Progress Report for the period 2003 - 2007

	blue - elastic, red - plastic phase
	blue - elastic, green - first plastic, red - second plastic phase

The phenomenon of elasto-plasticity has become a classical problem class in mechanics. The construction and analysis of efficient solution methods have now become very popular amongst engineers as well as mathematicians. Based on our previous experience in 3D calculations in elasticity and elasto-plasticity we carry out research on smart adaptive finite element discretization techniques of 3D elasto-plastic flow problems with hardening and on fast solution techniques for the arising elasto-plastic finite element equation. More precisely, we study:

• Adaptive Multilevel Solvers for 3D Solid Elasto-plastic Problems (h- and hr-versions)
  For our solver for elasto-plastic problems we prove the robustness and convergence of the algorithm. The algorithm is enriched with an adaptive refinement technique approximating the interface between elastic and plastic zones (r-method). First results will be published soon.
• Adaptive Multilevel Solvers for 3D Solid Elasto-plastic Problems (hp- and hpr-versions)
  For hp-methods in elasticity it's known that no locking-effects occur for appropriately chosen p. We want to use hp-methods in plasticity, and in combination with the r-method we expect exponential convergence of the solver. Here we cooperate with Start project Y-192 on hp-fem of the co-investigator.
• Adaptive Multilevel Solvers for 3D Structural Elasto-plastic Problems (hp- and hpr-versions)
  We plan to use high-order elements for full 3D computations of thin structures as plates or shells to obtain a fast and robust solver.

In addition, we study the use of our elasto-plastic field problem solver for inverse and optimization problems in cooperations with subprojects F1308 and F1309.

With subprojects F1303 and F1305 we cooperate on symbolic solution techniques for the computation of the plastic strain in the multi-yield case.

NETGEN and NGSolve (both developed in our group) provide the right programming environment for an efficient implementation of these more advanced models and algorithms.

• Construction of fast and robust solvers
• Analysis of these methods
• Application and evaluation

List of Publications.