A variational formulation of small strain ductile fracture, based on a phase-field modeling crack propagation, is proposed. The an effective stress description gradient plasticity, combined with AT1 model. Starting from established statements finite-step elastoplasticity for generalized standard materials, mixed statement consistently derived, incorporating in rigorous way update both the elast...

Acknowledgments It is my pleasure to express my thanks to my supervisors Professor Dr. C. Carstensen for suggesting this topic to me, for many valuable discussions, and for their supervision during my stays in Kiel and Munich. I wish to thank all of my colleagues at the Lehrstuhl für Wissenschaftliches Rechnen and Dr. G. Grammel for scientific advice. I am grateful to Dr. J. Alberty and R. Klos...