Multiphysics Phase-Field Fracture

Modeling, Adaptive Discretizations, and Solvers

Thomas Wick

• Editorial: De Gruyter
• Año: 2020
• ISBN:
  9783110497397
• Edición: 1
• Categoría: Mathematics
• Categoría: Applied Mathematics

This monograph is centered on mathematical modeling, innovative numerical algorithms and adaptive concepts to deal with fracture phenomena in multiphysics. State-of-the-art phase-field fracture models are complemented with prototype explanations and rigorous numerical analysis. These developments are embedded into a carefully designed balance between scientific computing aspects and numerical modeling of nonstationary coupled variational inequality systems. Therein, a focus is on nonlinear solvers, goal-oriented error estimation, predictor-corrector adaptivity, and interface conditions. Engineering applications show the potential for tackling practical problems within the fields of solid mechanics, porous media, and fluidstructure interaction.

Índice

• Preface and personal acknowledgments
• Classes and schools related to this monograph
• Research funding acknowledgments
• Own related work
• Contents
• 1 Introduction
• 2 Notation, prerequisites, and prototype model problems
• 3 Classifications of partial differential equations and variational inequalities
• 4 Modeling of variational phase-field fractures
• 5 Numerical modeling part I: regularization and discretization
• 6 Simulations I: a phase-field slit domain
• 7 Numerical modeling part II: linearizations, nonlinear solvers, and linear solution
• 8 Simulations II: single edge notched shear test
• 9 Numerical modeling part III: adaptive concepts
• 10 Simulations III: goal-oriented error control for a phase-field slit and time control for a screw
• 11 Multiphysics extensions involving fracture
• 12 Simulations IV
• 13 Research software development
• 14 Conclusions and future interest
• 15 The end
• Bibliography
• Index