A quasi-static boundary value problem in multi-surface elastoplasticity: Part 2 - Numerical solution

Mathematical Methods in the Applied Sciences

Volumn 28, Issue 8, 2005, Pages 881-901

  Brokate, Martin ^a   Carstensen, Carsten ^b   Valdman, Jan ^c  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

^b HUMBOLDT UNIVERSITY   (Germany)

^c JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

Author keywords

Elastoplasticity; Finite element method; Hysteresis; Multi yield Prandtl Ishlinskii model; Phase transition multi surface model; Variational inequalities

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; ELASTOPLASTICITY; FINITE ELEMENT METHOD; HYSTERESIS; KINEMATICS; MATHEMATICAL MODELS; PHASE TRANSITIONS; PROBLEM SOLVING;

MULTI-YIELD PRANDTL-ISHLINSKII MODEL; PHASE TRANSITION MULTI-SURFACE MODEL; TIME-SPACE DISCRETIZATION; VARIATIONAL INEQUALITIES;

BOUNDARY VALUE PROBLEMS;

EID: 18744398128     PISSN: 01704214     EISSN: None     Source Type: Journal    
DOI: 10.1002/mma.593     Document Type: Article

References (13)

1. Brokate M, Carstensen C, Valdman J. A quasi-static boundary value problem in multi-surface elastoplasticity: part 1 - analysis. Mathematical Models and Methods in Applied Sciences 2004; 27:1697-1710.
2. Han W, Reddy BD. Plasticity: Mathematical Theory and Numerical Analysis. Springer: New York, 1999.
3. Alberty J, Carstensen C. Numerical analysis of time-depending primal elastoplasticity with hardening. SIAM Journal on Numerical Analysis 2000; 37(4):1271-1294.
4. http://www.sfb013.uni-linz.ac.at/projects/F1306/beam2d.evolution.gif
5. Ciarlet PG. The Finite Element Method for Elliptic Problems. North-Holland: Amsterdam, 1978.
6. Alberty J, Carstensen C, Funken SA, Klose R. Matlab implementation of the finite element method in elasticity. Computing 2002; 69(3):239-263.
7. Hackbusch W. Multi-Grid Methods and Applications. Springer: Berlin, Heidelberg, 1985.
8. Carstensen C. Domain decomposition for a non-smooth convex minimalization problems and its application to plasticity. Numerical Linear Algebra with Applications 1997; 4(3):177-190.
9. Valdman J. Mathematical and numerical analysis of elastoplastic material with multi-surface stress-strain relation. Ph.D. Thesis, Christian-Albrechts- Universität zu Kiel, 2002.
10. Kienesberger J, Valdman J. Multi-yield elastoplastic continuum-modeling and computations. In Numerical Mathematics and Advanced Applications. Proceedings of ENUMATH 2003, Feistauer M, Dolejší, Knobloch P, Najzar K (eds), Lecture Notes in Computer Science. Springer: Berlin, 2003; 539-548.
11. Valdman J. Two-yield elastoplasticity Matlab solver. Download: http://www.sfb013.uni-linz.ac.at/~jan/solver.zip
12. Kienesberger J. Multigrid preconditioned solvers for some elastoplastic problems. In Proceedings of LSSC 2003, Lirkov I, Margenov S, Waśniewski J, Yalamov P (eds), Lecture Notes in Computer Science, vol. 2907. Springer: Berlin, 2004; 379-386.
13. Schöberl J. Netgen/Ngsolve - mesh generator/3d finite element solver software package. Download: http://www.hpfem.jku.at/netgen/