stored energy of a heterogeneous material governed by finite-strain elastoplasticity with hardening. Assuming that the

References

SHOWING 1-10 OF 36 REFERENCES
Homogenization in BV of a model for layered composites in finite crystal plasticity
Abstract In this work, we study the effective behavior of a two-dimensional variational model within finite crystal plasticity for high-contrast bilayered composites. Precisely, we consider materials
Homogenization of layered materials with rigid components in single-slip finite crystal plasticity
We determine the effective behavior of a class of composites in finite-strain crystal plasticity, based on a variational model for materials made of fine parallel layers of two types. While one
Single-Slip Elastoplastic Microstructures
Abstract.We consider rate-independent crystal plasticity with constrained elasticity, and state the variational formulation of the incremental problem. For generic boundary data, even the first time
Asymptotic Behavior of Crystal Plasticity with One Slip System in the Limit of Rigid Elasticity
TLDR
A family of models in elastoplasticity describing crystals with one active slip system and linear hardening in two spatial dimensions is considered, determining explicitly the $\Gamma$-limit of the energy functionals underlying the variational model and showing it coincides with the relaxation of a variational problem with rigid elasticity.
Existence for dislocation-free finite plasticity
  • U. Stefanelli
  • Materials Science
    ESAIM: Control, Optimisation and Calculus of Variations
  • 2019
This note addresses finite plasticity under the constraint that plastic deformations are compatible. In this case, the total elastoplastic deformation of the medium is decomposed as y = ye ○ yp,
Asymptotic Rigidity of Layered Structures and Its Application in Homogenization Theory
In the context of elasticity theory, rigidity theorems allow one to derive global properties of a deformation from local ones. This paper presents a new asymptotic version of rigidity, applicable to
Two-Scale Homogenization for Evolutionary Variational Inequalities via the Energetic Formulation
TLDR
The classical model of linearized elastoplasticity with hardening is treated, and it is shown that these two functionals have a suitable two-scale limit, but now involving the macroscopic variable in the physical domain as well as the microscopicvariable in the periodicity cell.
Asymptotic analysis of deformation behavior in high-contrast fiber-reinforced materials: Rigidity and anisotropy
We identify the restricted class of attainable effective deformations in a model of reinforced composites with parallel, long, and fully rigid fibers embedded in an elastic body. In mathematical
Incompatibility-governed elasto-plasticity for continua with dislocations
  • S. Amstutz, N. Van Goethem
  • Engineering
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2017
In this paper, a novel model for elasto-plastic continua is presented and developed from the ground up. It is based on the interdependence between plasticity, dislocation motion and strain
...
1
2
3
4
...