Preface and personal acknowledgments

Finishing this book was a challenging exercise!1 Let me start differently than usual. First of all, I wish to thank De Gruyter and notably Nadja Schedensack as well as the managing editor of this book series, Ulrich Langer, for this opportunity and their endless patience and professional cooperation. When I proposed the concept in April 2016, I had a tranquille2 life as a Post doc at the Radon Institute of Computational and Applied Mathematics (RICAM) in Linz, Austria. Originally, this monograph was envisaged as part of the habilitation procedure as final qualification for a university career. I am sure that I would have achieved the goal of completing this book if I had stayed longer at RICAM. Suddenly, however (luckily as I can say today!), I was overtaken by events: I got an offer as maître de conférences from École Polytechnique in Palaiseau (near Paris), France, and soon after a (permanent) professorship position at the Leibniz University Hannover inGermany. Iwas incredibly lucky to get involved in somany activities since then. I neverwanted tomiss all of these activities. But there is one task I did not pursue as I should have: this book! In Spring 2020, I found the most valuable treasure of our times in my profession: time! Time for both my children3 and this book.4 I shall now briefly introduce the main topic, which is to discuss recent developments in mathematical modeling, design of algorithms, and numerical simulations in multiphysics variational phase-field fracture propagation. Variational modeling of fracture has been influential in several communities since 1998 when the first paper by Gilles Francfort and Jean-Jacques Marigo appeared. The simplified prototype structure of a phase-fieldmodel for fracture propagation is: Find vector-valued displacements u : B→ Rd and a scalar-valued, smoothed, indicator function φ : B→ R such that