Non-convex potentials and microstructures in finite-strain plasticity

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 458, Issue 2018, 2002, Pages 299-317

  Carstensen, Carsten ^a   Hackl, Klaus ^a   Mielke, Alexander ^a  

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

Continuum mechanics; Finite elastoplasticity; Incremental formulation; Quasi convexity; Relaxation; Variational problems

Indexed keywords

EID: 67049125713     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.2001.0864     Document Type: Article

References (40)

1. Adaptive numerical analysis in primal elastoplasticity with hardening
2. Crystal plasticity
3. Convexity conditions and existence theorems in nonlinear elasticity
4. Fine phase mixtures as minimisers of energy
5. Proposed experimental tests of a theory of fine microstructure and the two-well problem
6. Thermodynamics with internal state variables
7. A-quasiconvexity: A necessary and sufficient condition for lower semicontinuity under PDE constraints
8. Energy functionals depending on elastic strain and chemical deposition
9. Induced anisotropy in large ice shields: Theory and its homogenization
10. Generalized standard media and variational principles in classical and finite strain elastoplasticity
11. Sur les matériaux standards généralisés
12. Computational plasticity and numerical analysis
13. Variational convergence for nonlinear shell models with directors and related semicontinuity and relaxation results
14. Elastic-plastic deformation at finite strains
15. On the representation of Prandtl-Reuß tensors within the framework of multiplicative elasto-plasticity
16. A canonical model of multiplicative elasto-plasticity, formulation and aspects of the numerical implementation
17. Finite elastoplasticity, Lie groups and geodesics on SL(d)
18. A mathematical model for rate-independent phase transformations with hysteresis
19. A variational formulation of rate-independent phase transformations using an extremum principle
20. Sur les lois de frottement, de plasticité et de viscosité
21. Application of convex analysis to the treatment of elastoplastic systems
22. Nonconvex energy minimisation and dislocation in ductile single crystals
23. Inelastic constitutive relations for solids: An internal-variable theory and its application to metal plasticity
24. A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition. I. Continuum formulation
25. A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition. II. Computational aspects
26. A unified approach to finite deformation elastoplastic analysis based on the use of hyperelastic constitutive equations
27. Sur les équations de la plasticité: Existence et régularité des solutions
28. Discontinuities and plasticity
29. The derivation of constitutive relations from the free energy and the dissipation function