Quasistatic Evolution Problems for Linearly Elastic–Perfectly Plastic Materials

@article{Maso2004QuasistaticEP,
  title={Quasistatic Evolution Problems for Linearly Elastic–Perfectly Plastic Materials},
  author={Gianni Dal Maso and Antonio DeSimone and Maria Giovanna Mora},
  journal={Archive for Rational Mechanics and Analysis},
  year={2004},
  volume={180},
  pages={237-291}
}
The problem of quasistatic evolution in small strain associative elastoplasticity is studied in the framework of the variational theory for rate-independent processes. Existence of solutions is proved through the use of incremental variational problems in spaces of functions with bounded deformation. This approach provides a new approximation result for the solutions of the quasistatic evolution problem, which are shown to be absolutely continuous in time. Four equivalent formulations of the… 
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References

SHOWING 1-10 OF 38 REFERENCES
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
The variational formulation of viscoplastic constitutive updates
An internal variable theory of elastoplasticity based on the maximum plastic work inequality
The methods of convex analysis are used to explore in greater depth the nature of the evolution equation in internal variable formulations of elastoplasticity. The evolution equation is considered in
A Variational Formulation of¶Rate-Independent Phase Transformations¶Using an Extremum Principle
Abstract We propose a rate-independent, mesoscopic model for the hysteretic evolution of phase transformations in shape-memory alloys. The model uses the deformation and phase-indicator function as
Quasistatic Crack Growth in Nonlinear Elasticity
Abstract.In this paper, we prove a new existence result for a variational model of crack growth in brittle materials proposed in [19]. We consider the case of n-dimensional nonlinear elasticity, for
Plasticity: Mathematical Theory and Numerical Analysis
Preface to the Second Edition.- Preface to the First Edition.-Preliminaries.- Continuum Mechanics and Linearized Elasticity.- Elastoplastic Media.- The Plastic Flow Law in a Convex-Analytic Setting.-
The mathematical theory of plasticity
1. Introduction 2. Foundations of the thoery 3. General theorems 4. The solution of plastic-elastic problems I 5. The solution of plastic-elastic problems II 6. Plane plastic strain and the theory of
Dual spaces of stresses and strains, with applications to Hencky plasticity
We prove the existence of a dual pairing between admissible stress and displacement fields in the context of Hencky plasticity. We apply this to show (i) that an extremal displacement field exists
Existence results for energetic models for rate-independent systems
We consider mechanical models which are driven by an external loading on a time scale much slower than any internal time scale (like viscous relaxation times) but still much faster than the time
...
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